_ _ _ _ _ _ _ _ _ _ . VM EGG-CAAD-5433 June 1981 AN EVALUATION OF THE CAPABILITIES OF RELAP4/M006, i RELAP4/ MOD 7, RELAP5/ MOD"0" AND TRAC-PlA TO CALCULATE THE THERMAL-HYDRAULIC BEHAVIOR OF REACTOR SAFETY / RELIEF VALVE SYSTEMS f''K f' b " ,ec1nica : ,g[[[jf[D ' N RC Researca anc, .. . l's. J.F. J. R. Larson * 38 Assistance Report - D @ =1- & s v * U.S. Department of Energy Idaho Operations Office = idaho National Engineering Laboratory r i N '- t fj ' ~ .[l %f ; g 4 I N ' I . a m s' u. . . e P 8' ] a g q " " " " " . " " " " " ' - - - xt, 3r .L . ;: |m a , - - - . - - - -h % M. E , mm n seenmiser tM A's_:.s , ' bbs=s y s w n n% ..:,:gy;-gtmf ,'~, m__ _, d =~~7 :^ 7 =s v '. M & -m ._ ~- - , m _.t .e, . , - ---m. . ,; Q. . .~_ ',}~+= 9;- - ,-. u ;.. ._ g . . . , g - - - % - .m..p ; ~. _ '& * ' - This is an informal report intended for use as a preliminary or working document g Prepared for the U.S. Nuclear Regulatory Commission ; T Under DOE Contract No. DE-AC07-76ID01570 FIN No. A6356 U ' EGnG ,a,n. 8108280471 810630 PDR RES "' " * #7' "" I - - - - - - - - - - - - - -
Transcript
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VMEGG-CAAD-5433
June 1981
AN EVALUATION OF THE CAPABILITIES OF RELAP4/M006,
i RELAP4/ MOD 7, RELAP5/ MOD"0" AND TRAC-PlA TO CALCULATE
THE THERMAL-HYDRAULIC BEHAVIOR OF REACTOR SAFETY / RELIEF
VALVE SYSTEMS
f''K f'b"
,ec1nica : ,g[[[jf[D'
N RC Researca anc,.. .
l's. J.F.J. R. Larson
* 38Assistance Report -D @ =1-& s
v*
U.S. Department of EnergyIdaho Operations Office = idaho National Engineering Laboratory
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-h % M. E , mm n seenmiser tM A's_:.s ,'
bbs=s y s w n n% ..:,:gy;-gtmf ,'~, m__ _, d =~~7 :^ 7 =s v r~ W .g-'. M& -m._
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,; Q. . .~_ ',}~+= 9;-.
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This is an informal report intended for use as a preliminary or working documentg
Prepared for theU.S. Nuclear Regulatory Commission;
T Under DOE Contract No. DE-AC07-76ID01570FIN No. A6356
U 'EGnG ,a,n.
8108280471 810630PDR RES"' " * #7' ""I
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__
hEGcG....xOIf.',,'% *jV INTERIM REPORT'
Accession No.
Report No. EGG-CAAD-5483e
Contract Program or Project Title: Code Assessment and Applications Division
Subject of this Document: An Evaluation of the Capabilities of RELAR4/M006, RELAP4/ MOD 7,RELAPS/ MOD"0" and TRAC-PlA to Calculate the Thermal-HydraulicBehavior of Reactor Safety / Relief Valve Systems
Type of Document: Technical Report
1=
Author (s): J. R. Larsen g{C 80
8 Date of Document: June 1981
a
Responsible NRC Individual and NRC Office or Division: H. Gregg, NRC-RSR
This documert was prepared primarily for preliminary or internal use. it has not receivedfull review and approval. Since there may be substantive changes, this document shouldnot be considered final.
EG&G Idaho, Inc.Idaho Falls, Idaho 83415
Prepared for theU.S. Nuclear Regulatory Commission
a Washington, D.C.'Jnder DOG Contract No. DE-AC07 761D01570
The report evaluates three thermal-hydraulic computer programs with i
respect to their capability to calculate the behavior of a BWR and PWRsafety / relief valve system when challenged by an overpressure transient. 4
The report describes the facility modeled by the computer programs, themodels, the calculations performed, the calculational results, conclusions,and recommendations concerning application of the programs to safety / relief
valve systems.
The work was performed in support of the NRC Safety / Relief Yalve
Program for which EG4G Idaho acted as a system integrator.
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StH4ARY
! EG8G Idaho, Inc., has the responsibility to recommend computerprograms to the Nuclear Regulatory Comission (NRC) for the calculation ofthe thermal-hydraulic and structural behavior of BWR and PWR safety / relief*
valve systems when the systems are challenged by postulated operationaloverpressure transients. This report describes a qualitative evaluation ofseveral thermal-hydraulic computer programs.
To carry out the evaluation, calculations of the thermal-hydraulicresponses to five postulated fluid conditions were made by three computerprograms used by NRC and by its contractors. The programs existed anf werepublicly available. The programs were RELAP4/ MOD 7, RELAP5/ MOD"0" (an
experimental version), and TRAC-Pl A. The piping system modeled for thesecomparison calculations was a valve test facility being built by Cont >ustionEngineering for the Electric Power Research Insti'ute who is conducting thePWR Owners Group Safety / Relief Yalve Program as required by NURF0 0578.
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The Combustion Engineering system has been designed to represent PWRsafety / relief valve systems. It will test valve and system response at PWRdesign conditions. Calculations were made for five basic fluid conditionspostulated to occur upstream of the valves and to cause their actuation.
| The fiuid conditions were: (a) steady-state saturated liquid,(b) steady-state saturated vapor, (c) transient saturated vapor,(d) transient saturated liquid, and (e) transient saturated vapor changingto saturated liquid. The same valve orifice flow area and a systam backpressure value were used for all calculations. System design pressures
typical of PWRs were used for the steady-state cases. For the transientcases the pressure was based on test conditions proposed for the facility.Pressure ramp rates were imposed on the transient cases to increase thepressure to the valve set point value.
The results of TRAC and RELAP5 calculations appeared reasonable and
The responses calculated by RELAP4/M007 differed significantly from
those cal';dlated by the other two programs. The RELAP4/ MOD 7 calculation
could not be made with a valve opening time less than one second because of .
pressure instability exceeding the thermodymic property table limitsthus, terminating the calculation. Long valve opening times are .
unacceptable since some safety and relief valves can open in40 milliseconds or less.
RELAP4/M006 was initially considered but was disqualified because
static pressure instead of stagnation pressure is used as input to thecritical mass flow correlation.
The capability of the three computer programs to model the operation
of a relief valve was also assessed. RELAP5 was the only program which
allowed multipic trip logic to be used on the saw component. Thiscapability permitted valve cycling to be modeled based on valve pressure
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set points. Valve operation was modeled with TRAC-PI A by using a pressure'
trip to open the valve. To close the valve, the calculation was halted at
the appropriate pressure and the trip was reset. Yalve operation was
mode 17d with RELAP4 by inserting a second valve at the junction downstreamof the relief valve. The relief valve w&s opened at a high pressure trip
set point. The flow was terminated by closing the downstream valve at the
reseat pressure trip set point. The inability to recycle the valve was themain deficiency in TRAC-P1 A and RELAP4 for valve modeling.
Based on the evaluation performed, it was reccmmended that RELAPS be
considered further. Since TRAC-PlA has been superseded by TRAC-PD2,
TRAC-PD2 should receive further evaluation. The versions of RELAP4 are notrecommended for calculations involving a safety / relief valve system.
This study has helped identify a number of concerns regarding thecapability of thermal-hydraulic computer programs to predict the flow rateand structural forcing functions of safety / relief valve systems. These ,
concern', include the capability to track pressure wave propagation,modeling air or water vapor in piping downstream of the valve, modeling the .
relief tank at the discharge piping exit, prediction'of flow choking,
O tracking a discrete liquid-vapor interface, piping wall heat transfer, andthe form of the forcing *metion.4
Additional exercising of the computer programs is outlined and*
recommended in this report to resolve these concerns. The proposed effortincludes modeling the Combustion Engineering loop seal test configuration,additional analytical studies and comparison with West German (Heiss DampfReaktor facility) and Combustion Engineering test data.
This report presents and sumarizes the work of several people ,
involved in the task. Calculations were performed by H. H. Nielson,S. T. Polkinghorn and J. C. Watkins under the technical direction of -
D. G. Hall . Figure preparation and report typing were performed byD. L. Terry and J. M. Mosher respectively. Programatic and technicalreviews were performed by J. A. Hunter and A. C. Peterson.
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CONTENTS i,
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i e ABSTRACT .......................................... .................. ii II
51. Cebustion Engineering short vertical inlet configuration ... ... .,
2. Fluid transient conditions for typical safety and relief valve6( s team or l i qu i d ) tes ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
avii
103. RELAP4/ MOD 7 model nodali zation and identification . . . . . . . . . . . . . . .
4. RELAP5/M00"0" model nodalization and identification ............. 12
5. TRAC-P1 A model nod ali zati on and identification . . . . . . . . . . . . . . . . . . 13 ,
6. Safety valve area fraction open as a function of time after17initiation of opening ...........................................
.
7. Safety valve area fraction open as a function of time after18initiation of closing ...........................................
8. Pressure distribution in the piping frcm the pressurizer f.o20the piping end for Problem 1 ....................................
9. Pressure distribution in the piping from the pressurizer to23the piping end for Problem 2.....................................
10. Pressure upstream of the safety valve for Problem 324(vapor inlet condition) .........................................
11. Pressure downstream of the safety valve for Problem 325(vapor inlet condition) .........................................
12. Mass flow rate at the safety valve for Problem 326(vapor inlet condition) .........................................
.
13. Pressure upstream of the safety valve for Problem 4(liquid inlet conoition) ........................................ 29
14. Pressure downstream of the safety valve forProblem 4 (liqu'd inlet condition) .............................. 30
15. Mass flow rate at the safety valve for31Problem 4 (li quid inlet cc,di tion) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16. Pressure upstream of the safety valve forProblem 5 (vapor to liquid transition inlet condition) .......... 33
17. Pressure downstream of the valve forProblem 5 (vr.por to liquid transition inlet condition) .......... 34
18. Mass flow rate at the safety valve for35Problem 5 (vapor to liquid transition inlet condition) ..........
TABLE
1. COMPARISON OF MASS FLOW RATES CALCULATED FOR PR0dLEM l AND 2 ,
WITH THE HEM CORREuATION ........................................ 19
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1. INTRODUCTION
EG&G Idaho, Inc., is the system integrator for the Nuclear RegulatoryCommission (NRC) for the Safety / Relief Valve Program developed by theElectric Power Research Institute (EPRI) as requested by the PWR utilities
,
and developed by General Electric for the BWR utilities as required byReference 1. The EPRI and General Electric programs are in response to aNRC request that utilities operating and constructing nuclear power plantsdevelop a program for performance tes ting of sa4ty and relief valves andassociated piping used in overpressure protection systems and to evaluatethe adequacy of the systems to perform as intended. One of the
responsibilities of the system integrator is to evaluate and recommendcomputer programs to the NRC for calculation of the thermal-hydralic andstructural behavior of the safety / relief valve systems. The NRC can thenuse the computer programs to determine if the design values for mass flowrate and for stresses are adequate for particular plant specific systemsunder consideration.
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The basic ground rules guiding the EG&G effort to evaluate
.r thermal-hydraulic and structural computer programs are as follows:
1. Existing computer programs are being evaluated. No new programs
are being developed.
2. Publicly available computer programs are being evaluated. Noinaccessible proprietary programs are being considered.
3. Existing computer programs can be modified as required to achieveaccurate models of safety / relief valve systems.
4. The thermal-hydraulic and structure computer programs will bedecoupled.
5. A mechanistic valve model is not being developed.*
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6. The final computer program package will possess the capability toperform an American Society of Mechanical Engineers ( ASME),
Section III analysis.i
As part of the evaluation process, three thermal-hydraulic computer.
programs were used to model a valve test f acility being built by CombustionEngineering (CE) for EPRI.2 The facility is to obtain performance dataon safety / relief valves and piping systems representative of PWRs over arange of anticipated normal, accident, and transient fluid conditions. Themodels were applied to five problems with fluid conditions representativeof conditions proposed for the facility. The purpose of these calculationswas to gain experience about the capabilities and characteristics of theprograms related to safety / relief valve system application. This
preliminary information was used to eliminate several candidate programs,gain additional insight into capabilities needed to calculate systemthermal-hydraulic behavior and provide a basis for further evaluation.This report summarizes the work accomplished during this task.
.
The test configuration modeled is described in Section 2. The
| computer programs considered were RELAP4/M006, RELAP4/M007,4 .
RELAP5/M00"0",5 and TRAC-Pl A.6 They are briefly described along with
tne models applied to the problems in Section 3. These computer programs
were selected because they are in general usage for reactor calculations.
RELAP4/ MOD 6 was initially considered as a candidate program. However,
because of a deficiency in the method used to compute critical mass flow,it was determined that the program was not suitable for the proposedapplication. Specifically the program uses the static pressure insteadof the stagnation pressure as input to the critical mass flow correlation.As a result the safety / relief valve system flow rate and pressuredistribtuion would be distorted. Correcting the mass flow rate byaltecning the tafety valve area would not eliminate the problem as flowchoking would also be expected to occur at the discharge pipe exit. Thedeficiency has beer overcome in previous applications (pipingbreakflow) '
by enlarging the
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upstream ficw area to reduce tho fluid momentum and minimize the differencebetween the two pressures. This technique was riot consicered practical forthe safety / relief valve application.'
The five problems considered were steady-state flow of saturated vapor*
and liquid (designated Problems 1 and 2 respectively) and transient flow ofsaturated vapor, saturated liquid and saturated vapor initially followed byliquid being supplied to the system (designated Problems 3, 4 and 5respectively). A qualitative comparison of the results is found inSection 4. Conclusions and recommendations are found in Section 5. The
reconnendations include the proposed plan for additional code evaluation.
References are found in Section 6.
Tne computer program DAPSY was evaluated separately after thework in this report was acccuplished. The version available to EG&G wasfound to contain coding errors and could not operate with liquid upstreamof the valve. The work is reported separately.10
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Selected results were also used as the hydraulic forcing functiont
input for several structural analysis computer programs. This analysis
provided an evaluation of the capability of the structural codes tocalculate the behavior of the safety / relief valve systems. The structuralanalysis is summarized separately.
The Combustion Engineering Company valve test facility has several .
configurations developed to provide representative conditions for a varietyof PWR systems. The configuration selected for modeling was the short, -
vertical inlet test configuration for safety valves.2 The configurationis shown schematically in Figure 1. The configuration is representative offull size PWR safety / relief valve systems and includes a representative
safety valve and discharge piping. A supply vessel and test initiationvalve in the line connecting the supply vessel to the accumulator are notsh own . The accumulator represents a PWR pressurizer and the supply vesselsiraulates the fluid inventory in the remainder of the PWR system. Thedimensions shown on Figure 1 were based on preliminary facility sketches.
The configuration was designed for tests with liquid, vapor and atransition from vapor to liquid flows. Another configuration to be usedfor testing is a loop seal arrangement.
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A typical transient planned for the safety and relief valve tests isshown in Figure 2. For vapor tests the supply vessel is initially
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pressurized to a higher value than the accumulator. The test initiationvalve is opened and the accumulator pressure increases at the desired rampra te . The increase in accumulator pressure results in the safety / relief
valve opening when the set point is exceeded. The upstream pressure
continues to increase until the valve ha opened sufficiently permitting
enough mass to leave the system so that U e pressure declines. As the
pressure drops to the reseat value the safety / relief valve will close. Theinitial ramp rate, set points and expected peaks vary depending on thesupply vessel pressure, the particular test valve and upstream pipingconfi gura tion. The blmdown period shown in the figure corresponds to the
pressure difference between the valve lift and reseat set points.
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- Test initiation valve.
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Figure 1. Combustion Engineering short vertical inletconfiguration.
Valve closureValve openir.ginitiatedinitiated Time
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Figure 2. Fluid transient conditions for typical safety andrelief valve (steam or liquid) tests.
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3. MODEL DESCRIPTION
b,V Many computer programs have been developed to treat the system
behavior of a reactor during a blowdown. For the application to thesafety / relief valve system only a few of the many capabilities of a,
caputer program are needed. The major phenomena is flow from a high
pressure source to a low pressure environment initiated by valve opening.The rapid opening of the valve causes a transient pressure wave propagationand mass flow distribution. Air initially in the piping downstream of thevalve increases the calculational complexity if the air must be modeledexplicitly. Liquid-vapor interfaces may also be present in the piping.The pressure differences across the pipe are so large that choking canoccur at the valve, other piping flow area changes and at the pipe exit.The effective ficw area through the valve is an unknown because of thecomplex flow path provided by the valve. The determination of systembehavior not only includes solving for the mass flow through the system butperhaps more importantly calculating the pressure and momentumdistributions that combine in a rcsultant hydraulic load applied to the*
O piping system.*h
Calculational models were developed for the facility configurationdiscussed in Section 2. The CE facility is far simplier than a plantsystem which consists of a piping network, several valves and finallypiping dicharging into a relief tank containing subcooled liquid. Thisfacility was used for modeling because it would eventually provide data for
j comparisoa and did contain most of the features of a plant system. Themodels were somewhat different for each computer program to conform withspecific capabilities and requirements and to best represent the particularproblem being modeled. The differences are described later. Nodalizationt
or time step parameter studies were not performed.
Analytically, the valve was treated as a time dependent variablediameter orifice and it was actuated based on the upstream pressure
*exceeding a set value. To treat the valve in a more detailed manner wouldrequire additional knowledge of the valve characteristics and a computer
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program capable of modeling the characteristics. Knowledge of the valvecharacteristics is not currently available and the modeling capability doesnot exist today in the codes evaluated. .
For the transient problems the supply vessel was modeled to provide '
the pressure ramp. When the supply vessel pressb.e equaled the peak
pressure set point the valve connecting the supply nssel to theaccumulator (test initiation valve in Fig'.'re 1) was closed instantaneouslypermitting the blowdown. As the pr essure decreased to the reseat set pointthe safety valve was closed. Shortly thereafter the calculations weretermina ted. The following sections describe the computer programs, model
! nodalization, program options and the initial and boundary conditions forthe problems.
3.1 Computer Program Description
. 3.1.1 RELAP4/M006 and RELAP4/ MOD 71
These are the latest version of the RELAP4 series. The fluid model isbased on a one-dimensional homogeneous equilibrium approximation. Most
changes between the two versions are not significant in modeling the reliefvalve system. One major improvement made in the MOD 7 version which results
in a more accurate calculation than obtained with the MOD 6 version is theuse of the stagnation pressure instead of the static pressure as input tothe critical flow correlation.
3.1. 2 RELAP5/ MOD"0"
RELAP5 is an advanced, one-dimensional computer program for analysis
of reactor systems. It is based on a nonhomogeneous, nonequilibrium
hydrodynamic fluid model . The fluid is described by a continuity andmomentum equation for each phase and a mixture energy equation. Choked
flow is calculated by a correlation. Correlations for wall friction, form ,
losses, interphase friction and mass transfer and wall heat transfer to themixture are also included. A valve model capable of repetitive cycling is ,
included. Air in the piping is also treated thermodynamically. The !
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numerical solution technique is semi-implict. RELAPS has the simplest
fluid model of the advanced codes.
3.1. 3 TRAC-P1A*
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TRAC-P1 A is an advanced best estimate computer program for reactor
system analysis. The model for piping type components ie based on one
l' hydrodynamic model consists of a vapor and mixture continuity equation, a
| mixture momentum equation and energy equations for the vapor and mixture.
Additionally, wall friction, form losses, interphase friction, masstransfer and heat transfer, and wall heat transfer to each phase are
included. A drift flux correlation relates the phasic velocities. Cycling
of the valve is not possible without restarting the program after changing,
| the trip logic. Choked flow is computed within the equation set. Air inthe pipe cannot be treated. The numerical solution technique issemi-implicit except where high velocities are encountered when a fullyimplicit technique is available for cpolication.*
A
U 3.2 Nodalizationr
This section presents the nodalization applied to each program todescribe the system. The nodalization was nearly the same for allprograms. However, some differences were necessary because of particular
program characteristics and differences in the problems. The nodalization
selected was based on engineering judgement. Sensitivity studies were notconducted to determine the nuntier of nodes needed to obtain convergence.The dimensions assumed for all models are those shown in Figure 1.
3. 2.1 RELAP4/ MOD 7
Figure 3 shows the nodalization scheme for the RELAP4/ MOD 7 program.The model consisted of 23 volumes and junctions and 3 valves. The supply
&vessel was volume 23 which was modeled as a time dependent volume to
Tee turned gSupply vessel(time dependent volume) sideways
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Figure 3. RELAP4/ MOD 7 model nodalization and identification.'
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provide the pressure ramp rate shown in Figure 2. The accumulator was
volume 1. Junction 23 represented the valve in the line connecting the twoV vessels which closed instantaneously when the peak pressure was reached.
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The vessels were initially filled with liquid or vapor depending on problemrequirements. A vapor volume was included in the accumulator for-
Problem 5. The safety valve was at junction 3. An additional valve was
placed at junction 4. This valve provided the means to close the flow pathwhen the pressure in the piping decreased to the reseat pressure setpoint.The horizontal tee at the exit was represented by volume 21. It is turnedin the figure for clarity. Volume 22 reprcsented the atmosphere to which
the tee discharged through junctions 21 and 22.
3.2.2 RELAPS/ MOD"0"
The nodalization for RELAPS is shown in Figure 4. The model consisted
of two pipe can'j anents (located before and after the relief valve), twovalve components, three single volume components (pressurizer and pipingdownstream of the branch), three time dependent volumes (atmosphere and*
b supply vessel), one branch component (tee at piping end where nultipleV junctions were necessary), and four single junctions. The supply vessel
and test initiation valve were deleted for the steady-state problems. ForProblem 5 the pressurizer was divided into 10 volumes with the top volumebeing filled with vapor and the remainder of the volumes liquid filled toprovide the desired vapor to liquid transition. Multiple trip logic wasapplied to the safety valve to open it at the high pressure setpoint and
jclose it at the reseat pressure setpoint. The tee at the piping end wasmodeled with three junction flow paths between the branch and two single
vol umes. Deletion of the junction designated 800 would have eliminated
any potential for flow circulation. However, no flow was observed in the
cal cula tions. Two volumes were necessary to represent the atmosphere.
3.2.3 TRAC-P1A
.
The model for the TRAC-P1 A program is shown in Figure 5. The model
consisted of 2 YALVE components and 2 BREAK components. One VALVE,
Figure 4 RELAPS/M0D"0" model nodalization and identification.
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23 24 25 26 27VALVE components _ g End break -
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Figure 5. TRAC-PlA model nodalization and identification,
component represented the prr qsurizer, supply vessel and connecting valve.For Problem 5 the supply vessel was divided into 2 equal cells and thepressurizer was divided into P .. .is with the top two cells initially vapor s
filled. The other VALVE comporant represented the piping and safety
val ve . A BREAK component was used to provide the pressure ramp in the .
supply vessel and to maintain the atmospheric pressure at the pipe exit.The minimum flow area of the safety valve was modeled as a
converging-diverging nozzle, a technique recommended to avoidinstability.Also as recommended the noding at the break was divided intofiner spacing to achie,e a better calculated value for the break flowrate. Hwever, the noding at the safety valve and break were not optimizedto obtain a converged solution for the mass flm rate as also recommended.
Multiple trip logic does not exist in the program so the calculation wasrestarted with the safety valve closed at the lw pressure setpoint. Thetee was not modeled explicitly; only the actual exit area was simulated.Application of the TEE cmponent could have provided the saae exit geometryas modeled with RELAP4 and RELAP5.
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3.3 Code Options
This section presents the options selected for each program. Thedefault or built in options were used except as noted belm.
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3. 3.1 RELAP4/ MOD 7
| The HEM critical flow model was used with a nultiplier of 1.
Additional pressure loss coefficients were applied to the pipingelbows (0.23 at junctions 2, 7 and 17) and the tee (0.48 at junction 20),and at the valve (1.5 at junction 3).
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3.3.2 RELAP5/ MOD"0"
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Additional pressure loss coefficients were applied to the pipingelbows (0.23 at junctions 304 and 314) and to each leg of the tee (0.9 at
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junctions 402 and 403).
3.3.3 TRAC-P1A.
The semi-implicit numerial technique was used for the VALM component-
representing the two vessels. The fully implicit technique we.3 used in theVALVE component representing the safety valve and break.
Additional pressure loss coefficients were applied at the pressurevessel to piping junction (0.49 at junction 3 of the first VALVEcmponent), safety valve (1.5 at junction 6 of the second VALVE component),elbows (0.23 at junctions 13 and 21 of the second VALVE component), and the
tee (1.42 at junction 27 of the second VALVE component).
3.4 Initial and Boundary Conditions
The initial and boundary conditions for the 5 problems are listedbel ow. Problems 1 and 2 were steady-state problems, whereas', Problems 3, 4"
and 5 were similar to the blowdown shown in Figure 2. The downstream
*U piping fluid was assumed to be water vapor in the transient problems. Thepressure ramp rate was applied to the supply vessel .
Problem 1: Steady state flow with saturated vapor in the accumulatorAccumulator pressure--18.28 MPa (2650 psia)
Atmospheric pressure--0.689 MPa (100 nsia)
Problem 2: Steady state flow with saturated liquid in the accumulatorAccumulator pressure--18.28 MPa (2650 psia)
Atmospheric pressure--0.689 MPa (100 psia)
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Problem 3: Biadown with initially saturated vapor upstream of thesafety valveInitial upstream pressure--16.55 MPa (2400 psia) ,
Problem 4: Blowdown with initially saturated liquid upstream of thesafety valvePressure ramp rate--0.689 MPa/s (100 psi /sec)
Other conditions as listed for Problem 3.
Problem 5: Blowdown with initially saturated vapor enterine the pipingchanging to liquidInitial vapor volume in accumulator
33 (2.51 ft ) for RELAP5/ MOD"0" '--0.071 m33 (6.57 ft ) for TRAC-Pl A--0.186 m
'
Pressure ramp rate--1.72 MPa/s (250 psi /sec)
| Other conditions as listed for Problem 3.
The opening rates of the safety valve and the closing rates of eitherthe safety valve or lcw pres;ure trip valve used in the RELAP4 studier areshown in Figures 6 and 7 respectively. The differences are partially dueto user option and also due to calculational difficulties. Thedifficulties with the RELAP4 calculations were that severe instability
occurred resul ting in fluid conditions exceeding the thermodynamic property
| table limits when faster opening rates were applied. Similar problemsexisted with TRAC calculations, requiring the valve initial opening rate to
;
be more gradual than the linear rate specified for RELAPS.
Figure 7. Safety valve area fraction open as a function oftime after initiation of closing.
.
S 9 ) b
- _ _ _ _ _ _ _ _ _
4. COMPARISON OF RESULTS
This section presents a few selected results for the steady-state and-
transient problems. Only one RELAP4/ MOD 7 calculation was performed
(Problem 3) because of resource limitations.*
4.1 Steady-State Results
Significant differences occurred between the calculated mass flowrates and pressure distributions during the steady-state runs. The
cause(s) of these differences was not identified or corrected prior tomaking the transient calculations. The mass flow rate calculated by tha
computer programs is shown in Table 1.
TABLE 1. COMPARISON OF MASS FLOW RATES CALCULATED FOR PROBLEM 1 AND 2WITH THE HEM CORRELATION
,
Computer Problem 1 Problem 2'a
Program (kg/s) (kg/s)
*b' RELAPS/ MOD"0" l'0 156
TRAC-P1A 63 134
bHEM CORRELATION 82 1 32
a. RELAP4/ MOD 7 calculations were not performed.
b. Based on safety valve fim area and accumulator fluid conditions.
The pressure distribution in the piping for Problem 1 is shown inFigure 8.
RELAP5 calculated flow choking or critical flow at junction 401, theinlet to the branch conponent, and the two junctions, 600 and 1000,representing the piping ends where discharge to the atmosphere occurred*
t tts n swioD ir+ 0 ' o d deh e zsi a eit b rr+ 0 '
L ( uussssee+ 0 '
rrPp
+ 0 '
.
8
e e+ 0 i
v ri ua g
v + O 0 iLty i
r Fo0 =O ag' i l
ut ma uo c .rg h
i cA
T
- - --
O.O
0 5 0 5 02 1 1
* E e5:* .c
8
|1
m
-_ - -.
(Figure 4). Critical flow was not computed at the valve. RELAPS/M00"0"
had an acknowledged problem at high void fraction where the critical flowmodel was calculating mass flow rates that were too large. Thisdiscrepancy was illustrated by the results shown in Table 1.
P
Supersonic flow is not permitted downstream of an orifice in RELAPS(or RELAP4), thus a subsonic condition was assumed downstream of the
valve. (Supersonic flow is considered likely downstream of the valve until'
oblique shocks and wall friction force a return to subsonic flow.) Thepressure downstream of the valve depends on the atmospheric pressure, the
pressure drop across the piping ex -t, and the pressure drop related to massflow rate and wall friction. The downstream pressure is thereforeuncoupled from the upstream conditions if choking at the valve occurs.
.
TRAC-PlA output does not indicate when critical flow is calculated.I However, on the basis of the pressure and vt icity distribution it appears
that critical flow was calculated at the safety v61ve and the piping end.Supersonic flow was calculated in the downstream portion of the nozzle with,
p the Mach number reaching about 2. In the diverging sectic, of the nozzle
i the velocity dropped back to a subsonic condition with tSe Mach number naar
0.5. The pressure recovery after the nozzle throat with TRAC-PlA wascalculated inherently and must be consistent with the pressure drop
;
! throughout the downstream piping. The TRAC-P1A calculation is thus abetter approximation to expected physical behavior immediately downstreamof the valve than the RELAP5 results. However, distortion in thecalculation was caused by numerical truncation and numerical diffusion
because of the finite element structure of the code. Incorporation of a
finer mesh spacing in the TRAC model likely would have resulted in anincreased mass flow rate, better correspondence with the HEM value, ahigher throat pressure and with more pressure recovery downstream of thevalve.
Figure 9 shows the calculcted pressure distribution along the pipingfor Problem 2. The calculations for diverging portions of the nozzle in
the TRAC-Pl A model again indicated sup.1 sonic flow. At the junction,
between the nozzle and the dcwnstream piping the flow " shocked" back to asubsonic condi tion. The diverging portion of the nozzle representing the ,
safety valve in the TRAC-P1 A model seemed to promote slip between the
phases. The slip ratio calculated by TRAC-Pl A in the downstream streampiping was about 1.85 while for the RELAP5 calculation it was close tounity. (Upstream of the valve the slip ratio was unity for RELAP5 andabout 1.1 for TRAC.) The down stream void fractions were approximately the
same (0.95) for both calculatiens. For this problem, RELAPS calculatedcritical flw at the safety valve as well as at the 3 locations fr: thetee. Modeling the exit tee with a single break opening with TRACapparently had a minor effect on the pressure distribution immediatelyupstream of the break when compared to RELAPS results as shown in
Figure 9. The correspondence between the TRAC and RELAP5 results was much
better than for Problem 1 as indicated by the mass flow rates shown inTable 1 and the pressure distribution shown in Figure 9. The RELAPS mass s
flow rate was still larger than what would be expected based on the HEM'correlation however.
4.2 Transient Resul ts
The resul ts of the RELAP4/M007, RELAPS/MCD"0" and TRAC-Pl A computer,
|programs for Problem 3 are show in Figures 10,11 and 12. Figure 10 shows
j the system pressure in the volume just upstream of the safety valve,Figure 11 shows the pressure in the volume just downstream of the safety
| valve and Figure 12 shows the mass flow rate through the valve.
The RELAP4/ MOD 7 calculated pressure upstream of the safety valve
(pressure of volume 3 shown in Figure 10) reached the pressure setpointfirst (0.41 s for MOD 7, 0.52 s for others) although the value for the tripwas the same for each code. With the opening of the safety va;ve, the M007
*calculation indicated upstream pressure oscillat. ions although the valve
O'22
,... - - ---- ,-.-_- - - - _-__ . ---
. . < s - '
f6 @ 0
.20 -
8 d)
+ RELAP/ MOD"0"Oi O TRAC-PlA
15 -
^
E-
3* 10 -
aEro
" I 4+ + + + +5 - O
+ + + + + + g.b-@O O C OThroat O O
+.
*OO t ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '
A---Val ve LElbow Elbow dAccumuhtor. Distance along the pipin9.i Atmosphere~
(based on RELAP4 volume cell spacing)
Figure 9. Pressure distribution in the piping from thepressurizer to the piping end for Problem 2.
:.
+
*
;'
o..
0.
4n
n
2 n
de 5 r
"0s .
o o3 f7 l e"D D f c~
OO f 2 ei
AMM o e n vl // vPS4 t l l
nPP u a 8 a .CAA h v v).
ALL sREE y 3 nTRR 2 t
f n yol d
i tie e es f ets1 23 s a no fie S adl i
c 5v - isr. .oy 2 e 2 ecl v i
p 3 l ha )p a ttsu v e. . (S
N Am fl .s 0 e on3 a me i eir 2 T mu3 t e arsn eoi.
\ m% gi w rpeo ta
D\ 5 sve
'p(,
.
N' ) u1i 3
k e
D'5 e rms
- n uei
f - e sls
,, - kU s 7,or ip 0 sb
eo.
DO e 1 rr
i
M v PP'
/l a
4 a
#'aP vr .
A 0i
L y 5E,t 1
.
R e| 9 ef i
- .i a r- S i
ua g
in
- - ~ 0 F-
,- - - ' ~* -
~.__ 5 j5 0 5 8
-_ _ -.
0 05
8 8 7 7 6 6 51 1 1 1 1 1 1
_2c- e u : $ c.=
.
e.m*
)l| || ' |||||
( _ _ _ _ _ _ _ _ - _ _ _ _ _ _ __.
. . . s - ~
hJ -
t
20i
'
l TRAC-PlA_
2 RELAP5/h0D"0",
'~
2 3 3 RELAP4/M007^
,
15 -
a x-
Downstream valve closed-
E -
5 a-
-.
5 10Supply vessel isolatedm
.
$ /-s a -, -a. -y ~
_
j , Safety valve completely_
- openy5m - x
\~
~ '
1 ' Safety valve closedi:
J -
. , e u e , -,
0 i e n i i i r i y ni e' ' iJt n-
9 1 2 3. 4
Time (s)
Figure 11. Pressure downstream of the safety valve forProblem 3 (vapor inlet ccndition).
________ _ _ _ _ _ _ -_ _ _ _ _ _
140-
t ?> , Supply vessel120 ..
h shut off*
I-
100 -safety valve closed_
0 -
E 80 s,: HEM calculation>rs ,-
- Downstream valve closed32 .
|* *
50 -' '^
N 1 TRAC-PlAk 2 RELAP5/ MOD"0"2 -
{ 4g \ 3 RELAP4/ MOD 7 _
[ l: -
/ -safety valve closedE 20m
cw
g | !! 7 2': 3;32 2 2 2
'''' ' ' '' '''' '''' '''' '''' '''' ''''-20
O.8 S.5 1.8 1.5 2.0 2.5 3.0 3.5 4.8
Time (s)
Figure 12. Mass flow rate at the safety valve for Problem3 (vapor inlet condition).
O. . O. . O. .
L
opening time was set to be 1 s. The code calculation became unstable andterminated with shorter valve opening times. The printed results indicated'
that the code was apparently using the input maximum of 5 msec for time.
step size during the oscillatf ons from 0.4 to 0.9 seconds, that is, thecode time step control did not force a smaller time step which may have-
smoothed the oscillations.
The pressure upstream of the safety valve increased until the pressurein the accumulator reached the set point of the valve connecting the supplyvessel and the accumulator (junction 23 in Figure 3). With the supplyvessel isolated the upstream pressure decreased rapidly until the reseatset point was reached instanteously tripping the downstream valve closed.The slow pressure increase downstream of the safety valve (volume 4) isshown in Figure 11. The increase corresponded to the slow valve openingtime shown in Fig 9re 6. The mass flow rate through the safety valve (seeFigure 12) also increased slowly corresponding to the increase in safetyvalve open fitw area. The mtss flow was tenninated by closure of the
# downstream valve. Flow choking was indicated at the valve (junction 3)while it was open. Choking was indicated also at the tee entrance,
_
(junction 20) and the two exits (junctions 21 and 22) from sometime between
0.75 and 1.0 seconds until the downstream valve closed.
Frca the shape af the mass flow rate and the large pressure differenceacross the safety valve (Figure 10 compared to Figure 11) it is postulatedthat the chcking at the safety valve contrc31ed the system mass flow rate.
The RELAP5 and TRAC-P1 A calculations were generally similar and closer
to expected behavior than those for RELAP4/ MOD 7. The safety valve opened
: at the same time for both codes. The upstream pressure calculated byRELAP5 (volume 101 of Figure 4) dropped more sharply than calculated by
TRAC-P1 A (volume 2 of Figure 5). This more rapid drop in pressure was theresult of a more rapid safety valve opening rate in RELAPS and a largermass leaving the upstream volume through the valve compared to TRAC-P1 A.
$
The higher mass flow rate (see figure 12) and downstream pressure (see
.
'
27
L. _ _ - _ . - _ . _ _ _. _ _ __
f
Figure 11) calculated by PELAPS was consistent with the results determinedfor Problem 1. That is choking was not calculated to oc:ur at the safetyvalve, and the mass flow was higher and pressure drop was less across thevalve than calculated by TRAC. With the valve completely open at .
0.6 seconds the flow rate reached a maximum and the upstream pressure'
increased at the ramp rate value. The supply vessel was isolated at aboutl.25 seconds which caused the upstream pressure to sharply decrease
(Figure 10) and the valve flow rate to decline (Figure 12). The safetyvalve closed when the upstream pressure reached the reseat set point at
about 1.5 seconds.
To check the program calculated mass flow rates for Problem 3, a handcalculation performed using the HEM correlation calculated a value of about80 kg/s for the time interval around 1 second.
Selected results for Problem 4 are shown in Figures 13, 14 and 15.
The pressure in the volume upstream of the safety valve is shown inFigure 13, the pressure in the volume downstream of the valve is shown in
'
Figure 14 and the mass flow rate through the valve is shown in Figure 15.Calculations for RELAP5/M00'0" and TRAC-PIA are shown. ,
The general hydraulic rerponse to Salve actuation shown by the plots| was similar to that of Problem 3 and is not described in total. The
pressure ramp rate was half of Problem 3 so the safety valve was actuatedat 0.99 s for RELAP5, and 1.035 s for TRAC-PlA.
The RELAP5 calculatei mass flow rate responded rapidly as the safety
valve opened (in 100 msec) and resulted in a pressure drop upstream of thevalve. With the valve completely opened the RELAP5 calculated pressurerecovered to the same value as calculated by TRAC-P L' The mass flow rate
through the valve maintained a near steady value until the supply vesselwas isolated. The code controlled time step was about 0.3 msec while the
Figure 15. Mass flow rate at the safety valve forProblem 4 (liquid inlet condition).
The TRAC calculated response was similar to that of RELAPS. The valve
was opened very slowly initially with 90% of the opening occurring in thelast 50 msec. This delayed the increase in downstream pressure ,
(Figure 14). The TRAC and RELAP5 mass flow rates through the valve were
much closer for Problem 4 than for Problem 3. The code controlled time ,
step size was 10 msec in the TRAC calculation while the valve was open.This time step was considerably larger than used in the RELAPS calculation.
Selected results for Problem 5 are shown in Figures 16,17 and 13.The upstream pressure is shown in Figure 16, the downstream pressure isshown in Figure 17 and the valve mass flow rate is shown in Figure 18. The
pressure ramp rate was larger than for the previous problems. Thus, theinitiation time for the opening of the valve was 0.42 s and the elapsedtime for valve opening was 100 msec for both RELAPS and TRAC-Pl A. The
trends are generally the same as shown for Problems 3 and 4.
The transition from single phase vapor flow to liquid or two-phasemixture is readily apparent in Figure 18. This transition is shown by the 4
sharp i'ncrease in the mass flow rate after the valve had opened and the'
flow rate became nearly constant. The mass flow rate for RELAP5 became
essentially constant after liquid reached the valve because the accumulatorwas liquid filled and the upstream quality was zero. For the TRAC-P1A
calculation however the top 2 cells of the accumulator (Figure 5) slmlyfilled with liquid and never became liquid full and the upstream qualityapproached zero resulting in a continued increase in the mass flow rate.This di fference was likely due to the larger vapor volume initially in theTR,,J-P1 A accumulator model and the lower vapor mass flow rate taking longer
j to clear vapor fran the accumulator than for RELAP5.|
The calculated slip ratio between the phases was higher for TRAC-P1 A
! than for RELAP5 (as ncted for Problem 2) although the void fractions were
ncarly equivalent.
#
| The code controlled time step sizes used during the flow period wereslightly larger than 1 msec for TRAC-P1 A, and 0.3 msec for RELAP5/ MOD"0".
O'|
32|
_J
. . _ _ . _ _ . . _ _ _ _ . - - _ _ _ _ . -_
e a s o ~ *
19.0I"
~
l TRAC-PlA
{2 RELAP5/ MOD"0"-~
18'0 '
~
- Supply vessel isolated~
~
.~
7 17.0 ',l.
9: ~. k , n. ., ., ,-
3 LI- ' - ' " - '.
g - , =,
5 :m .
E16.0 g*o. Valve closure:
O 3:
15.0 .~
~
~.,
: -
'' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '''' ''''14.0
9.0 05 1.0 15 2.0 2.5 39Time (s) '
Figure 16. Pressure upstream of the safety valve forProblem 5 (vapor to liquid transition inletcondition).
- _ _ _ _ _ _ _ _ _ _ _ _ _ .. ____
1
!4
| 20.0I
'
. -
| 1 TRAC-PlA i.
2 RELAP5/ MOD"0",
i
1 -
15.0'
| *I
j FJi
-
, =_
| {10.0, -
o'
g -
0 ""w . -. ga. -
'5.0
h D-
: ; <-
-
4 P _l '
^'_ % O S %
' ' ' '''' '' ''''' ' ' ' '***"' '""0.0
9.0 05 1.0 1.5 2.0 2.5 3.0Time (s)
Figure 17. Pressure downstream of the valve for Problem 5(vapor to liquid transition inlet condition).
O. . O. . O. .
C.
_ _ _
, a s o , s
O O~
350 -
,
y,
.
."
300."
Supply vessel isolated
250 Liquid reaches
~ valve l
1 TRAC-PlA-~
2 200 2 RELAP5/fiOD"0"'
/g .
\-
158~
2 :"
100 valve closure __t-
$ :wem .
50. ,. . .
l I,a L0< . s s.. , .
. .. , - - -..
' ' ' ' ' ''' ' ''' '' ' ' ' ' '' ' ' ' '-50,
00 0.5 1.0 15 2.0 2.5 3.9
Time (s)
Figure 18. Mass flow rate at the valve for Problem 5(vapor to liquid transition inlet condition).
|
_ _ - _ _ _ ,
5. CONCLUSIONS AND RECOMMENDATIONS
Based on the qualitative analyses and comparisons shown previously the
following recomendations and conclusions are presented concerning the -
capability of the computer programs evaluated to perform plant-specific'
safety / relief valve calculations.
The RELAP4/M007 program did not perform satisfactorily with valve
opening times of short duration necessary to represent actual valvebehavior. Of less importance RELAP4/M007 lacks multiple valve trip
capability necessary to respond to potential piping pressure fluctuationswhich could cause valve oscillations. (This capability is of lesserimportance as a mechanistic valve model is also necessary to correctlycalculate oscillatory behavior.) RELAP4/M006 was disqualified becausecritical mass flow rates and the piping pressure distribution could not beLorrectly calculated. No further evaluation of RELAP4 is recommended.
RELAP5/M00"0" performed better with liquid flow conditions than withThe code version exercised had an identified problem when computingvapor.
high quality steam flow rates through a sharp contraction. This problem ,
has been corrected with the M001 version. Further evaluation of the M001
version is recommended.
TRAC-P1A handled the calculations in a reasonat'le manner. The codehas several limitations. These are the recommended procedure treating the
isharp area change as a finely noded converging-diverging nozzle, the
arecommended procedure to finely nodalize the piping rupture and the lackof multiple valve trip capability. Since this code has been superseded by
TRAC-PD2, no further evaluation of TRAC-PlA is recommended. TRAC-PD2 is
recommended for further evaluation.
Techniques other than nodalization have been used with TRAC-PD2. ,a.
~
G36
a
None of the computer programs could be expected to correctly calculatethe pressure immediately downstream of a sharp expansion where a supersonic
ficw condition might be expected. '
,
Following the completion of the task described in this report, a*
number of concerns were itemized about the capability of thermal-hydrauliccodes to model the actual physical behavior of a relief valve system andconsequently calculate the correct mass flow rate and hydraulic loading.
l2These have been previously reported and are listed below.
Pressure Wave Propagation: Numerical techniques and finitenodalization tend to smooth waves and change the wave velocity and
magnitude and consequently produce changes in the hydraulic loading.The proper time step and node size may minimize wave distortion.
Downstream Fluid: It is necessary to explicitly model air in thepiping to obtain the correct hydraulic loads? Could a water vapor be
! * used as a substitute if the correct sound velocity were maintained?1
Relief Tank: The piping exit is submerged in subcooled liquid withair filling the remainder of the tank. The piping pressuredistribution and pressure wave reflection at the tank junction will beinfluenced by the tank behavior.
Choking Location: The ficw is expected to choke at the valve andother area changes. Piping elbows are also a possible choking planeloca tion.
Fluid Phase Interface: A discrete liquid-vapor interface will be lostin a finite element code structure.
Wall Heat Transfer: Will condensation reduce hydraulic loads? Wallheat transfer to the gas or vapor will cause a sharpening of a
'pressure wave which could increase downstream loading. If
condensation occurs, the loading will be reduced.
bG.
37
I
_ _.
I
Momentum Equation: Current EG&G techniques used to calculate thehydraulic load neglect the change in mctnentum with time term. This isconservative but may overpredict loudings when valves open over finite ,
time intervals..
To aid in resolution of these items additional exercising of computer
program capabilities was reccnnended with models of the CE loop sealcon fi guration. The programs reconinended for further evaluation were
RELAP5/ MODI and TRAC-BDl. TRAC-PD2 was included initially but was dropped
because of difficulty in getting the code to operate and because ofresource limitations. The fluid conditions considered were similar tothose described in Problems 1 through 4 with additions as follows:
1. Transient b1mdown with subcooled liquid in the loop seal2. Inclusion of a relief tank containing subcooled liquid3. Additional parameters such as air in the downstream piping, vapor in
downstream piping matching sonic velocity of air, saturated liquid inloop seal, piping wall heat transfer and the minimen expected valve *
opening time (10 msec).
(Additional tasks have also been specified to aid the evaluationprocess and are listed belm.
Wave Propagation: A model of a reservoir-pipe configuration filledwith subcooled liquid is to be made. A time step and noding sizestudy will then be conducted to evaluate wave tracking in subcooledliquid.
Plant Specific: A model of a piant-specific system will be developedand calculations with represer.tative conditions will be made.
Hydraulic Forcing Function: The function will be modified to includethe tenn describing the momentum change with respect to time.
,i Data Comparisons: The West German Heiss Damp Reaktor piping system f
; e.ontaining subcooled liquid and a check valve will be modeled and the |
|calculations compared to data. Comparison of pretest and posttest |
| analysis will also be made with CE experiment data. The comparison'
;Lwith data will provide the best evaluation of the program capability
,*
to calculate the mass flow rate and piping pressure distribution.
(4'
i
:!. .
1r
,
i
il
i I
.' '!
::f
i4
I
i
|
1
!
l
|4
4,
| *
)4
!,
39
L.- _ _ _ ,--
_ __ _ _ ____ _ _ _ _ _
6. REFERENCES
1. TMI-2 Lessons Learned Task Force Status Report and Short TermRecomendations, Nuclear Regulator Comn'ission, NUREG-0578, July 1979. s
2. Program Plan for the Performance Testing of PWR Safety and Relief*Valves, Revision 1, Electric Power Research Institute, July 1, 1980.
3. RELAP4/M006--A Computer Program for Transient Tnermal-HydraulicsAnalysis of Nuclear Reactors and Related Systems, User's Manual, EG&GIdaho, Inc., CDAP-IR003, January 1978.
4. G. W. Johnsen, et al., RELAP4/ MOD 7 (Version 2) User's Manual, EG&GIdaho, Inc., CDAP-TR-78-036, August 1978.
5. V. H. Ransom, et al., RELAP5/ MOD"0" Code Description, Volume 1, RELAPSCode Development, EG&G Idaho, Inc., CDAP-TR-057 (Volumn 1), May 1979,
6. TRAC-P1A, An Advanced Best-Estimate Computer Program for PWR LOCAAnalysis, Los Alamos Scientific Laboratory, LA-////-MS, May 19/9.
7. G. W. Johnsen, et al., A Comparison of "Best-Estimate" and " EvaluationModel" LOCA Calculations: The BE/EM Study, EG&G Idaho, Inc.,PG-R-76-009, December 1976.
8. T. Grillenberger, DAPSY--Ein Rechenprogram Fur Druckwellenausbreitung 3Im Reaktorkuh1kreislauf, Technische Universitat Muchen Report,MR'l-P-24, October 1976.
,
9. T. Grillenberger, The Computer Code DAPSY for the Calculation ofPressure Wave Propagation in the Primary Coolant System of Light WaterReactors, Technische Universitat Muchen Report, MlR-I-66, April 1976.
10. R. L. Williamson, Analysis of Relief Valve Transients Using the DAPSYHydrodynamics Code, EG&G Idaho, Inc., RE-A-81-010, March 1981.
11. B. F. Saffell Jr., " Comparison of Codes for Structural Analysis ofSafety / Relief Valve Plant-Specific Systems," letter, EG&G Idaho, Inc.,March 12, 1981.
12. 8. F. Saffell Jr., " Analysis Meeting at Electric Power ResearchInstitute (EPRI) and Valve Test Meeting at WyleLaboratory--Safety / Relief Valve Program," letter, EG&G Idaho, Inc.,March 26, 1981.
