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Supercritical Water-Cooled Reactors

Guest Editors Jiejin Cai Claude Renault and Junli Gou

Science and Technology of Nuclear Installations





Copyright copy 2014 Hindawi Publishing Corporation All rights reserved

This is a special issue published in ldquoScience and Technology of Nuclear Installationsrdquo All articles are open access articles distributed underthe Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium providedthe original work is properly cited

Editorial Board

Nusret Aksan SwitzerlandA Alvim BrazilWon Pil Baek KoreaStephen M Bajorek USAGeorge Bakos GreeceJozsef Banati SwedenRicardo Barros BrazilAnis B Salah BelgiumGiovanni B Bruna FranceNikola Cavlina CroatiaXu Cheng ChinaLeon Cizelj SloveniaA Clausse ArgentinaFrancesco Drsquo Auria ItalyMarcos P de Abreu BrazilGiovanni DellrsquoOrco FranceJuan C Ferreri ArgentinaNikolay Fil RussiaCesare Frepoli USAGiorgio Galassi ItalyRegina Galetti Brazil

Michel Giot BelgiumValerio Giusti ItalyHorst Glaeser GermanySatish Kumar Gupta IndiaAli Hainoun SyriaKeith E Holbert USAKostadin Ivanov USAY Kadi Republic of KoreaAhmed Khedr EgyptTomasz Kozlowski USATomoaki Kunugi JapanMike Kuznetsov GermanyH-Y Lee Republic of KoreaB Limmeechokchai ThailandJiri Macek Czech RepublicAnnalisa Manera USABorut Mavko SloveniaOleg Melikhov RussiaRafael Miro SpainJOZEF Misak Czech RepublicRahim Nabbi Germany

Manmohan Pandey IndiaYuriy Parfenov RussiaYves Pontillon FranceNik Popov CanadaPiero Ravetto ItalyFrancesc Reventos SpainEnrico Sartori FranceCarlo Sborchia FranceMassimo Sepielli ItalyArkady Serikov GermanyJames F Stubbins USAIztok Tiselj SloveniaRizwan Uddin USAE Uspuras LithuaniaRichard Wright NorwayChao Xu ChinaX George Xu USAYanko Yanev BulgariaZhiwei Zhou ChinaEnrico Zio ItalyMassimo Zucchetti Italy

Contents

Supercritical Water-Cooled Reactors Jiejin Cai Claude Renault and Junli GouVolume 2014 Article ID 548672 2 pages

Core Flow Distribution from Coupled Supercritical Water Reactor Analysis Po Hu and Paul P H WilsonVolume 2014 Article ID 178129 8 pages

Code Development in Coupled PARCSRELAP5 for Supercritical Water Reactor Po Hu and Paul WilsonVolume 2014 Article ID 286434 8 pages

Preliminary Development ofThermal Power Calculation Code H-Power for a Supercritical WaterReactor Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao GuoVolume 2014 Article ID 279092 10 pages

A Simplified Supercritical Fast Reactor withThorium Fuel Peng Zhang Kan Wang and Ganglin YuVolume 2014 Article ID 405654 9 pages

Experimental Investigation on Flow-Induced Vibration of Fuel Rods in Supercritical Water LoopLicun Wu Daogang Lu and Yu LiuVolume 2014 Article ID 769432 9 pages

EditorialSupercritical Water-Cooled Reactors

Jiejin Cai1 Claude Renault2 and Junli Gou3

1 Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen University Zhuhai Guangdong 519082 China2 INSTNPSNE The French Alternative Energies and Atomic Energy Commission (CEA) Saclay 91191 Gif-sur-Yvette France3 School of Nuclear Science and Technology Xirsquoan Jiaotong University Xirsquoan Shaanxi 710049 China

Correspondence should be addressed to Jiejin Cai chiven77hotmailcom

Received 24 July 2014 Accepted 24 July 2014 Published 18 August 2014

Copyright copy 2014 Jiejin Cai et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Supercritical water-cooled reactor (SCWR) is the water-cooled reactor using supercritical pressure water as coolant[1] It is considered as one of the promising Generation IVreactors due to its advantages of plant simplification and highthermal efficiency [2 3]

Several design concepts of SCWRs have been proposed(a) supercritical water-cooled thermal neutron reactor (b)supercritical water-cooled fast neutron reactor (c) super-critical water-cooled mixed neutron spectrum reactor (d)supercritical water-cooled pebble bed reactor (e) supercrit-ical heavy-water-cooled reactor The detailed design param-eters of some typical SCWR concepts around the world aresummarized in Table 1 [4] Recently the use of thorium in theSCWRs has been investigated [5 6]

The advantages of the SCWRs are shown as follows [1](i) Supercritical water has excellent heat transfer proper-

ties allowing a high power density a small core and asmall containment structure

(ii) The use of a supercritical Rankine cycle with its typi-cally higher temperatures improves efficiency (wouldbe sim45)

(iii) This higher efficiency would lead to better fuel econ-omy and a lighter fuel load lessening residual (decay)heat

(iv) SCWR is typically designed as a once-through directcycle whereby steam or hot supercritical water fromthe core is used directly in a steam turbine whichmakes the design simple

(v) Water is liquid at room temperature cheap nontoxicand transparent simplifying inspection and repair(compared to liquid metal cooled reactors)

(vi) A fast SCWR could be a breeder reactor which couldburn the long-lived actinide isotopes

(vii) A heavy-water SCWR could breed fuel from thorium(4x more abundant than uranium) with increasedproliferation resistance over plutonium breeders

Some challenges in SCWRs are the subjects of researchwork which need us to research among which are thefollowing [4ndash7]

(i) Lower water inventory (due to compact primaryloop) means less heat capacity to buffer transientsand accidents (eg loss of feedwater flow or largebreak loss of coolant accident) resulting in accidentand transient temperatures that are too high forconventional metallic cladding

(ii) Higher pressure combined with higher temperatureand also a higher temperature rise across the coreresult in increased mechanical and thermal stresseson vessel materials that are difficult to solve

(iii) The coolant greatly reduces its density at the exit ofthe core resulting in a need to place extra moderatorthere

(iv) Extensive material development and research onsupercritical water chemistry under radiation areneeded

(v) Special start-up procedures are needed to avoid insta-bility before the water reaches supercritical condi-tions

(vi) A fast neutron SCWR requires a relatively complexreactor core design in order to achieve a negative voidcoefficient

Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 548672 2 pageshttpdxdoiorg1011552014548672

2 Science and Technology of Nuclear Installations

Table 1 Some typical SCWR concepts around the world

Name Proposed by Design concept ModerateRatedpower(MW)

Outlettemperature

(∘C)

Pressure(MPa)

Net efficiency()

W21 Tokyo University Thermal neutronspectrum SCWR H2O 1570 508 25 44

TWG1 Water TWG (Japan) Fast neutronspectrum SCWR H2O 1728 Alternative Alternative 38sim45

W6-1

AECL (Canada)

CANDU-X-MARK1

D2O

910 430 25 41W6-2 CANDU-XNC 370 400 25 41W6-3 CANDU-ALX1 950 450 25 406W6-4 CANDU-X-ALX2 1143 650 25 45mdash Europe HPLWR H2O 1000 500 25 44

mdash INEL (USA) Thermal neutronspectrum SCWR H2O 1600 500 25 44

B500SKD1 Russia Integrative SCWR H2O 515 381 236 38

In order to help readers understand the development ofthe SCWRs in the world we sponsored a special issue onthe supercritical water-cooled reactor and hoped to get somepapers from the topics which include but are not limited tothe following

(i) reactor core and fuel designs(ii) materials chemistry and corrosion(iii) thermal-hydraulics and safety analysis(iv) plant systems structures and components(v) computational fluid dynamics (CFD) and coupled

codes(vi) neutronic properties(vii) balance of plant(viii) other applications

Now the special issue is published which includes 5papers The contents include a new concept of core designlike ldquoA simplified supercritical fast reactor with thorium fuelrdquocalculation code development like ldquoPreliminary developmentof thermal power calculation code H-power for a supercriticalwater reactorrdquo ldquoCode development in coupled PARCSRELAP5for supercritical water reactorrdquo and flow distribution one ofthe important issues of thermal hydraulics in the nuclearreactor like ldquoCore flow distribution from coupled supercriticalwater reactor analysisrdquo It also contains some experimen-tal results like ldquoExperimental investigation on flow-inducedvibration of fuel rods in supercritical water looprdquoWe hope thatreaders of this special issuewill find not only the developmentstatus of SCWRs and updated reviews on SCWRs but alsothe formulation of important questions to be resolved suchas how to develop the codes for SCWRs

Jiejin CaiClaude Renault

Junli Gou

References

[1] Y Oka S Koshizuka Y Ishiwatari and A Yamaji Super LightWater Reactors and Super Fast Reactors SpringerNewYorkNYUSA 2010

[2] S Liu and J Cai ldquoConvergence analysis of neutronicther-mohydraulic coupling behavior of SCWRrdquoNuclear Engineeringand Design vol 265 pp 53ndash62 2013

[3] S Liu and J Cai ldquoNeutronic and thermohydraulic character-istics of a new breeding thorium-uranium mixed SCWR fuelassemblyrdquo Annals of Nuclear Energy vol 62 no 1 pp 429ndash4362013

[4] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010

[5] S Liu and J Cai ldquoNeutronics assessment of thorium-based fuelassembly in SCWRrdquo Nuclear Engineering and Design vol 260pp 1ndash10 2013

[6] S Liu and J Cai ldquoDesign amp optimization of two breedingthorium-uranium mixed SCWR fuel assembliesrdquo Progress ofNuclear Energy vol 70 pp 6ndash19 2014

[7] Ph Marsault C Renault G Rimpault P Dumaz and OAntoni ldquoPre-design studies of SCWR in fast neutron spectrumevaluation of operating conditions and analysis of the behaviorin accidental situationsrdquo in Proceedings of the InternationalConference of Asian Political Parties (ICAPP rsquo04) Pittsburgh PaUSA June 2004

Research ArticleCore Flow Distribution from Coupled Supercritical WaterReactor Analysis

Po Hu1 and Paul P H Wilson2

1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA

Correspondence should be addressed to Po Hu pohusjtueducn

Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 15 May 2014

Academic Editor Jiejin Cai

Copyright copy 2014 P Hu and P PHWilson This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper introduces an extended code package PARCSRELAP5 to analyze steady state of SCWR US reference design An 8 times8 quarter core model in PARCS and a reactor core model in RELAP5 are used to study the core flow distribution under varioussteady state conditions The possibility of moderator flow reversal is found in some hot moderator channels Different moderatorflow orifice strategies both uniform across the core and nonuniform based on the power distribution are explored with the goalof preventing the reversal

1 Introduction

The supercritical water reactor (SCWR) is a next generationnuclear reactor concept It is essentially a light water reactor(LWR) operating at higher pressure and temperature with adirect cycle Its higher thermal efficiency and considerableplant simplification have distinguished it from the currentreactors Oka and his team presented both a thermal and fastSCWR design [1 2] and Buongiorno presented a thermalSCWRas theUS reference design [3] andKim et al andXu etal presented various mixed spectrum (thermalfast) SCWRdesigns [4 5]

In the US reference SCWR design the majority of thecoolant firstly flows downward as a dedicated moderatorin separated water rods and then flows upward adjacentto the fuel pins as coolant Because of the large change inwater density through the pseudocritical point heat transferbetween the coolant and the moderator has an importantimpact in accurate SCWR reactor analysis This paper usesan extended code package which couples the core simulatorPARCS to the thermal-hydraulics simulator RELAP5 toanalyze both steady state and transient of SCWR design An8 times 8 quarter core model in PARCS and a reactor core modelin RELAP5 [6] are used to study the core flow distributionunder various steady state conditions

2 Analysis Methodology

21 Extended Code Package PARCS is a 3D core simulatorusing the nodal method to solve diffusion equation It isable to analyze PWR and BWR designs in which wateris used as both coolant and moderator in a single flowchannel In this work PARCS was modified to accommodatethermal-hydraulic feedback to the nuclear cross-sections ofthe separated coolant and moderator channels in SCWR Inaddition changes have been made to the communicationbetween PARCS andRELAP5 to accommodate these separateflows [7]

To enable the feedback from separated moderator a newsubroutine is added to look up macroscopichomogenizedcross-section information based on three thermal hydraulicproperties fuel temperature coolant density and moderatordensity The homogenized cross-section data is prepared bythe lattice transport code HELIOS [8]

Coupled PARCS and RELAP5 use lookup files to shareinformation between corresponding computational units(nodes for PARCS hydrodynamic volumes and heat struc-tures for RELAP5) In the original lookup file the nodesin PARCS correspond to the hydrodynamic volumes repre-senting the single fluid and the heat structures representing



Water rod (times36)Fuel rod (times300)

Instrumentation pin

Control rod (times16)

Fuel assembly (1352MWdkgU)Fuel assembly ( 776MWdkgU)Full assembly (0001MWdkgU)Reflector

A1 B C D E F G

2

3

4

5

6

7

Figure 1 Fuel assembly and quarter core assembly arrangement

fuel cladding and other core structure components in twoseparate tables After the modification there are three tablesin the lookupfile one representing the coolant hydrodynamicvolumes one representing the moderator channel hydrody-namic volumes and one representing the heat structures

22 Core Models An 8times8 quarter core model is used inPARCS as show in Figure 1 with water reflectors at lateralboundaries and reflective boundary condition at top andbottom of the core The fuel arrangement shown in Figure 1is used in all the following calculationsThese particular bur-nupswere chosen to give an indication of the effect of burnupa real equilibrium core loading would have larger burnupsfor partially used fuel After considerations for symmetry the37 fuel assemblies in the PARCS model are coupled to 21unique flow paths in the RELAP5 model Both the PARCSand RELAP5 models have 12 axial nodes through the coreFlow paths in downcomer moderator upper plenum coreand lower plenum are modeled in RELAP5 A schematicof the flow path is shown in Figure 2 a moderator channeland a coolant channel represent one assembly in the coreIn addition to being in contact with the fuel heat structurethe coolant channel is thermally coupled to the moderatorchannel through another heat structure representing themoderator channel wall The majority of the inlet flow (90)to the core flows up to the moderator upper plenum and

FlowHeat

Moderator upper plenum

Coolant upper plenum

Dow

ncom

er

Lower plenum

Coolantchannels

Moderatorchannels

Figure 2 Flow pattern in RELAP5

then flows downward through moderator channels Nextall the moderator flow mixes with the downcomer flowand finally flows upwards through coolant channels andthe coolant upper plenum and to the outlet of vessel Thedesign parameters are shown in Table 1 Previous research

Science and Technology of Nuclear Installations 3

Table 1 SCWR nominal design parameters (Buongiorno et al 2003 [3])

Fuel pin CoreFuel material UO2 Thermal power 3575MWFissile enrichment 5 Number of fuel assemblies 148Fuel radius 0436 cm Active height 427mCladding material Stainless steel Effective diameter 393mCladding thickness 0063 cm Volumetric power density 69MWm3

Fuel pitch 112 cm Average linear heat rate 192 kWmPD 112

Fuel assembly Thermal-hydraulic parametersNumber of fuel rods 300 System pressure 25MPaNumber of water rods 36 Coolant flow rate 1843 kgsNumber of control rods 16 Moderator bypass 120573 10 (184 kgs)Assembly pitch 286 cm Inlet temperature 280∘CWater rod width 336 cm Outlet temperature 500∘CWater rod wall thickness 004 cm Thermal efficiency 4480

Table 2 Moderator flow rate and assembly power in the reference case

Flow rate (kgs) minus156 minus136 minus152 minus137 minus157 minus155 minus171Power (MW) 252 277 257 273 248 253 182Flow rate (kgs) minus136 minus75 minus131 36 minus136 minus137 minus172Power (MW) 277 268 278 248 274 274 161Flow rate (kgs) minus152 minus131 minus148 minus129 minus114 minus165Power (MW) 257 278 263 279 283 225Flow rate (kgs) minus137 36 minus129 minus104 minus156 minus172Power (MW) 273 248 2791 282 250 166Flow rate (kgs) minus157 minus136 minus114 minus156 minus171Power (MW) 248 274 283 250 179Flow rate (kgs) minus155 minus137 minus165 minus172Power (MW) 253 274 225 166Flow rate (kgs) minus171 minus172Power (MW) 182 161

[9] showed that the heat transfer between the coolant andmoderator channels could reduce the axial power peak bychanging the equivalent moderator density which representscombined moderation from moderator and coolant Theseresults were generated with a thermal hydraulic model insidePARCS assuming a fixed flow distribution in both moderatorand coolant channelsThis paper studies flow distributions insteady state using coupled PARCSRELAP5 The possibilityof moderator flow reversal is found in some hot moderatorchannels Different moderator flow orifice strategies bothuniform across the core and nonuniform based on the powerdistribution are explored with the goal of preventing thereversal

3 Reference Case

The reference model uses a uniform orifice size for eachmoderator flow channel with a ratio of the orifice area to themoderator area of 020 This results in flow reversal in somemoderator channels as shown in Table 2 Negative flow rates

indicate a downward flow as intended These results showthat two assemblies have reverse flow

31 Pressure Balance in Moderator Channel Due to buoy-ancy the flow rate in hotmoderator channels is lower than theflow rate in colder moderator channels Inmost of moderatorchannels a stable downward flow occurs as designated Inthe highest power channels due to the large density changethrough the pseudocritical point the buoyancy effect is solarge that the stable flow can be changed to flowupwardsThiscan result in a stable core flow distribution in which the flowin few moderator channels is upward while the flow in therest of moderator channels is downward

A reactor core designed with downward moderator flowmay not behave well when the flow reverses as unexpectedreversed channels will have power peak at the bottom forboth moderator and coolant that are flowing upwards andtheir densities are decreasing accordingly and these peaksmay be difficult to deal with during the depletion consideringthe control rods withdrawing from the top of the core and


0

2 4 6

1234567

0

061

081

102

2 4 6

2 4 6

1

2

3

4

5

6

7100

200

300

400

500

2 4 6

1234567

Moderator flow rate (kgs) Normalized assembly power

2 4 6

1234567

0

061

081

1021234567

0

200

400

600

2 4 6

1234567


2 4 6

1

2

3

4

5

6

70

061

081

102

2 4 6

1

2

3

4

5

6

70

200

400

600

2 4 6

1

2

3

4

5

6

7


minus156 minus136

minus136

minus152 minus137 minus157 minus155 minus171

minus136 minus75 minus131 36 minus137 minus172

minus152 minus131 minus149 minus129 minus114 minus165

minus137 36 minus129 minus104 minus156 minus172


minus155 minus137 minus165 minus172

minus171 minus172minus15

minus10

minus5

0

minus15

minus10

minus5

0

minus15

minus10

minus5

r = 020

r = 018

r = 015

523 476 513 477 525 519 583

476 373 466 310 475 477 595

513 466 502 461 433 552

477 310 461 415 523 592

525 475 433 523 585

519 477 552 592

582 595

Equivalent density (kgm3)



105 116 107 114 103 105 076

116 112 116 104 114 115 067

067

107 116 110 117 118 094

114 104 117 118 105 069

103 114 118 105 075

105 115 094 069

076

103 115 107 115 102 103 073

115 117 117 115 115 114 065

107 117 110 118 119 092

115 115 118 119 103 067

102 115 119 113 073

103 114 092 067

073065

525 486 524 487 537 532 593

486 392 473 388 485 490 604

524 473 512 469 444 564

487 388 469 427 535 601

537 485 444 535 595

532 490 564 601

593 604

minus142 minus128 minus139 minus129 minus142 minus142 minus151






minus151 minus151







minus159minus160

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071063

Figure 3 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in different orifice area ratio119903 = 119860

119900

119860mod

the flow reversal may vanish over the cycle Therefore itis important to study the circumstances under which thisreversal occurs Furthermore there are at least two waysto manageprevent the moderator flow reversal A thermal-hydraulics approach based on flow orifices in the moderatorchannels is discussed here A neutronics approach basedon using control rods burnable absorbers and axial fuelenrichment variance to change the power distribution will bestudied in the future [10]

As shown in Figure 2 moderator enters the channelfrom the moderator upper plenum flows downwards in thechannel and then exits to the lower plenum The pressurebalance through the moderator channel is dominated bythree terms the elevation pressure loss (gain in this case) and

the entranceexit pressure lossesThe pressure balance can bewritten as follows

int

out

in120588119892119889119897 minus

1

2119860

2

mod

119870119898

2

120588

119900

= Δ119875 (1)

where Δ119875 represents the pressure difference of upper andlower plenum for an individual channel In RELAP5 theabrupt orifice friction lost coefficient is defined as [11]

119870 = (

119860mod119860

119888

minus 1)

2

(2)


Nonreverse channel

1 2 3 40

1

2

3

Pow

er (M

W)

1 2 3 40

1

2

3Po

wer

(MW

)

Reverse channel

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

600

650

700

750

800

850

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

1 2 3 4

600

650

700

750

800

850

Coolant moderator Coolant

moderator

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

r = 020

r = 018

r = 015 r = 020

r = 018

r = 015

Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases


where 119860119888is the physical minimum flow area It is defined as

119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)

where119860119900is cross-section of orifice and119860mod is cross-section

of moderator channelSince the hot channel has a lower water density than

the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860

119900 the increased loss

coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal

In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers

4 Results

41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem

Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as

120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)

where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core

Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat

Table 3 Orifice arrangement

02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02

The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds

Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred

42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)

The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution

5 Discussion

In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking


0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567




minus144minus119 minus139 minus116 minus126 minus157


minus150 minus126 minus126 minus148minus161


minus161 minus162 minus15

minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063

Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case

0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800

Core height (m)1 2 3 4


Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015

Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case

is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis

Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and

lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]

6 Conclusion

A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices


orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal

Nomenclature

119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049

References

[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001

[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246

[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003

[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004

[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011

[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005

[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004

[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-

flowing moderator and coolant in a supercritical water reactorrdquo

in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006

[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006

[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and

G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013

Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor

Po Hu1 and Paul Wilson2





Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized

1 Introduction

The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible

for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]

2 Existing Coupling Mechanism

Current study analyzes the SCWR using extended codepackage PARCSRELAP5

PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5

RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled



Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS

Variable mapping file

Figure 1 PARCSRELAP5 coupling mechanism

behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33

In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model

To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges

The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes

The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and

Start

Coarse mesh finite difference (CMFD) solver

Nodal expansion Method analytic Nodal method

(NEMANM) solver

Updated power profile

(Internalexternal)thermal

hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r

Figure 2 Solving scheme for steady state eigenvalue problem inPARCS

coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]

3 Modifications on PARCS

Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified

(i) water and cladding thermophysical property func-tions or tables are modified accordingly

(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels

(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files



Instrumentation pin

Fuel rod (times300) Water rod (times36)

Figure 3 The cross sections assembly of US reference design [2]

31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis

The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index

Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]

32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately

The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879

119898)Δ119879

119898

represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863

119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)

2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]

Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)

33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5

As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format

In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible

These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of


Table 1 PARCSRELAP5 mapping input file

lowast

Table 1lowastRELAP volume number PARCS node

numberWeightingfactor

335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast

lowastHeat structure to node tablelowast

Table 2lowastRELAP structure number PARCS node


3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1

lowastData ignored from the original table And the ldquo rdquo means the more similar

input lines are ignored

the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node

Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes

Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties

150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)

New water table Original water table

Density (kgm3)

675K larr 654K

Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5

4 Modification on RELAP5

There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR

41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)

The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly

The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification


Table 2 SCWR parameters

Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm

Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3

BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU

Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C

Thermal efficiency 4480

Table 3 Temperatures and densities of moderator and coolant

Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)

1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927

RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable

42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between

1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point

5 Preliminary Test of the Modifications

The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which


1 2 3 4 5 6 7 8 9 10 11 12Node number

Transport cross section of energy group 1

HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)

Figure 5 Comparison of cross sections from PARCS and HELIOS

Table 4 Densities from coupled PARCS node and RELAP5 volumes

From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657

is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly

51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the

same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium

52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays


Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod

Figure 6 Flow path model of RELAP5 test

the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower

53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7

6 Discussion

The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases

For other transients such as LOCA in which largepressure excursion exists the current modification is not

210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)

Original RELAP5Modified RELAP5

645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105

Figure 7 Pressure and temperature from test case with original andmodified RELAP5

enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point

Nomenclature

119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel




Acknowledgments

The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina

References

[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003

[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003

[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009

[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004

[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010

[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004

[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004

[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009

[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984

[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf

[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005

[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13

Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor

Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo

School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China

Correspondence should be addressed to Fan Zhang hdhxyzf126com

Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014


Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR

1 Introduction

SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area

For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]

According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published

IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967

We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays

H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific



READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop

Figure 1 H-Power modules diagram

enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le

100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions

2 Theoretical Modeling

The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine

H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis

21 Thermodynamic Properties Subroutine

211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine

We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume

which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated

Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured

The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2

212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid

22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]

As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875

1is obtained by (1) taking pressure loss Δ120596

caused by the existence of orifice plate into account

119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)

H-Power adopted the following equation for flow ratemeasurement

119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902

119898is mass flow rate 120573 is ratio of 119889 (diameter of

orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588

119906

is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows

119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4

R 3 iterativecomputations

Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97

If119863 lt 7112mm (4) should add the following term

0011 (075 minus 120573) (28 minus

119863

254

) (5)

As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re

119863 which is

dependent on 119902119898in turn so the calculation of mass flow rate

119902

119898has to be iteratedDiameters in the formula for calculating should be cor-

rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter

is 119889119896) on the plate the 119889 should be corrected by the following

equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)

where the 119889119898have already been corrected by temperature as

follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889

0is the measurement value under the standard

temperature 1199050 120582 is the coefficient of linear expansion and

119905 is the operating temperature


Pressure measuring point

Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa

Figure 3 Pressure measuring schematic by orifice plate

Re119863is the Reynolds number calculated by119863 (diameter of

internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation

Re119863=

4119902

119898

120583120587119863

(8)

where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine

119871

1(= 119897

1119863) is the ratio of the distance from the upstream

tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows

119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2

119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows

119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)

The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42

23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above

Pump

Reactor

Turbine

Condenser

Control rods

Figure 4 Sketch of SCWR with one loop

the critical point of water (119879119888= 647096K 119901

119888= 22064MPa)

The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4

The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation

119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)

where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω

0(trmin) is the

ideal speed of pump and 119867

ℎminus 119867

119888(kjkg) is the difference

between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine

24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5

Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second


Pump

Reactor

Turbine

Condenser

Pressurizer Steam generator

Control rods

Figure 5 Sketch of SCWR with two loops

loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR

Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation

119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)

where the 119882119877is the core thermal power (MW) 119882SG

119894

is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882

ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor

The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876

119890and specific enthalpy 119867

119890flows into the steam generator

through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876


119901 The

thermal power in ith steam generator can be calculated withfollowing equation

119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)

where119867V is thewet steam enthalpy in steam generator export119867

119901is the blowdown enthalpy119876

119901is the flow rate of blowdown

in second loop 119867119890is the feedwater enthalpy in second loop

and 119876119890is the flow rate of feedwater in second loop

The feed water satisfies the law of conservation of mass asfollows

119876

119890= 119876V + 119876119901 (14)

Simplify (13) and (14)


where feedwater enthalpy 119867

119890and blowdown enthalpy 119876

119901

are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876

119890can be obtained from flow rate

calculation subroutine and the flow rate of blowdown 119876119901is

a measured valueThe wet steam always consists of saturated steam and

saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation

119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)

where the 119867V119904 is the enthalpy of saturated steam and 119867

119897119904is

the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine

3 Uncertainty Analysis of Double-Loop SCWR

The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula

Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)

where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882

ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop

Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872

is the max uncertainty of each steamgeneration

Assuming that

119882SG119894119882

=

1

119894

(19)

We can obtain the following equation

Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater

Core heat production

Entranceheat loss

Pump

PumpChargingstream operation

streamLetdown

Reactor

Pressurizer

Figure 6 Heat balance principle diagram of double-loop SCWR

31 The Calculation of Δ119882119878119866119882

119878119866 The following equation

can be obtained by error propagation formula

Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)

Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range

Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)

Equation (22) can be deduced by the above formula

Δ119909

119909

=

1 minus 119909

119909

(23)

Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows

Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)

and the uncertainty caused by pressure measurement can becalculated by following equation

(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)

where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement

120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899

119894is given in IAPWS-IF97 and 120587 =

01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast

= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1


(Δ119867V119904119867V119904)2

119891

is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97


119890119904 The uncertainty of sat-

urated water enthalpy Δ119867

119890119904119867

119890119904and feedwater enthalpy

Δ119867

119890119867

119890can be estimated by the method the same as

Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902

119898119902

119898can be

described by the following equation

120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)

The uncertainty of discharge coefficient is given by

119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)

If 120573 gt 05 and Re119863lt 10000 the above values should add

the following relative uncertainty

+05 (30)

The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)

for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can

be estimated by the following equation

120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)

where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large

determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows

(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)

and the uncertainty caused by temperature measurement canbe calculated by following equation

(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)

Table 2 The main parameters reference design of the US SCWR

Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs

Table 3 The input and output values calculated by H-Power

Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW

Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above

The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by

experience values

4 Validation of H-Power Code

41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present

The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3

42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II

Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument

It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation


Table 4 Input parameters of H-Power using the values of Qinshan Phase II

Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261

Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power

Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088

5 Conclusions

The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published



References

[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998

[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005


[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009

[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010


[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003

[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008

[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997

[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries

[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000

[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003

[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009

[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010

Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel

Peng Zhang12 Kan Wang1 and Ganglin Yu1

1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China

Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom

Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014


Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR

1 SCFR Conceptual Design

In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]

The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in

which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]

However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it

A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work

The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing



Fuel rod

Stainless steel12060170mm

ZrH layer

11 cm

255 cm

Blanket assembly

Figure 1 A typical SCFR blanket assembly design

Table 1 SCFR core design parameters

Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16

Average power densityMWm3 140

Table 2 SCFR assembly design parameters

Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063

Cladding materialMA956 Fe-215Cr-575Al-

06Ti-07Y2O3725 gcm3

Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10

Assembly widthmm 1822

in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2

Table 3 The different fuel forms chosen for study

Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM

Table 4 SCFR core parameters with different fuel options

Parameters Th-MOX ThMOX +MOXFuel forms

Inner (RGPu +Th)O2 (RGPu +Th)O2

Outer (RGPu +Th)O2 (RGPu + DU)O2

EnrichmentInner 85 85Outer 75 60

Batch numberInner 3 3Outer 4 5

Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM

Inner 572 684Outer 710 645Whole core 629 670

Maximum dischargeburnupMWdkgHM

Inner 611 760Outer 742 718

FIRInner 101 101Outer 081 101Whole core 093 101

2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method

MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays

A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy


Assemblies with downward flow

Assemblies with upward flow

25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9

Figure 2 Conceptual design of SCFR core and assembly

Initialize materialcomposition and burnup

information

Run ORIGENto half-step

Run ORIGENto full-step

Run MCNP CE

Update burnup step

All burnup stepsfinished

Finish assembly burnupsimulation

Yes

No

Get burnup-dependent cross

sections

Cross-sectionparameterization

module

RunMCNP MG

Powerdistribution

Update burnupdistribution


Refuelingfinished

Finish core burnupsimulation

Yes

Yes

No

No

MCBurn MCCBurn

Figure 3 Two-step Monte Carlo core burnup analysis system

Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states

The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed


06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)

kinf MCBurnkinf MCCBurn G2P1Err ()

Figure 4 A BWR assembly model and its burnup calculation results

0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)

Inner coreOuter core

PWRSFR

Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR

to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions

In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right

3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX

In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3

and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study

We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U

31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower


0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR

fis Pu = 6fis Pu = 75fis Pu = 9

Figure 6 Inner cell burnup performances with DU-MOX fuel


0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR

Figure 7 Outer cell burnup performances with DU-MOX fuel

32 Cell Burnup Performance

321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption

rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material

From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly


0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR

fis Pu = 6fis Pu = 75


Figure 8 Inner cell burnup performances with Th-MOX fuel



0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR

Figure 9 Outer cell burnup performances with Th-MOX fuel

and it increases slowly with burnup CR and FIR decreasessignificantly

322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept

negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail

Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively


52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83

(a) Inner 3-batch outer 4-batch

52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113

(b) Inner 3-batch outer 5-batch

Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)

0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

keff C1keff C2keff C3keff C4keff C5keff C6


0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)

Bud ave inBud ave outBud ave

Bud max outBud max in

Figure 11 Multicycle burnup simulation results for Th-MOX core

33 Core Burnup Performance

331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics

Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550




0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)

Bud max inBud max out

Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core

days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10

332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)

Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85

and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4

4 Conclusion

In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design




Acknowledgments

This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)

References

[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994

[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001

[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007

[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)

[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996

[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005

[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008

[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009

[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005

[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011

[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006

[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003

[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011

[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994

[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003

Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop

Licun Wu Daogang Lu and Yu Liu

Nuclear Science and Engineering North China Electric Power University Beijing 102206 China

Correspondence should be addressed to Licun Wu wlc121126com

Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014


Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration

1 Introduction

The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature

of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper

In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it



R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator

Test sectionwith 4 fuel rods

Figure 1 Concept of the active channel for SCWR fuel qualification

Low pressurecoolant injection

Recir-culationpump

Emergency pump

Depressurizationsystem

Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel

Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test

Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach

Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the

flutter instability will happen when the flow rate is larger thanthe critical flow rate

Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence

Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode

Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration

2 Theoretical Models

Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as

119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)

where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898

119886is the added mass 119879

0is the initial axial tension

119862

1015840

119879

is the form drag coefficient at the free end 119862119881is the

effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is


Table 1 Natural frequency of the fuel rod

Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz

y

zU

l

c1 c2

k2k1

Figure 3 Schematic diagram of the fuel rod in axial flow

unsupported or elastically supported 119862119879is equal to 119862

119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)

where 119862119891is the drag coefficient due to shear forces and 119862

119898is

added mass coefficientThe appropriate boundary conditions associated with the

equation of motion are as followsFor 119911 = 0

119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)

where 1198961and 1198962are displacement spring constants and 119888

1and

119888

2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions

(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions

3 Details of Experiment

31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with

Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection

Figure 4 Schematic diagram of experimental loop

Table 2 Experimental conditions and geometry parameters of thetest section

Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm

water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide

The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5

In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the


A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm

Figure 5The collocation and geometry of the fuel assembly and testsection

Hole Clearance

Fuel rod

(a)

Spacer

(b)

Figure 6 Schematic diagram of two types of spacers

top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo

32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it

projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data

However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment

Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows

The thickness of the container 119889

1is the same as the

thickness of channel 11988910158401

in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889

2is equal to that from fuel rod to the inner wall

of the channel 11988910158402

Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909

119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )

The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as

119910 = 072582119909 minus 1790196 (5)

where 119909 is the actual position of the micrometer and 119910 is themeasured position

Assuming the actual position is 1199091 themeasured position

is 1199101 then (5) becomes

119910

1= 072582119909

1minus 1790196 (6)

Moreover if the actual position is 1199092and the measured

position is 1199102 (5) becomes

119910

2= 072582119909

2minus 1790196 (7)

Subtracting (7) to (6) gives

119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)

Noting (1199092minus119909

1) is the actual displacement of micrometer

Δ119909 and (1199102minus119910

1) is the correspondingmeasured displacement

Δ119910 so (8) becomes

Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )

Figure 7 Measurement calibration device

350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)

Actual position of micrometer (120583m)

Experimental valueLinear fit curve

Figure 8 Measurement calibration curve

From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)

33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889

1to be larger than the actual

displacement 1198892 That has a substantial influence on the

result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of

fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840

1

is the same as the actualdisplacement 1198891015840

2

34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)

4 The Experimental Results and Analysis

41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases

Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider

119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)

Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of


Position 1

Position 2

X

Y

d2d1

SensorO

(a) Original structure 1198891gt 1198892

d998400

2d998400

1

Sensor

(b) Improved structure 11988910158401

=

119889

1015840

2

3m

m

3mm

05

mm

(c) Size of metal sheet

Figure 9 Schematic of improved structure

Displacement of the

Displacement

Correctionmodule

sensor

Final displacementsignals signals signals

Digital signalsComputer

Initial displacement Initial voltage

Analog signalsinstrument

Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)

Figure 10 Schematic diagram of data acquisition system

supercritical water according to (10) it can be noted thatthe average value of fluid exciting force

119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop

42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process

43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]

As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from


Table 3 Root mean square displacement of the fuel rod in through hole case

Flow rate (m3h)Root mean square displacement (120583m)

1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 11 Displacement power spectral density of the fuel rod inthrough hole case

6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz

Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration

It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 12 Displacement power spectral density of the fuel rod inblind hole case

0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)

Through hole caseBlind hole case

Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h


0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h

at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value

44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)




Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h


20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05

Figure 17 Root-mean-square displacement changing with flow ratein two cases

the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well

45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found


Left Right

Spacer

Fuel rod

V

Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability

that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop

5 Conclusions

An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows

(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that

(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of

boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly

(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop



References

[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977

[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982

[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987

[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983

[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985

[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998

[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002

[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006

[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007

[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984

[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984

[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970







Editorial Board




Contents


































Outlettemperature

(∘C)

Pressure(MPa)

Net efficiency()



W6-1

AECL (Canada)

CANDU-X-MARK1

D2O









Junli Gou

References
















1 Introduction










Instrumentation pin



A1 B C D E F G

2

3

4

5

6

7




FlowHeat



Dow

ncom

er

Lower plenum

Coolantchannels

Moderatorchannels











3 Reference Case






0

2 4 6

1234567

0

061

081

102

2 4 6

2 4 6

1

2

3

4

5

6

7100

200

300

400

500

2 4 6

1234567


2 4 6

1234567

0

061

081

1021234567

0

200

400

600

2 4 6

1234567


2 4 6

1

2

3

4

5

6

70

061

081

102

2 4 6

1

2

3

4

5

6

70

200

400

600

2 4 6

1

2

3

4

5

6

7


minus156 minus136

minus136








minus10

minus5

0

minus15

minus10

minus5

0

minus15

minus10

minus5

r = 020

r = 018

r = 015

523 476 513 477 525 519 583

476 373 466 310 475 477 595

513 466 502 461 433 552

477 310 461 415 523 592

525 475 433 523 585

519 477 552 592

582 595




105 116 107 114 103 105 076

116 112 116 104 114 115 067

067

107 116 110 117 118 094

114 104 117 118 105 069

103 114 118 105 075

105 115 094 069

076

103 115 107 115 102 103 073

115 117 117 115 115 114 065

107 117 110 118 119 092

115 115 118 119 103 067

102 115 119 113 073

103 114 092 067

073065

525 486 524 487 537 532 593

486 392 473 388 485 490 604

524 473 512 469 444 564

487 388 469 427 535 601

537 485 444 535 595

532 490 564 601

593 604







minus151 minus151







minus159minus160

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071063


119900

119860mod




int

out

in120588119892119889119897 minus

1

2119860

2

mod

119870119898

2

120588

119900

= Δ119875 (1)


119870 = (

119860mod119860

119888

minus 1)

2

(2)


Nonreverse channel

1 2 3 40

1

2

3

Pow

er (M

W)

1 2 3 40

1

2

3Po

wer

(MW

)

Reverse channel

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

600

650

700

750

800

850

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

1 2 3 4

600

650

700

750

800

850


moderator

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

r = 020

r = 018

r = 015 r = 020

r = 018

r = 015




119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)







4 Results



120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)




02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02





5 Discussion



0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References


















Editorial Board




Contents


































Outlettemperature

(∘C)

Pressure(MPa)

Net efficiency()



W6-1

AECL (Canada)

CANDU-X-MARK1

D2O









Junli Gou

References
















1 Introduction










Instrumentation pin



A1 B C D E F G

2

3

4

5

6

7




FlowHeat



Dow

ncom

er

Lower plenum

Coolantchannels

Moderatorchannels











3 Reference Case






0

2 4 6

1234567

0

061

081

102

2 4 6

2 4 6

1

2

3

4

5

6

7100

200

300

400

500

2 4 6

1234567


2 4 6

1234567

0

061

081

1021234567

0

200

400

600

2 4 6

1234567


2 4 6

1

2

3

4

5

6

70

061

081

102

2 4 6

1

2

3

4

5

6

70

200

400

600

2 4 6

1

2

3

4

5

6

7


minus156 minus136

minus136








minus10

minus5

0

minus15

minus10

minus5

0

minus15

minus10

minus5

r = 020

r = 018

r = 015

523 476 513 477 525 519 583

476 373 466 310 475 477 595

513 466 502 461 433 552

477 310 461 415 523 592

525 475 433 523 585

519 477 552 592

582 595




105 116 107 114 103 105 076

116 112 116 104 114 115 067

067

107 116 110 117 118 094

114 104 117 118 105 069

103 114 118 105 075

105 115 094 069

076

103 115 107 115 102 103 073

115 117 117 115 115 114 065

107 117 110 118 119 092

115 115 118 119 103 067

102 115 119 113 073

103 114 092 067

073065

525 486 524 487 537 532 593

486 392 473 388 485 490 604

524 473 512 469 444 564

487 388 469 427 535 601

537 485 444 535 595

532 490 564 601

593 604







minus151 minus151







minus159minus160

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071063


119900

119860mod




int

out

in120588119892119889119897 minus

1

2119860

2

mod

119870119898

2

120588

119900

= Δ119875 (1)


119870 = (

119860mod119860

119888

minus 1)

2

(2)


Nonreverse channel

1 2 3 40

1

2

3

Pow

er (M

W)

1 2 3 40

1

2

3Po

wer

(MW

)

Reverse channel

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

600

650

700

750

800

850

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

1 2 3 4

600

650

700

750

800

850


moderator

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

r = 020

r = 018

r = 015 r = 020

r = 018

r = 015




119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)







4 Results



120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)




02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02





5 Discussion



0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References















Editorial Board




Contents


































Outlettemperature

(∘C)

Pressure(MPa)

Net efficiency()



W6-1

AECL (Canada)

CANDU-X-MARK1

D2O









Junli Gou

References
















1 Introduction










Instrumentation pin



A1 B C D E F G

2

3

4

5

6

7




FlowHeat



Dow

ncom

er

Lower plenum

Coolantchannels

Moderatorchannels











3 Reference Case






0

2 4 6

1234567

0

061

081

102

2 4 6

2 4 6

1

2

3

4

5

6

7100

200

300

400

500

2 4 6

1234567


2 4 6

1234567

0

061

081

1021234567

0

200

400

600

2 4 6

1234567


2 4 6

1

2

3

4

5

6

70

061

081

102

2 4 6

1

2

3

4

5

6

70

200

400

600

2 4 6

1

2

3

4

5

6

7


minus156 minus136

minus136








minus10

minus5

0

minus15

minus10

minus5

0

minus15

minus10

minus5

r = 020

r = 018

r = 015

523 476 513 477 525 519 583

476 373 466 310 475 477 595

513 466 502 461 433 552

477 310 461 415 523 592

525 475 433 523 585

519 477 552 592

582 595




105 116 107 114 103 105 076

116 112 116 104 114 115 067

067

107 116 110 117 118 094

114 104 117 118 105 069

103 114 118 105 075

105 115 094 069

076

103 115 107 115 102 103 073

115 117 117 115 115 114 065

107 117 110 118 119 092

115 115 118 119 103 067

102 115 119 113 073

103 114 092 067

073065

525 486 524 487 537 532 593

486 392 473 388 485 490 604

524 473 512 469 444 564

487 388 469 427 535 601

537 485 444 535 595

532 490 564 601

593 604







minus151 minus151







minus159minus160

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071063


119900

119860mod




int

out

in120588119892119889119897 minus

1

2119860

2

mod

119870119898

2

120588

119900

= Δ119875 (1)


119870 = (

119860mod119860

119888

minus 1)

2

(2)


Nonreverse channel

1 2 3 40

1

2

3

Pow

er (M

W)

1 2 3 40

1

2

3Po

wer

(MW

)

Reverse channel

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

600

650

700

750

800

850

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

1 2 3 4

600

650

700

750

800

850


moderator

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

r = 020

r = 018

r = 015 r = 020

r = 018

r = 015




119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)







4 Results



120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)




02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02





5 Discussion



0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References













Editorial Board




Contents


































Outlettemperature

(∘C)

Pressure(MPa)

Net efficiency()



W6-1

AECL (Canada)

CANDU-X-MARK1

D2O









Junli Gou

References
















1 Introduction










Instrumentation pin



A1 B C D E F G

2

3

4

5

6

7




FlowHeat



Dow

ncom

er

Lower plenum

Coolantchannels

Moderatorchannels











3 Reference Case






0

2 4 6

1234567

0

061

081

102

2 4 6

2 4 6

1

2

3

4

5

6

7100

200

300

400

500

2 4 6

1234567


2 4 6

1234567

0

061

081

1021234567

0

200

400

600

2 4 6

1234567


2 4 6

1

2

3

4

5

6

70

061

081

102

2 4 6

1

2

3

4

5

6

70

200

400

600

2 4 6

1

2

3

4

5

6

7


minus156 minus136

minus136








minus10

minus5

0

minus15

minus10

minus5

0

minus15

minus10

minus5

r = 020

r = 018

r = 015

523 476 513 477 525 519 583

476 373 466 310 475 477 595

513 466 502 461 433 552

477 310 461 415 523 592

525 475 433 523 585

519 477 552 592

582 595




105 116 107 114 103 105 076

116 112 116 104 114 115 067

067

107 116 110 117 118 094

114 104 117 118 105 069

103 114 118 105 075

105 115 094 069

076

103 115 107 115 102 103 073

115 117 117 115 115 114 065

107 117 110 118 119 092

115 115 118 119 103 067

102 115 119 113 073

103 114 092 067

073065

525 486 524 487 537 532 593

486 392 473 388 485 490 604

524 473 512 469 444 564

487 388 469 427 535 601

537 485 444 535 595

532 490 564 601

593 604







minus151 minus151







minus159minus160

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071063


119900

119860mod




int

out

in120588119892119889119897 minus

1

2119860

2

mod

119870119898

2

120588

119900

= Δ119875 (1)


119870 = (

119860mod119860

119888

minus 1)

2

(2)


Nonreverse channel

1 2 3 40

1

2

3

Pow

er (M

W)

1 2 3 40

1

2

3Po

wer

(MW

)

Reverse channel

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

600

650

700

750

800

850

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

1 2 3 4

600

650

700

750

800

850


moderator

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

r = 020

r = 018

r = 015 r = 020

r = 018

r = 015




119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)







4 Results



120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)




02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02





5 Discussion



0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References













Contents


































Outlettemperature

(∘C)

Pressure(MPa)

Net efficiency()



W6-1

AECL (Canada)

CANDU-X-MARK1

D2O









Junli Gou

References
















1 Introduction










Instrumentation pin



A1 B C D E F G

2

3

4

5

6

7




FlowHeat



Dow

ncom

er

Lower plenum

Coolantchannels

Moderatorchannels











3 Reference Case






0

2 4 6

1234567

0

061

081

102

2 4 6

2 4 6

1

2

3

4

5

6

7100

200

300

400

500

2 4 6

1234567


2 4 6

1234567

0

061

081

1021234567

0

200

400

600

2 4 6

1234567


2 4 6

1

2

3

4

5

6

70

061

081

102

2 4 6

1

2

3

4

5

6

70

200

400

600

2 4 6

1

2

3

4

5

6

7


minus156 minus136

minus136








minus10

minus5

0

minus15

minus10

minus5

0

minus15

minus10

minus5

r = 020

r = 018

r = 015

523 476 513 477 525 519 583

476 373 466 310 475 477 595

513 466 502 461 433 552

477 310 461 415 523 592

525 475 433 523 585

519 477 552 592

582 595




105 116 107 114 103 105 076

116 112 116 104 114 115 067

067

107 116 110 117 118 094

114 104 117 118 105 069

103 114 118 105 075

105 115 094 069

076

103 115 107 115 102 103 073

115 117 117 115 115 114 065

107 117 110 118 119 092

115 115 118 119 103 067

102 115 119 113 073

103 114 092 067

073065

525 486 524 487 537 532 593

486 392 473 388 485 490 604

524 473 512 469 444 564

487 388 469 427 535 601

537 485 444 535 595

532 490 564 601

593 604







minus151 minus151







minus159minus160

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071063


119900

119860mod




int

out

in120588119892119889119897 minus

1

2119860

2

mod

119870119898

2

120588

119900

= Δ119875 (1)


119870 = (

119860mod119860

119888

minus 1)

2

(2)


Nonreverse channel

1 2 3 40

1

2

3

Pow

er (M

W)

1 2 3 40

1

2

3Po

wer

(MW

)

Reverse channel

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

600

650

700

750

800

850

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

1 2 3 4

600

650

700

750

800

850


moderator

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

r = 020

r = 018

r = 015 r = 020

r = 018

r = 015




119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)







4 Results



120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)




02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02





5 Discussion



0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References








































Outlettemperature

(∘C)

Pressure(MPa)

Net efficiency()



W6-1

AECL (Canada)

CANDU-X-MARK1

D2O









Junli Gou

References
















1 Introduction










Instrumentation pin



A1 B C D E F G

2

3

4

5

6

7




FlowHeat



Dow

ncom

er

Lower plenum

Coolantchannels

Moderatorchannels











3 Reference Case






0

2 4 6

1234567

0

061

081

102

2 4 6

2 4 6

1

2

3

4

5

6

7100

200

300

400

500

2 4 6

1234567


2 4 6

1234567

0

061

081

1021234567

0

200

400

600

2 4 6

1234567


2 4 6

1

2

3

4

5

6

70

061

081

102

2 4 6

1

2

3

4

5

6

70

200

400

600

2 4 6

1

2

3

4

5

6

7


minus156 minus136

minus136








minus10

minus5

0

minus15

minus10

minus5

0

minus15

minus10

minus5

r = 020

r = 018

r = 015

523 476 513 477 525 519 583

476 373 466 310 475 477 595

513 466 502 461 433 552

477 310 461 415 523 592

525 475 433 523 585

519 477 552 592

582 595




105 116 107 114 103 105 076

116 112 116 104 114 115 067

067

107 116 110 117 118 094

114 104 117 118 105 069

103 114 118 105 075

105 115 094 069

076

103 115 107 115 102 103 073

115 117 117 115 115 114 065

107 117 110 118 119 092

115 115 118 119 103 067

102 115 119 113 073

103 114 092 067

073065

525 486 524 487 537 532 593

486 392 473 388 485 490 604

524 473 512 469 444 564

487 388 469 427 535 601

537 485 444 535 595

532 490 564 601

593 604







minus151 minus151







minus159minus160

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071063


119900

119860mod




int

out

in120588119892119889119897 minus

1

2119860

2

mod

119870119898

2

120588

119900

= Δ119875 (1)


119870 = (

119860mod119860

119888

minus 1)

2

(2)


Nonreverse channel

1 2 3 40

1

2

3

Pow

er (M

W)

1 2 3 40

1

2

3Po

wer

(MW

)

Reverse channel

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

600

650

700

750

800

850

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

1 2 3 4

600

650

700

750

800

850


moderator

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

r = 020

r = 018

r = 015 r = 020

r = 018

r = 015




119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)







4 Results



120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)




02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02





5 Discussion



0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References
















Outlettemperature

(∘C)

Pressure(MPa)

Net efficiency()



W6-1

AECL (Canada)

CANDU-X-MARK1

D2O









Junli Gou

References
















1 Introduction










Instrumentation pin



A1 B C D E F G

2

3

4

5

6

7




FlowHeat



Dow

ncom

er

Lower plenum

Coolantchannels

Moderatorchannels











3 Reference Case






0

2 4 6

1234567

0

061

081

102

2 4 6

2 4 6

1

2

3

4

5

6

7100

200

300

400

500

2 4 6

1234567


2 4 6

1234567

0

061

081

1021234567

0

200

400

600

2 4 6

1234567


2 4 6

1

2

3

4

5

6

70

061

081

102

2 4 6

1

2

3

4

5

6

70

200

400

600

2 4 6

1

2

3

4

5

6

7


minus156 minus136

minus136








minus10

minus5

0

minus15

minus10

minus5

0

minus15

minus10

minus5

r = 020

r = 018

r = 015

523 476 513 477 525 519 583

476 373 466 310 475 477 595

513 466 502 461 433 552

477 310 461 415 523 592

525 475 433 523 585

519 477 552 592

582 595




105 116 107 114 103 105 076

116 112 116 104 114 115 067

067

107 116 110 117 118 094

114 104 117 118 105 069

103 114 118 105 075

105 115 094 069

076

103 115 107 115 102 103 073

115 117 117 115 115 114 065

107 117 110 118 119 092

115 115 118 119 103 067

102 115 119 113 073

103 114 092 067

073065

525 486 524 487 537 532 593

486 392 473 388 485 490 604

524 473 512 469 444 564

487 388 469 427 535 601

537 485 444 535 595

532 490 564 601

593 604







minus151 minus151







minus159minus160

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071063


119900

119860mod




int

out

in120588119892119889119897 minus

1

2119860

2

mod

119870119898

2

120588

119900

= Δ119875 (1)


119870 = (

119860mod119860

119888

minus 1)

2

(2)


Nonreverse channel

1 2 3 40

1

2

3

Pow

er (M

W)

1 2 3 40

1

2

3Po

wer

(MW

)

Reverse channel

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

600

650

700

750

800

850

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

1 2 3 4

600

650

700

750

800

850


moderator

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

r = 020

r = 018

r = 015 r = 020

r = 018

r = 015




119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)







4 Results



120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)




02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02





5 Discussion



0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References





















1 Introduction










Instrumentation pin



A1 B C D E F G

2

3

4

5

6

7




FlowHeat



Dow

ncom

er

Lower plenum

Coolantchannels

Moderatorchannels











3 Reference Case






0

2 4 6

1234567

0

061

081

102

2 4 6

2 4 6

1

2

3

4

5

6

7100

200

300

400

500

2 4 6

1234567


2 4 6

1234567

0

061

081

1021234567

0

200

400

600

2 4 6

1234567


2 4 6

1

2

3

4

5

6

70

061

081

102

2 4 6

1

2

3

4

5

6

70

200

400

600

2 4 6

1

2

3

4

5

6

7


minus156 minus136

minus136








minus10

minus5

0

minus15

minus10

minus5

0

minus15

minus10

minus5

r = 020

r = 018

r = 015

523 476 513 477 525 519 583

476 373 466 310 475 477 595

513 466 502 461 433 552

477 310 461 415 523 592

525 475 433 523 585

519 477 552 592

582 595




105 116 107 114 103 105 076

116 112 116 104 114 115 067

067

107 116 110 117 118 094

114 104 117 118 105 069

103 114 118 105 075

105 115 094 069

076

103 115 107 115 102 103 073

115 117 117 115 115 114 065

107 117 110 118 119 092

115 115 118 119 103 067

102 115 119 113 073

103 114 092 067

073065

525 486 524 487 537 532 593

486 392 473 388 485 490 604

524 473 512 469 444 564

487 388 469 427 535 601

537 485 444 535 595

532 490 564 601

593 604







minus151 minus151







minus159minus160

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071063


119900

119860mod




int

out

in120588119892119889119897 minus

1

2119860

2

mod

119870119898

2

120588

119900

= Δ119875 (1)


119870 = (

119860mod119860

119888

minus 1)

2

(2)


Nonreverse channel

1 2 3 40

1

2

3

Pow

er (M

W)

1 2 3 40

1

2

3Po

wer

(MW

)

Reverse channel

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

600

650

700

750

800

850

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

1 2 3 4

600

650

700

750

800

850


moderator

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

r = 020

r = 018

r = 015 r = 020

r = 018

r = 015




119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)







4 Results



120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)




02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02





5 Discussion



0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References















Instrumentation pin



A1 B C D E F G

2

3

4

5

6

7




FlowHeat



Dow

ncom

er

Lower plenum

Coolantchannels

Moderatorchannels











3 Reference Case






0

2 4 6

1234567

0

061

081

102

2 4 6

2 4 6

1

2

3

4

5

6

7100

200

300

400

500

2 4 6

1234567


2 4 6

1234567

0

061

081

1021234567

0

200

400

600

2 4 6

1234567


2 4 6

1

2

3

4

5

6

70

061

081

102

2 4 6

1

2

3

4

5

6

70

200

400

600

2 4 6

1

2

3

4

5

6

7


minus156 minus136

minus136








minus10

minus5

0

minus15

minus10

minus5

0

minus15

minus10

minus5

r = 020

r = 018

r = 015

523 476 513 477 525 519 583

476 373 466 310 475 477 595

513 466 502 461 433 552

477 310 461 415 523 592

525 475 433 523 585

519 477 552 592

582 595




105 116 107 114 103 105 076

116 112 116 104 114 115 067

067

107 116 110 117 118 094

114 104 117 118 105 069

103 114 118 105 075

105 115 094 069

076

103 115 107 115 102 103 073

115 117 117 115 115 114 065

107 117 110 118 119 092

115 115 118 119 103 067

102 115 119 113 073

103 114 092 067

073065

525 486 524 487 537 532 593

486 392 473 388 485 490 604

524 473 512 469 444 564

487 388 469 427 535 601

537 485 444 535 595

532 490 564 601

593 604







minus151 minus151







minus159minus160

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071063


119900

119860mod




int

out

in120588119892119889119897 minus

1

2119860

2

mod

119870119898

2

120588

119900

= Δ119875 (1)


119870 = (

119860mod119860

119888

minus 1)

2

(2)


Nonreverse channel

1 2 3 40

1

2

3

Pow

er (M

W)

1 2 3 40

1

2

3Po

wer

(MW

)

Reverse channel

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

600

650

700

750

800

850

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

1 2 3 4

600

650

700

750

800

850


moderator

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

r = 020

r = 018

r = 015 r = 020

r = 018

r = 015




119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)







4 Results



120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)




02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02





5 Discussion



0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References





















3 Reference Case






0

2 4 6

1234567

0

061

081

102

2 4 6

2 4 6

1

2

3

4

5

6

7100

200

300

400

500

2 4 6

1234567


2 4 6

1234567

0

061

081

1021234567

0

200

400

600

2 4 6

1234567


2 4 6

1

2

3

4

5

6

70

061

081

102

2 4 6

1

2

3

4

5

6

70

200

400

600

2 4 6

1

2

3

4

5

6

7


minus156 minus136

minus136








minus10

minus5

0

minus15

minus10

minus5

0

minus15

minus10

minus5

r = 020

r = 018

r = 015

523 476 513 477 525 519 583

476 373 466 310 475 477 595

513 466 502 461 433 552

477 310 461 415 523 592

525 475 433 523 585

519 477 552 592

582 595




105 116 107 114 103 105 076

116 112 116 104 114 115 067

067

107 116 110 117 118 094

114 104 117 118 105 069

103 114 118 105 075

105 115 094 069

076

103 115 107 115 102 103 073

115 117 117 115 115 114 065

107 117 110 118 119 092

115 115 118 119 103 067

102 115 119 113 073

103 114 092 067

073065

525 486 524 487 537 532 593

486 392 473 388 485 490 604

524 473 512 469 444 564

487 388 469 427 535 601

537 485 444 535 595

532 490 564 601

593 604







minus151 minus151







minus159minus160

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071063


119900

119860mod




int

out

in120588119892119889119897 minus

1

2119860

2

mod

119870119898

2

120588

119900

= Δ119875 (1)


119870 = (

119860mod119860

119888

minus 1)

2

(2)


Nonreverse channel

1 2 3 40

1

2

3

Pow

er (M

W)

1 2 3 40

1

2

3Po

wer

(MW

)

Reverse channel

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

600

650

700

750

800

850

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

1 2 3 4

600

650

700

750

800

850


moderator

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

r = 020

r = 018

r = 015 r = 020

r = 018

r = 015




119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)







4 Results



120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)




02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02





5 Discussion



0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














0

2 4 6

1234567

0

061

081

102

2 4 6

2 4 6

1

2

3

4

5

6

7100

200

300

400

500

2 4 6

1234567


2 4 6

1234567

0

061

081

1021234567

0

200

400

600

2 4 6

1234567


2 4 6

1

2

3

4

5

6

70

061

081

102

2 4 6

1

2

3

4

5

6

70

200

400

600

2 4 6

1

2

3

4

5

6

7


minus156 minus136

minus136








minus10

minus5

0

minus15

minus10

minus5

0

minus15

minus10

minus5

r = 020

r = 018

r = 015

523 476 513 477 525 519 583

476 373 466 310 475 477 595

513 466 502 461 433 552

477 310 461 415 523 592

525 475 433 523 585

519 477 552 592

582 595




105 116 107 114 103 105 076

116 112 116 104 114 115 067

067

107 116 110 117 118 094

114 104 117 118 105 069

103 114 118 105 075

105 115 094 069

076

103 115 107 115 102 103 073

115 117 117 115 115 114 065

107 117 110 118 119 092

115 115 118 119 103 067

102 115 119 113 073

103 114 092 067

073065

525 486 524 487 537 532 593

486 392 473 388 485 490 604

524 473 512 469 444 564

487 388 469 427 535 601

537 485 444 535 595

532 490 564 601

593 604







minus151 minus151







minus159minus160

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071063


119900

119860mod




int

out

in120588119892119889119897 minus

1

2119860

2

mod

119870119898

2

120588

119900

= Δ119875 (1)


119870 = (

119860mod119860

119888

minus 1)

2

(2)


Nonreverse channel

1 2 3 40

1

2

3

Pow

er (M

W)

1 2 3 40

1

2

3Po

wer

(MW

)

Reverse channel

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

600

650

700

750

800

850

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

1 2 3 4

600

650

700

750

800

850


moderator

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

r = 020

r = 018

r = 015 r = 020

r = 018

r = 015




119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)







4 Results



120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)




02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02





5 Discussion



0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














Nonreverse channel

1 2 3 40

1

2

3

Pow

er (M

W)

1 2 3 40

1

2

3Po

wer

(MW

)

Reverse channel

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

700

800

900

1000

1100

1200

1300

Fuel

tem

pera

ture

(K)

1 2 3 4

600

650

700

750

800

850

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

1 2 3 4

600

650

700

750

800

850


moderator

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

1 2 3 4100

200

300

400

500

600

Core height (m)

Equi

vale

nt d

ensit

y (k

gm

3)

r = 020

r = 018

r = 015 r = 020

r = 018

r = 015




119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)







4 Results



120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)




02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02





5 Discussion



0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References















119860

119888= 062119860

119900+ 038

119860

4

119900

119860

3

mod (3)







4 Results



120588eq =sum

12

119894=1

(120588cool119894119881cool119894 + 120588mod119894119881mod119894)

sum

12

119894=1

(119881cool119894 + 119881mod119894) (4)




02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02





5 Discussion



0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














0

2 4 6

1234567

061

081

102

2 6

1234567

0 0

200

400

600

2 4 46

1234567


2 4 6

1234567

0

061

081

102

2 4 6

1234567

0

200

400

600

2 4 6

1234567









minus10

minus5

0

minus15

minus10

minus5







minus151 minus151



539 488 528 489 541 537 596

488 418 472 414 486 502 607

528 472 515 467 457 567

489 414 467 438 538 604

541 486 457 538 597

537 502 567 604

596 607

103 114 106 114 101 102 071

114 124 116 122 114 115 063

106 116 109 116 121 091

114 122 116 121 102 066

101 114 121 102 071

102 115091066

071063

Varied r

r = 015

534 485 523 486 537 533 593

485 408 471 406 485 492 604

523 472 510 469 449 563

487 406 469 434 534 601

537 485 449 534 594

533 492 563 601

593 604

103 115 106 114 101 102 071

115 122 117 121 115 113 063

106 117 110 118 120 091

114 121 118 121 103 066

101 115 120 103 072

102 113 091 066

071 063


0

1

2

3

Pow

er (M

W)

800

1000

1200

Fuel

tem

pera

ture

(K)

1 2 3 4

600

700

800



Core height (m)

Mod

erat

or an

d co

olan

t te

mpe

ratu

re (K

)

Varied r r = 015

Varied r r = 015

Varied r r = 015





6 Conclusion




Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References















Nomenclature




Acknowledgments


References






















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References





















1 Introduction









Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














Other modules

RDMR

Other modules

PDMR

GI

RELAP5 PARCS








Start



(NEMANM) solver



hydraulics solver

converge

End

Updatetemperature

profile

Updatenuclear cross

section

No

Yes

TH

Dat

aN

eutro

nics

Keff Ψ and Tfueltr

ansfe

r










Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References















Instrumentation pin








119898)Δ119879

119898


119898)Δ119863

119898+

(120597

2

Σ120597119863

2

119898

)(Δ119863

119898)


Σ (120572 119879

119891 119879

119898 119879

119888 119863

119898 119863

119888) =Σ

119903+ 120572ΔΣ

119888119903+

120597Σ

120597radic119879

119891

Δradic119879

119891

+

120597Σ

120597119879

119898

Δ119879

119898+

120597Σ

120597119879

119888

Δ119879

119888

+

120597Σ

120597119863

119898

Δ119863

119898+

120597

2

Σ

120597119863

2

119898

(Δ119863

119898)

2

+

120597Σ

120597119863

119888

Δ119863

119888+

120597

2

Σ

120597119863

2

119888

(Δ119863

119888)

2

(1)







lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References















lowast



335010000 1 1335020000 2 1335030000 3 1

335880000 88 1335890000 89 1335900000 90 1lowast




3360001 1 13360002 2 13360003 3 1

3360088 88 13360089 89 13360090 90 1






150 200 250 300 350 400 450 500 55025

25526

26527

27528

28529

29530

Pres

sure

(MPa

)


Density (kgm3)

675K larr 654K
















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References






















1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927







1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














1 2 3 4 5 6 7 8 9 10 11 12Node number


HELIOSPARCS

1 2 3 4 5 6 7 8 9 10 11 12Node number


Mac

rosc

opic

cros

s

780E minus 01

760E minus 01

740E minus 01

720E minus 01

700E minus 01

680E minus 01

660E minus 01

640E minus 01

235E minus 01

230E minus 01

225E minus 01

220E minus 01

215E minus 01

210E minus 01

205E minus 01

200E minus 01

sect

ion

(cm

minus1)

Mac

rosc

opic

cros

s se

ctio

n (c

mminus1)









Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














Mod

erat

or ch

anne

l

Wat

er ro

d

Coo

lant

chan

nel

Fuel

rod




6 Discussion



210

220

230

240

250

260

270

117

735

352

970

588

110

5712

3314

0915

8517

6119

3721

1322

8924

6526

4128

1729

9331

6933

4535

2136

9738

7340

4942

2544

0145

7747

5349

2951

0552

8154

57

Data point number

Pres

sure

(Pa)


645

650

655

660

665

670

675

121

843

565

286

910

8613

0315

2017

3719

5421

7123

8826

0528

2230

3932

5634

7336

9039

0741

2443

4145

5847

7549

9252

0954

26

Tem

pera

ture

(K)

Data point number


times105



Nomenclature





Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References
















Acknowledgments


References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References





















1 Introduction









READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop


















119875

1= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 120573

19

) (2)


119902

119898=

119862

radic1 minus 120573

4

120576 sdot

120587119889

2

4

radic2Δ119875120588

119906 (3)

where 119902



119906


119862 = 05961 + 00261120573

2

minus 0216120573

8

+ 0000521(

10

6

120573

Re119863

)

07

+ (00188 + 00063119860) 120573

35

(

10

6

Re119863

)

03

+ (0043 + 0080119890

minus101198711minus 0123119890

minus71198711) (1 minus 011119860)

120573

4

1 minus 120573

4

minus 0031 (119872

1015840

2

minus 08119872

1015840

2

11

) 120573

13

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1

)ℎ(kJkgminus1

)119904(kJkgminus1

Kminus1

)119906(kJkgminus1

)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














Input p T

27315 le T le 227315

0 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus

119863

254

) (5)


119863 which is


119902




equation

119889 = 119889

1198981 + 055(

119889

119896

119889

119898

)

2

(6)


follows

119889

119898= 119889

0+ 119889

0120582 (119905 minus 119905

0) (7)

where 119889






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References















Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902

119898

120583120587119863

(8)


119871

1(= 119897



119871

1=

0 corner tappings

1 119863 and 119863

2

tappings254

119863

flange tappings

119860 = (

19000120573

Re119863

)

08

119872

1015840

2=

2119871

1015840

2

1 minus 120573

(9)

119871

1015840

2

(= 119897

1015840

2


119871

1015840

2

=

0 corner tappings

047 119863 and 119863

2

tappings254

119863

flange tappings

(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 times

Ω

Ω

0

times

(119867

ℎminus 119867

119888)

1000

(MW) (11)


0(trmin) is the


ℎminus 119867






Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














Pump

Reactor

Turbine

Condenser


Control rods




119882

119877=

119873

sum

119894=1

119882SG119894

minus119882

ΔPr (12)


119894








119901 The









119876

119890= 119876V + 119876119901 (14)





119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)


119897119904is




Δ119882

119882

= [

119899

sum

119894=1

[

119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [

119882

ΔPr119882

Δ(119882

ΔPr)

119882

ΔPr]

2

]

12

(17)



Δ119882SG119894Δ119882

le [

Δ119882SGΔ119882

]

119872

(18)

where [Δ119882SGΔ119882]

119872


Assuming that

119882SG119894119882

=

1

119894

(19)


Δ119882

119882

=

1

119894

[

Δ119882SG119882SG

]

2

119872

+ [

119882

ΔPr119882

times

Δ119882

ΔPr119882

ΔPr]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer





Δ119882SG119882SG

=

[

[

[

[

[

[

[

119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [

119867

119890119876

119890

119882SG

Δ119867

119890

119867

119890

]

2

+ [

119867

119901119876

119901

119882SG

Δ119867

119901

119867

119901

]

2

+[

119876

119890(119867V minus 119867119890)

119882SG

Δ119876

119890

119876

119890

]

2

+ [

119876

119901(119867V minus 119867119901)

119882SG

Δ119876

119901

119876

119901

]

2

]

]

]

]

]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909

]

2

+ [

119867V119904

119867V119909

Δ119867V119904

119867V119904]

2

+[

119867

119890119904

119867V(1 minus 119909)

Δ119867

119890119904

119867

119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909

=

119909

1 minus 119909

Δ119909

119909

= 1 (22)


Δ119909

119909

=

1 minus 119909

119909

(23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (

Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(

Δ119867V119904

119867V119904)

119875V

=

119875V

119867V119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597119867V119904

120597119875V

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum

119894=1

119899

119894119869

119894(120591 minus 05)

119869119894minus1

119868

119894(

01119875V

119901

lowast

)

119868119894minus1

(

1

119901

lowast

)

(26)

where 119868

119894 119869

119894 119899


01119875V119901lowast

120591 = 119879

lowast

119905119890 119901

lowast



(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














(Δ119867V119904119867V119904)2

119891





119890119904119867


Δ119867

119890119867



119898119902

119898can be


120575119902

119898

119902

119898

= ((

120575119862

119862

)

2

+ (

120575120576

120576

)

2

+ (

2120573

4

1 minus 120573

4

)

2

(

120575119863

119863

)

2

+(

2

1 minus 120573

4

)

2

(

120575119889

119889

)

2

+

1

4

(

120575Δ119901

Δ119901

)

2

+

1

4

(

120575120588

1

120588

1

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus

119863

254

) (29)



+05 (30)




120590

119863=

005 times 119889

119894

times 2

radic3

= 005 times 119889

119894

times 115 (31)



(

Δ120588

120588

) = [(

Δ120588

120588

)

2

119905119890

+ (

Δ120588

120588

)

2

119891

]

12

(32)


(

Δ120588

120588

)

119905119890

=

119905119890

120588

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

120597120588

120597119905119890

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ119905119890

119905119890

(33)







experience values












5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References


















5 Conclusions




References
































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References







































Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References






























Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














Fuel rod


ZrH layer

11 cm

255 cm

Blanket assembly








06Ti-07Y2O3725 gcm3















Inner 611 760Outer 742 718








25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References
















25mm

1822

mm1 2

222

2 23

33

3

3 3

4

44

4

4 4

5 6 7 8

56

78

9

9

56

78

56789

9

56

78

9

56

78

9



information



Run MCNP CE

Update burnup step



Yes

No


sections


module

RunMCNP MG

Powerdistribution



Refuelingfinished


Yes

Yes

No

No

MCBurn MCCBurn





06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














06

07

08

09

1

11

12

13

14

15

kin

f(D

M=03

gcc

)

0 20000 40000 60000 80000

Burnup (MWDtU)

minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

err (

)



0

0005

001

0015

002

0025

003

Flux

1E minus 09 00000001 000001 0001 01 10 1000

Energy (MeV)


PWRSFR










0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

1

105

11

115

12

125

kin

f

minus60

minus40

minus20

0

20

40

CVR

(pcm

vo

id)

08

09

1

11

12

13

14

CR

08

09

1

11

12

13

FIR




0 20000 40000 60000 80000 100000

Burnup (MWDtU)0

0

20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

09

095

1

105

11

115

12

125

kin

f

07

08

09

1

11

CR

minus80

minus60

minus40

minus20

20

40

60

80

CVR

(pcm

vo

id)

08

085

09

095

1

105

FIR







0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)

08

09

1

11

12

kin

f

minus120

minus100

minus80

minus60

minus40

minus20

0

20

CVR

(pcm

vo

id)

08

1

12

14

16

CR

09

1

11

12

13

14

FIR






0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

0 20000 40000 60000 80000 100000

Burnup (MWDtU)0 20000 40000 60000 80000 100000

Burnup (MWDtU)

095

1

105

11

115

kin

f

075

08

085

09

095

1

105

CR

minus300

minus250

minus200

minus150

minus100

minus50

0

CVR

(pcm

vo

id)

065

075

085

095

105

FIR







52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














52

1010

40

20

20

3050

6030

71

62

80

81

11

51

22

91

102

70

21

72

90

92

31

41

32

100

101

103

71

61

12

110

82

93

62

42

120

111

123

80

121

122

113

81

11283

83


52

1010

40

20

20

3050

6030

71

62

81

83

11

51

22

91

93

70

21

72

80

82

31

41

32

90

92

94

71

61

12

100

111

84

62

42

110

102

114

81

101

112

104

83

103113

113



0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff



0 100 200 300 400 500 600

EFPD

1

11

12

13

14

15

16

PPF

C7simC12 average

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle

0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)










0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References
















0 5000 10000 15000 20000 25000 30000

Burnup (MWDtU)

0

102

104

106

108

keff

0 100 200 300 400 500 600

EFPD

C7simC12 average

0

12

14

16

18

2

22

PPF

0 2 4 6 8 10 12 14

Cycle0 2 4 6 8 10 12 14

Cycle


0

20000

40000

60000

80000

Burn

up (M

Wd

tHM

)

0

20000

40000

60000

100000

80000

Burn

up (M

Wd

tHM

)







4 Conclusion





Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References
















Acknowledgments


References
























1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References





















1 Introduction






R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator




Recir-culationpump

Emergency pump


Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-po

wer

Active channel










119864119868

120597

4

119906

120597119911

4

+ 120578119868

120597

5

119906

120597119905120597119911

4

+ 119898

119886119880

2120597

2

119906

120597119911

2

minus 120574119879

0

120597

2

119906

120597119911

2

minus

1

2

119862

119879

119898

119886119880

2

119863

[(1 minus

1

2

120574) 119897 minus 119911]

120597

2

119906

120597119911

2

minus

1

2

(1 minus 120574)119862

1015840

119879

119898

119886119880

2120597

2

119906

120597119911

2

+ 2119898

119886119880

120597

2

119906

120597119911120597119905

+

1

2

119862

119873

119898

119886119880

2

119863

120597119906

120597119911

+

1

2

119862

119873

119898

119886119880

119863

120597119906

120597119905

+ 119862

119881

120597119906

120597119905

+ (119898 + 119898

119886)

120597

2

119906

120597119905

2

= 119892 (119909 119905)

(1)




119862

1015840

119879






y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References
















y

zU

l

c1 c2

k2k1



119873and

defined as

119862

119873= 119862

119879=

4119862

119891

120587119862

119898

(2)


119898is



119896

1119906 + 119864119868

120597

3

119906

120597119911

3

= 0 119888

1

120597119906

120597119911

minus 119864119868

120597

2

119906

120597119911

2

= 0(3)

and for 119911 = 119897

119896

2119906 minus 119864119868

120597

3

119906

120597119911

3

= 0 119888

2

120597119906

120597119911

+ 119864119868

120597

2

119906

120597119911

2

= 0(4)


1and

119888





Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection








A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm


Hole Clearance

Fuel rod

(a)

Spacer

(b)








1is the same as the






119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )


119910 = 072582119909 minus 1790196 (5)




119910

1= 072582119909

1minus 1790196 (6)



119910

2= 072582119909

2minus 1790196 (7)


119910

2minus 119910

1= 072582 (119909

2minus 119909

1) (8)



Δ119909 and (1199102minus119910



Δ119910 = 072582 sdot Δ119909 (9)


Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d998400

2

d998400

1

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )


350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)










1


2





119865 prop 120588 sdot 119881

2 (10)

119865 prop 120588 sdot (

119876

119904

)

2

(11)



Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














Position 1

Position 2

X

Y

d2d1

SensorO


d998400

2d998400

1

Sensor


=

119889

1015840

2

3m

m

3mm

05

mm



Displacement of the

Displacement

Correctionmodule

sensor





Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)











0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References

















0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h





0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h


0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)




0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














0 5 10 15 20 25Frequency (Hz)


30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)


0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)







0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)






20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05





Left Right

Spacer

Fuel rod

V



5 Conclusions








References














Left Right

Spacer

Fuel rod

V



5 Conclusions








References













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