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DOE/PC/88651-T1DE90006270)
MHD COMPRESSOR-EXPANDER CONVERSION SYSTEM INTEGRATED WITH
A GCR INSIDE A DEPLOYABLE REFLECTORProject Final Report
R E P R O D O C E O FA V O P Y
April 20,1989
Work Performed Under Contract No. AC22-88PC88651
ForU. S. Department of EnergyPittsburgh Energy Technology CenterPittsburgh, Pennsylvania
ByANSALDOS.p.A.Genova, Italy
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DISCLAIMER
Portions of this document may be illegible inelectronic image products. Images are producedfrom the best available original document.
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Progettoproiect
NUCLEAR MHO CONVERTERIdentificativoflocuTient no
RD-12-01-FNPR
Rev Paginarev page
1
DOE/PC/88651-T1(DE90006270)
Distribution Category UC-112
6 . Tu n i n e t t i ^
E. Botta, C. Criscuolo. P. Riscossa^^
F. Giammanco* , M. R o s a - C l o t " *
D 0 E / P C / 8 8 6 5 1 ~ T
DE90 006270
Research Division, A N B A L D O SDA
Nuclear Division, AN5Ai_D0 SpA
'Deoartment o-f Pnvsics, University o-f Pisa
Department o-f Pnvsics. University o-f Florence
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NUCLEAR MHD CONVERTER RD-12-01-FNPR l 3
CONTENTS
EXECUTIVE SUMMARY 5
1 INTRODUCTION 6
1.1 Project UDjectives S
1.2 Reoort Organization . . . . . . . . . 9
TaDies ana Figures 10
2 PROJECT DESCRIPTION 11
3 REFLECTOR MODELING 13
3.1 Symoois. Terms ana Abbreviations 13
3.Z Re-ference Core De scription 15
3.3 Analysis Coaes 19
3.4 Fea tur es o-f Fer-formed Cal cul ati ons 21
3.5 Nuclear Cross Section Calculation s 23
3.6 Reactor Calculations 26
3.7 Reactivity Reauirements 27
3.S Re-ferences 30
Tables ana Figures 3Z
4 1
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NUCLEAR MHD CONVERTER RD-12-G:-FNPR i 4
5.2 Channel Characteristics and Conauctivity 73
5.3 Fission and Gamma Density in the Channel 77
5.4 Conductivity Calculations 81
5.5 Re-ferences 91
Tables and Figures 93
6 SUMMARY AND CONCLUSIONS 106
7 REPORT DISTRIBUTION LIST HO
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NUCLEAR MHD CONVERTER aocument no p D _ i2 - 0 1 - F N P R '*' 1 " ^ '
EXELL'~IVE SUMMARY
CONTRACT TITLE AND NUMBER:
M M D Como ressor - Exoanaer Conversion System Integratea with a GCR
Insiae a D eployao ie Re-flector,
DE-AC22-68PC8S651
CONTRACTOR NAME AND ADDRESS:
A N S A L D O S.D.A.
Corso P.M. Perrone, 2516161 Geneva - Italy
START DATE: 4-21-1988
COnnFLETION DATE: 4-20-1989
Tnis work origin ates -from the prooosal M H D ComoressorE;
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N UC L EA R MHD C O NV E RT ER R D - 1 2 - 0 1 - F N P R 1 6
be either uranium heAa-f luoriae or a m ixtu re o-f uranium
hexa-fluoride and helium, aaded to enna nce the heat trans-fer
pro pert ies. The original Stat ement o-f Wor , which concernea the
wnole conversion system, was suD seauently reairected and
focused on the basic mecn anis ms o-f neu tro nic s, react ivit y
cont rol, ionization ana electrical conauctivity in the PCu.
Furtherm ore, tne study was reauirea to oe inherently generic
sucn that the analysis and results can be aooliea to various
nuclear reactor ana/or MnD cnannei Designs .
Soeci-fic goa ls o-f the proj ect were:
- To eva lua te the oer-formance o-f tne e,;ternal re-flector.
- To dete rmine the in-fluence o-f a dai tio nal . -fission-inducea
mech anism s on the ionization levels o-f the working -fluid.
- To estimate the electrical conduct ivity levels that can be
attained in the M HD channe l, t a^lng into accoun t the e-f-fects o-f
F- or other negative ions.
Two major conc lusio ns can be drawn -from the accom oiisn ment o-f
this project:
- A reactor con-figuration has been o o t am ed whicn avoias to
deco uple the neut ron ics o-f the cavity and its internal
re-flector from the external shell, thus enabling t ne latter to
be used -for reactivity control.
In particular the results show that the movable re-flector is able
to make the reactor subcritical by 1000 pcm t least, and to
control th e reactor -from CZP to HFP condit ion , accoun ting -for a
reactivity change up to 3300 pcm associated to depletion.
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P r o g e t t o I d e n t i f i c a t i v o R e v P a g m a
' ^ NUCLEAR M HD CONVERTER ~= ' ' ' RD -12- 01-FN PR ' l '' '
- Tne conditions expected in the M HD channel show that tne
ionizatio n and con duct ivit y levels can be ampli-fied thr oug
'secondary' proces ses induced by the 'primary' hot electron s
which are directly generated by the -fission reactio ns.
The numerical calculation s suggest that conauctivit y levels in
the range 10-100 (ftm) * are consistent with the characteristics
o-f short no zzl e, high power dens ity gen erat ors . In -fact, tne
nozz le lengtn turns out to be o-f critical impo rtance becau se of
the sharp decrease of resiaual fission ana gamma aensities as a
function of tne aistance from tne reactor outlet.
Tnis conclusion remains true even if the effect of aissociation
ana attachment are mcluaea in the numerical moael.
Furtne rmore, a preliminary evaluation of the influence of wall
material and thickne ss snows the potential for tne fission ana
gamma densit ies in the duct to be increased of one order of
magnitude, m comparison with the values used in tne
conductivit y calculat ions, if a material with favourable
nuclear properties is adopted.
7
g
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' ^ " ^ ' NUCLEAR MHD CONVERTER ' ' "" " "" '" RD -12 -01 -FN PR ' 1 ' " ' " i
1 INTRODUCTION
l.i Project Objectiv es
This work concernea an innovati ve concept of nuclea r,
closed-cycle M HD converter for power generation on space-based
systems in the multi-megawatt range. A schematic diagram of the
concept IS shown in Fig. 1.1. The basic element of this converter
is the Power Conversion Unit (PCU) consisting of a gas core
reactor D irectly couoleo to an MHD expansion channel. The working
fluid could D e eitner uranium hexaf luoride or a mi xture of
uranium h exafiuo rioe ana helium, aaoea to enhance the heat
transfer orooerties.
Two major items, both concerning tne PCU, were adaressed in tne
project:
1. Because of the high levels of temoe rature expected m the
reactor cavity, reactivity control is not achievea by neutron
absorbers (control rods) located in the cavity, but by
moving part of the reflector, located outside the pressure
vessel, in order to change the amount of neutrons escaping
from the core.
2. The mere levels of temoerature, however, cannot sustain
levels of ionization and, hence, of conductivity, capable of
providing efficient power generation in the MHD chann el.
Fission products may represent a possible additional source
of ionization.
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NUCLEAR MHD CONVERTER oocument no J , D _ ^ 2 - 0 1 - F N P R '^ ' l ' * y
Tnis reoort aocu ments tne result s of worh aone to investigate
tnese aspects of tne co oo se a conceot. H I O H L - D J aGces seD ootn
Iter i. ana Z. : tne istter reauirea tne Bcienti-ric suDDQ' t a- f tne
unive rsiti es o-r ioren ce ana Fisa. D eoartmenr n-f Fnvsic s.
-I Reoort Organization
Section 3.. Re-riector iloaeiing, illustrat es tne reactor
configur ation, as aefined tnrougnout contract wor^ . cescrioes tne
cooes ana D''oceaure= aaootea in tne anai vsi s. ana oresen ts tne
resu lt s conce rn ing tnp oer-formance of t^e e terna i (T'o 'aDle
ret i ector.
Eection -, . ^or^lnq ^ laio Cna ract eris ticE . i-vestigates tne
f 1 ssion-incucea ionization mecnanisms acting i tne w c M n g gas.
and oroviaes a svstem of simoiifieo rate eauations for numerical
solution.
Section 5., Electrical Conauctivity Effe cts, adaresses tne stuav
of tne electrical conauc tivity levels in tne Mt-iD cha nne l, ana
presents the results of numerical estimates oerformea with
different gas ano ouct parameters.
References, Taoles ana Figures are located at tne ena of each
section.
n*
i
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00123
RE6. HX PCU
* ' R A D
I I 1 I I 1 II I I I I I I
R = REACTOR
HH D = HMD CHANNELREG.HX = REGhNER ATlVE HEAT EXCHANGEDHX = HEAT EXCHANGER
f
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^^' NUCLEAR MHD CONVERTER " ' ' " '" * " '" RD -12 -01- FN PR '*" 1 '11
2 PROJECT DESCRIPTION
This section is based on the contents of paragraph 4.2 in the
Statement of Work.
The work is divided into four tasks.
Task 1. Reflector Moaelino
Tnis task shall provide the nuclear anaivsis of the conce ot,
performed on a reference PCu geometry , using develooea ana ooen
comouter coaes availaole at A N S H L D O .
The reflector moaeling shall aadress the following items:
- Reflector reactivity worth.
- Power density distribution insioe the PCU, at constant core
power level.
Task 2. Working Fluid Characteristics
This task shall provide an analytical model enaoling the
prediction of the temoerature distribution and ionization levels
of the working fluid in tne PCU.
Since the equilibrium thermal ionization is not expected to
maintain sufficient electrical conductivity for efficient power
generati on, this task shall investigate additional ionization
mechanisms that can be present in a fissioning plasma.
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NUCLEAR MHD CONVERTER R D -1 2- 01 -F N P R 112
Task 3. Electrical Cond uctivity Effect s
This tas^ shall proviae aporooriate relations enabling tne
preaiction of the electrical con ductivity of the working g as. For
this purpo se, this task shall primarily address the evaluation
of the electron mobility in the gas. The possible contribution
(beneficial and/or detri ment al) to electric conduct ivity of the
other chargeo particles m the gas, such as F- ions, snail be
taken into account.
Tasi< 4. Reporting
This task concerns tne execution of the reporting reauirements
incorporatec in tne contract.
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NUCLEAR M H D CONVERTER RD-12-01-FNPR 1 .
7 REFLECTOR M O D E L I N G
7 . . Svmoois , Terms ana Hooreviations
a Absorotion
a/o Atom pe r cent
B O L Feginning of life
BU Fuel burn-uD
CZF Cola zer o pow er
f FlSElOn
riFF not -full po we r
HZF ho t zei'o power
a Energy grouD
pcm Percent mille ^a reactivity change of 1 pcm
ecuais a reactivit y chan ge of lOe-5 A ^ )
Power aensity T n e thermal power proauc ed pe r unit volume of
the core (w/cm~)
Reactivity
Change in reactivity, definea a s
A ^ = l n k 2 / k l ) , where kl and k 2 are t h e
9
A y
eigenva lues obtained from t w o calculations
that differ only in t h e values assigned t o
the indepenaent variables
Removal
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NUCLEAR MHD CONVERTER RD-12-01-FNPR 1 14
shutoown margin Tne amount of negative reactivity ( o ^ by
which a reactor is ma in ta me a m
subcritical state at CZP conditio ns after a
control trip
Teff Resonance effective temoerature of the fuel
tr Transport
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Reference Core Description
General
15
The results presented m this section are referred to
tne reactor reference configuration shown in Figures 3.1-3.2.
This configuration is a simolifiea arrangement suoject to
tne limitations of the coaes aoootea in the analysi s: in
partic ular, a coarse aiscre tization of both composition ana
geometry has oeen maae at the core inlet ana outlet conical
segments.
A simoie ax ia l- ml et flow pattern has oeen aaootea in tne
analysis; however , the cooling reauirements of tne wail maae it
necessary to add an internal diffuser that diviaes tne inlet
flow into two par ts, the larger flowing m the annulus between
the internal diffuser and the external one.
In this reactor the same fluid acts as working medium and fuel;
it flows across the reactor cavity and consists of highly
enriched gaseous UF6 (region 1 of Fig. 3. 1) ; 90'/. a/o enrichea
in U235 with the reactor at BOL.
The core supplies a thermal power of 277 Mw at full power.
The following parameters have been fixea for the power
density distribution calculations m s i d e the core and for
the reactivity integral worth evaluation of the movable
reflector:
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^ ' " ' ' N UCLEA R MHD CO NVERTER ' ' " " " ' " R D - 1 2 - 0 1 - F N P R " ' ' l ' ' ' '16
- Reactor at full power ( H F F ; ,
- B O L ,
- no Aenon, no 5m,
- inlet pressure 15 MFa,
- UFto flow ra te 1000 tg/ s.
- inlet temoerature 17Z0 t .
Tne rationale for tne selection OT rnese system parameters is
oroviaea m section 5.2.
Besiaes, in oraer to estimate tne reactivity reauirements auring
reactor operations , two aocitionai core conoitions nave oeen
aefineo:
e> conoition I:
- Core at cola zero power ^ L Z F J .
- B O L ,
- uFc) inlet ore ssure 52 oar.
- UFc> inlet temoeratu-'e 573 r .
- UPto flow rate iOOu fg / s ,
p; conoition II:
- Core at not zero oower ( M Z F ) ,
- BOL,
- UF6 inlet oressure 15 M Pa,
- UF6 inlet temperat ure 1720 K,
- UF6 flow rate 1000 Kg/s,
The above conditions are possible if the reactor control
system can assure that:
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NUCLEAR MHD CONVERTER RD-12-01-FNPR 1
A) condition I is reached without using nuclear heating to
attain the gaseous phase of tne fuel;
B) the fuel density at the core inlet is kept constant (0.36
g/cm~) by controlling the inlet parameters during reactor
operations.
Components
The dimensio ns of the reactor components (shown in Figures
3.1-3.2) have been fixed after some preliminary conside rations .
basea on the thermal and mecnanical feasioility of tne system
and on the basic neutronic reauireme nts enabling the core
reactivity to oe controlled by a movao ie reflect or, slicing
a x 1 ally on the external side of tne p ressure vess el.
As already pointed out in CI ] , the main proolem is the
selection of a pressure vessel material highly transoarent to
neutrons.
It can be shown that the adoption of the most common
metallic materials , such as nickel alloys or stainle ss-stee l.
introduces a strong reactivity penalty and decouples the inner
shells from the external movable reflector to such a degree
that reflector worth becomes negligible.
For the above reasons a Zr/Nb alloy (UN5=R60901) has been finally
selected as pressure vessel material.
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U^^' NUCLEAR MHD CONVERTER ' ' ' RD-1 2-01-FNPR ' 1 '^^
The cylinorical shell thickness (10 cm) has been evaluated
preliminarily in conformity with the ASME III Code C2] for a
permanent static load condition at 15 MPa. In order to
minimize creep Phenomena the pressure vessel maximum
temoerature has been supoosea to be lower than 620 K.
To keep tne pressure vessel temperature at such a low value
an active neat removal svstem has to be provided.
Since tne maximum temperature in the reactor cavity is expected
to reacn aoout 2800 K close to the wall, highly refractory
materials have been used: in partic ular, a graphite shell (10 cm
thick; ana a BeO shell (10 cm thick) have been interposed between
the fuel ana the pressure vessel.
These shells have to be cooled by helium gas flowing across a
number of coolant channels obtained m the shells themselve s.
Tne purpose of tne coolant system is twofold;
1) to remove the gamma and neutron heating from the inner shells:
2) to create a strong temperature gradient between fuel and
pressure vessel. Tab. 3.1 shows the radial temperature profile
assumed for the core reference configuration.
Further more, m order to avoid the corrosion reaction s between
UF6 and graph ite, a thin Mo-alloy liner (0.6 mm thick) has been
placed to insulate the fuel from the graphite surface.
An adequate liner material is TZM (UNS=P/M,R03640) that has a
high melting point (3300 K) and a liquidus temperature at
2895 K.
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NUCLEAR M HD CONVERTER RD-12-01-FNPR 1 19
Typical fields of application of this material ar e heat engines,
extrusion dies and nuclear reactors, as it retains good
mechanical performances at high temperature.
It should be pointed out that only M o-alloys can oe prohaaly
used for structural parts in the reactor cavity (e.g. tne
diffuser); however, since these alloys act as strong absorbers
in the proposed conceot of gas reacto r, their use shouio be
limited.
In this preliminary feasibility analysis, however, tne internals
( diffuser and gas coolant tubes) have been ignored; tne
reactivity penalty due to the internal materials can be
balanced by increasing fuel enrichment.
Finally, beryllium has been selectea as the material of the
movable reflector.
M ass and volume of the reactor components are summarizea in Tao.
Analysis Codes
The principal computer codes adopted in the analys is ar e GGC-4
C3] (zero-dimens ional), ANISN C43 (one-dimens ional), SQUID-3faO
[5] (two-dimensional ), WAPITI-GAS C6] (two-dimensiona l),
M ERCURE-IV C7] (thre e-dimensional). A brief presentation of these
codes IS provided below: additional information can be found in
the references.
So
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NUCLEAR MHD CONVERTER RD-12-01-FNPR 1 21
MERCURE-IV Code:
The Monte Carlo code MERCURE-IV comoutes in a three-dimensional
heterogeneou s geometry heating and gamma dose rat es, and by
the point-wise kernel attenuation in a straight line, the fast
fluxes.
Tabulated accumulation factors give the contribution of
the scattered gamma rays. The program calculates the
accumulation factors for mixtu res; for multi-layer media the
Kitazume formulation is used.
Additional suooort codes have been usea for soecial ca lculations
sucn as the correlation factors ana the cross section uodate
durina the iteration process between BOuID ana WAPITI.
3.'' Features of Performea Calculations
Fuel and structural material cross sections
In accordance with the scheme reported in Fig. 3.3 the cross
sections have been calculated by using:
a) GGC-4 for the fuel cross sections with:
- fast energy range from 14.9 MeV to 2.38 eV and Bl
approximation (GAM);
- thermal energy range from 2.38 eV to zero and BO
approx i mat i on (GATHER):
So
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NUCLEAR MHD CONVERTER RD-12-01-FNPR 1 22
- 50 grouD microscopic cross section generation i i fast
groups ana 9 thermal grouos ) to be input to ANISN coae in
oraer to generate fuel ana structural cross sections.
The assumed energy cuts are shown in Tao. 3.3.
b) GbL-4 as in item a) but for the structural cross sections
witn :
- Bl aooroximation in GATHER.
c; H(-.I5iv co ae using c vi inar ic ai geom et rv a no P0-5'+
aooro'imation in oraer to:
- investigate tne fuel 5 group cross section oeoenaence on tne
temoerature ana Density of tne fuel;
- generate tne structural material macroscooic cross sections
ana a 5 group cross section data set to calcul ate tne fuei
macroscopic cross sections to be input to SOUID coae as
a function of temperatu re and density at each iteration step.
The assumed energy cuts m the range 14.9 MeV - 0.0 eV are
14.9 MeV, 0.821 MeV, 150 KeV, 5.53 Ke V, 0.625 eV, 0.0 eV.
Reactor Calculations
In accordance with the scheme reported m Fig. 3.4 , total
reflector worth and the distri bution s of thermal pow er,
fuel te mper ature , ana fuel density ha ve been calculatea av using:
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NUCLEAR MHD CONVERTER RD-12-01-FNPR 1 23
a) SDUID-360 code with;
- simplified R-Z geometry and material comoositions,
- k-eff calculation,
- spatial fluxes calculations in order to evaluate the thermal
power aensity aistribution to be input to WAPITI code.
b) W A P I T I - G H 5 coae for the thermal-fluid analysis witn:
- R-Z geometry,
- turbulent flow,
- density ana temperature distributions of tne fuel to be input
to S Q L I D - 3 6 0 Coae.
3.5 Nuclear Cross Section Calculations
The macroscooic cross sections reauired as input data for the
full core R-Z SOUID calculat ions have been generatea by
using the proceaure outlinea in Fig. 3.3. The cross sections
are referred to :
-fuel,
-structural material.
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NUCLEAR MHD CO^fVERTER R D -1 2 -0 1 -F N P R ^ ^ p ge
Fuel cross sections
It has been assumed that in side the re-ference core con-figuration
(see par. 3.1) -fuel temperatu re and density may chang e in the
range 1600-3000 K and 0.15-0.45 g/cm , respectively, as shown in
Fig. 3 .5.
A sensitivity analysi s has been per-formea by applying the
proc edur e of Fig. 3.3 to each o-f the poin ts 1-9 o-f Fig. 3. 5.
The results are summarizeo below:
a) tne fuel microscooic cross sections cnange only:
- with fuel density in the 4th energetic group (eoithermal
range),
- with fuel temperatu re in the 5tn energetic group (tnermal
group);
b) the 5 group structural material cross section s are not
significantly affected by the fuel conditions unoer the
assumption that the radial tempera ture profile in the
structural material doesn't change.
Conseque ntly, in order to update the fuel macroscopic
cross sections during the iterative SDUID calculations of
reactor power distribution with thermal-fluid feedb ack, the
following correlations can be used:
g g n g= lf ~ si t j=tr ,a,f
I (T,n) = I ( To , n o ) or
J j no g=l?4 and j=r
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NUCLEAR MH D CONVERTER RD-12-01-FNPR 1 25
4 4 n 4
Z u . n ; = I (To ,no) +L Z (n) j=tr,a,f
J J no J
5 5 n 5
I 'T,n; = Z ( To , n o ) +AI (T> j=tr,a,f
: J no J
4
AZ in) = n^ajn' - ojn + cj ; j=tr,a,f
J
5
AI (T; = n(AjT= + BjT + Cj ;
J
where:
Cnj=g/ cm- LTj=f , no=0.3 g/cm- To=2l00 t -
The correlation coefficients a j , b j , c j , A j , Bj , Cj have oeen
estimated by using the previous ANISN calculations.
The results a re reported m Tab. 3 . 4 .
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(Proget toprotect
NUCLEAR MHD CONVERTER
Identihca^vodocument re
RD-12-01-FNPR
Rev Pagmarev page
1 28
b) reactivity changes due to changes in reactor power over tne
power range of operations;
c) reactivity changes due to fuel depletion;
d) reactivity associated to the minimum shutdown margin.
The reactivity cha nge associatea to each item is reported in Tab.
3.8.
The integral worth of the movab le reflector has oeen evaluated
by means of the reactor calculations: an uncertainty of about 107.
has been associated to the results.
The reactivity change between CZF and hZF does not appear
to be significant oecause in this reactor the Doooier effect has
been consiaered only for UZTS , as in the GAM library there
isn't any information about the Doooier effect in UZT5.
Finally, since it is not in the scope of this preliminary
analysis to mai e accurate assumptio ns about the system operatin g
modes. it has been supposed that the reactor is operated
at full power level contmuosly.
It has been estimated that, with a 3300 pern of reactivity change
available for deplet ion, reactor life is limited to a few
hours because of the strong Xenon poisoning that affects this
type of c ore. This time is a function of the UFo overall
plant/core mass ratio as shown m Fig. 3.9.
The full power level can be restored after an interval of time
whose length depends on the operational strategy; the process can
be repeated until fuel depletion allows it.
o
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NUCLEAR MHD CONVERTER
Identificativodocument no
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Rev Paginarev page
1 29
Fig 3.10 snows tne evolution of reactivity after a snutoown
pertormea at the eno of the first lifetime at full power , wnose
length is about 5 nours . In tnis cas e, whicn is referrea to a
UFfc mass ratio of 5, tne time reauireo for reactivity to pecome
positive again is approximately 30 hours from snutaown: tnis
waiting time is reducea by increasing the mass ratio.
The minimum value of reactivity that occur s 9 nours after
Shutdown in Fig. 3. 10, corresponding to a maximum of the Xe
concentration, is explained by tne presence of a source of Xel35,
tne raoioacti ve oecay of 1135, in competition witn its
aisaopearance aue to aecay to Csl35.
So
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Progetto Identificativo Rev Pagmaproiect Ml,/^T IT A n n u n r
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Pro getto Identificativo Rev Pagmaproiect document no rev oaoe
NUCLEAR MHD CONVERTER RD-12-01-FNPR i ^ 31
C8] Joanou G.D .D . and Dude> J. 5. , GAM-II-A B3 Code for the
Calculation of Fast Neutron Spectrum and Associated
Muitigroup Constants , GA - 4265 Seotemoer 1963.
C93 G.D. Jo anou et al . , GATriER-II, An IBM 7090 Fortran- II
Program for the ComDutation of Thermal-Neutron Spectra and
Associated Multigrouo Cross Sections , GA-4i32 1963.
[IOJ Orer 0. ana Garber D. , ENDF/B Summary D ocumentation,
ENDF-20r'. BNL 17451, Brool
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NUCLEAR MHD CONVERTER
Identificativodocument no
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R e v P a g m arev page
1 32
Tab. 3.1 Radial temperature profile in the core
reference configuration.
Radi al Rang e (*)
(cm )
Material Average Temperature
(K)
50.0-53.5
53.5-56.5
56.5-60.0
60.0-63.5
63.5-66.0
66.0-70.0
70.0-80.0
80.0-110.0
Graphite
BeO
Zr-Nb
Be
2200
1500
1200
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ProgettoprO)Cl
NUCLEAR MHD CONVERTER
IdentificativodOCuTieil nc
RD-12-01-FNPR
Tab . 3.2 Mass and volume summary for thecore reference configuration.
Rv Fac: 'arev pao*
1 ' 33
Reactor Material Average
Density
(kr3/dm3)
Volume
(dm3)
Masr,
(kg)'
o f
Tota l Mass
UF6 0.20 1723 500 1.9
T 2 M
Cr.-pl->ito
UcO
10.IG
1.71
3.02
: .G3
1320
1317
20
2 2 5 7
3 9 7 7
0.1
8.51^.9
,r-Nb alloy
Dc
6.5
1.B5
1634
5012
10G21
9 2 7 2
39 .8
3-1. e
Tota l Reac to r Mass 2G65G 100.0
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i
5
T
r
5
r
X r
^
~
fN
r
.T
T
XO
c
*
-
T
xr.CCC
J
^T
.^
x;
~
7 r
^
z
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NUCLEAR MHD CONVERTER
Identificativodocument no
RD-12-01-FNPR
Re v Pagmarev page
1 35
Tao . 3.4 C c r r e l a t i o n c c e f f :c ler.t 3
c r 3 5 5 s e c t i o n u p d a t e .
-.r.e ma cr cs cc oi c
f o r
1k
t r
k
r
33
. 5 7 0 5 5 - 3 3
. 1 1 1 5 5 - 3 7
. 5 5 7 4 5 - 3 3
^ '
- . 1 3 4 9 3 - 0 4
- . 2 5 4 9 5 - C 4
- . 1 3 3 8 5 - 0 4
C3
. 1 3 9 7 6 - 0 1
. 2 7 7 1 7 - 0 1
. 1 3 3 9 1 - 0 1
f o r
Ft r
k'f
O-a
A J
. 7 5 1 5 3 - 0 1
. 8 9 4 3 3 - 3 1
. 5 8 1 3 9 - 0 1
3 J
- . 7 9 9 3 0 - 0 1
- . 9 3 4 1 4 - 0 1
- . 6 0 5 2 3 - 0 1
C J
. 1 7 5 3 9 - 0 1
. 2 0 4 0 1 - 0 1
. 1 3 1 9 9 - 0 1
so5
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t h M P E R A n i H H S
1 4 b I E1 4 S i FI Of , 1 F1 4 h / F1 1 / O t1 4 H . LI O -J ^ LI ' . n O F
1 s 1 ; F' s a n tI b 4 b tI ' . ( ) J F' ' .H 1 I11,11 ; 'e11> (. ' (H > 4 / II / H i t1 / *j r t
(14 0 0 0 0 0 0 0 0 u o DO (10 n o (14 U4 t j o II .1 1)0 00 0 0 DO U J
ooootoooot0 0 0 0 1 :i b j o eI ' j b O h' ' i 3 H F) > 7 4 F
' / 0 2 tt / 7 O t
1 H 4 7 E1 'J n o K? r i 3 ? F? 1 9 4 E/ J S . M :2 3 9 ' Li i o o o eU i l O O L
0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 4 0 4 0 4
0 4 0 4 0 4 0 4 0 4 0 4 0 0 0 0
1 4 5 1I 0 ',.I Oh II 4 h /1 4 7 41 O b JI 4
1 ' . 9 111 l> 1 .)
I ( .0 ;1 (>BHI / H ' >1 H 9 ' .1 'J u :>
E ' O Or 0 0r. 0 0E ^ O Ofc 0 4I U 0r 0 0
1 0
O O O O FO O O O Lo o o o t1 f a 4 J t1 t j J 4 t1 b 7 7 eu> ;> 0 F1 7 a 7 EI 7 9 I F1 7 / t
l 9 i O L^ 0 0 () F? 1 4 ? r
2 4 i y EO O O O Fo o o o to o o o t
0 0 00 0 0 0 4 0 4 0 4 0 4 0 4 0 4 0 4
0 4 0 4 0 0 0 4 00 0 0 1101 00
1 4 5 1 t1 0 S ( , FI 0 6 2 F1 0 b 9 i
. 1 0 H 11 L1 0 -J / I
. I ' . U I M
. t S < .' 11 -, r, H F1 "l H b FI t.1 1 2 F
1 t) J> ) l1 t . l i / 11 / l i s t1 / 7 U1 'H I 1 '2 0 ^ . .
. 2 U .1 J 1.
0 0 n o 0 0 0 4. 0 4. 0 0< 0 0 0 0 0 0 0 4 0 0
0 0. I ) . l. 0-1t o o
. 114 0 0. O'l
O O O O FO O O O Eo o o o to o o o t180 7 t1 6 0 0 F1 (>')HF1 7 9 F > Fi a 9 0 t1 9 H ' . F
2 0 ( > H t2 I'D 1 C2 2 .1 ll 17 U i O l2 0 / 7 1 ;o o o o tO O O t OO O O O L
0 0 0 0 0 0 0 0 0 4 0 4 0 4 0 0 0 4 0 4
0 4 0 0. 0 0 0 0 0 0 0 0 0 0 0 0
. 1 O-b If .1 0 S ' i tI S O ( > t
. 1 b 1 ' i t
. I b b / l
. l b ' , H I
. l ' > l , l . l
. 1 S H H I
. 1 6 1 3 1
. I b J H F
. I b b O F
. 1 b ' ) 2 (1 / 2 0 1
. 1 / 7 ' , (
. I H 7 0 1
. 2 l ) 2 H t
. 2 1 2 2 12 1 )
0 4 0 0 0 4 0 0 0 0 O-^. 0 0 0 01 0 0 0 41 0 41 0 . 1I n o1 n o n o 0 0 0 0. o o
1 2
O O O O FO O O O Fo o o o tO O O O L18 J 2 t1 b H 3 F1 7 t > . l l1 8 / H II 9 H 2 I2 0 7 2 L
2 I b O l2 2 2 b t2 3 0 2 r2 4 1 S I2 b J 0 Lo o o o tO i i O O lO O O O L
o n 0 0 0 0 0 0 0 4 0 4 0 4 0 0 0 0 0 4
0 4 1)4 0 0 0 4 0 0 0 0 0 0 o o
I O S I [
1 ' l ' , ' > l
1 o ( , n iI O b . F1 ( i ' j 2 t1 > I 111 II o 0 ' . . L1 l . / b l1 t . ' i O FI b / '1 FI 7 n 2 (
1 7 3 .111 7 / 1 1' H ) / I1 I . l l
2 1 2 0 12 1 7 (IO O O O L
1 i
0 0 no no 0 0 0 0 oo (10 0 0 0 0 04 0 0
. 0 0I 0 0111 0. D O no no un
O O O O FO O O O Fo o o o to o o o to o o o t1 7 7 1 F1 H 2 2 11 ^ 2 7 t. ' i 2 M t2 1 1 ) t
2 1 H 7 I2 2 ' , H 12 \?ni2 0 2 01o n o n io n o n io i m n iO O O O L
0 0 0 0 0 0 0 0 0 0 n o n o 0 4 0 4 0 0
0 0> 0 0 o o 0 0 0 0< 0 0t o o 0 0
o o o o t1 O ' . ' l f1 0 < > 0 l
. 1 O b ' l l
. 1 O O O l
. 1 0 ' i 0 1
. 1 0 2 2 11 ( , 3 H F1 b b f l F
. 1 7 0 I F
. 1 7 3 b F
. 1 7 / 2 t
. 1 M 1 111
. 1 ' 1 0 0 12 l l O ' ) l2 I ' l H I
. 2 2 0 ' ) lO O O O L
0 0, n o n o 0 4 0 0< n o 0 0 0 4 0 0 0 4 0 0
114 0-1. 0 0
. n o o o 0 01 o n
O O O O FO O O O F0 0 0 0 10 0 0 0 10 0 0 0 12 0 3 ' ) l1 ') 7 212 0 3 3 F2 10 112 1 0 / 1
^ / ) 0 I2 2 ' l ) l2 1 ' , / I2 0 ' , H I( I I I O O I0 1 1 0 0 1o o o o tO O O O L
> O I I 0 0 0 0 0 0
0 0 o o n o 0 0 0 0 0 4
0 0. 0 0 0 0 0 0 0 0 0 0 o o. o o
, 0 0 0 0 1o o o o t1 t^iri'ji
. 1 4 H ' ) 1
. 1 4 'J'.) 1
. 1 ' , 11 0 1
. 1 S 3 t . l1 '> '>0 I
. 1 b O H t
. M i M M t
. 1 7 0 9 t
. l H n 2 LI H l . ' l tI ' l H O I. I ' . ' l l2 2 1 . 7 1o i i n o i
. O O O O L
0 0 n o. n o 0 0> 0 4 0 4 0 0 0 4 0 4 0 4 0 4
OO. 0 0. OO1 n o 11 1
n o 0 0
15
O O O O FO o o o to o o o to o o o to o o o to o o o t2 1 4 . 12 I H I F2 2 0 H F2 2 4 ' j L
2 2 9 O 12 1 0 / L2 ) ) 7 12 0 ' l 2 tO O O O FO O O O FO O O O LO O O O L
0 0 0 0 0 0 OO o o o o. 0 0 o o 0 4 OO
OO 0 01 0 0 0 0< 0 0' 0 0. 0 0
> o u
Tab. 3.5 Temperature distribution in the reactor cavity.External reflector 10 0% in anti 65 % of the fuelthrough the annular diffuser.
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I L M P F H A 1 UHti>
Z-
I B1 7IC1 ')1 01 i1 Z
1 1lO
9n/t 0 0 ' . l ' , / 3 t . 0 0 ' 1 0 1 , 5 1 ' O Ol ^ / H t ' . l O ' I O H ' , 1 I M I ' . I ' . / b l . 0 0 ' 11 , / 1 , 1 . 11 01 4 H H I m o 1 0 0 ( 1 1 n o ' I ' . i . / i . n o i b i ' , i . n oI ' . O O F t O O ' 1 5 1 1 , 1 . 11 .1 ' 1 5 / 7 1 n o l b , ' 7 l t n o1 . 1 7h 0 0 ' . 1 ' . 0 11 . 0 0 ' . 1 bO I I 0 4 ' . 1 1,0.11 . 0 01 5 3 / 1 ' 0 0 ' 1 ' . / 11 . 1 ) 0 . i b 3 . ' i ' O O ' M j i . ' j t . n oI ' . b O l . n o ' 11 ,11 0 1 .11.1 . 1 b b 1 1 0 0 ' 1 1 , 1 / 1 . n o1 5 H b l > 0 0 ' . 1 1 , l l . l . l l - l ' . 1 0 9 1 1 OO . 1 / . / 1 . n o
1 b 1 o t n o 11 . b i l l . n o 1 7 2 3 F 0 0 ' . 1 7 b 1 1 . 0 0I b 4 2 t + O 0 ' . l / O l l . l l O ' I 7 b 0 1 0 0 ' . I H O O I ' O O1 b 7 9 + 114 ' 1 74 / I n o ' . 1 H 1 01 0 4 ' . 1 H b ' . l < 0 41 7 .131 no 1 u 1 /1 no ' . 1 90111 > no . i I O M I . no
I H . i . l . 1 10 ' l ' ) . ) i . 1 1 0 ' . ' 1 1 . " . i . 1 ) 0 . i m o i . n oI ' l i i i i " O O . . '1 1 . ' n i . ( i . i ' . ' D ' j M . n o ' . ' 1 1 1 1 . n o1 9 3 11 0 0 ' .2 n i i n . n o ' . 2 i n .' i . n 0 ' n n 11 n i < n n
10 11 ' 12 ' 13
O o o o t 0 0 ' . n o o o t ^ o o . o o o o t . n o . o o ( i o t o oO O OO l + 0 O ' . 0 0 (1 1 0 ' O O ' . o o o o L ' i H ) ' . o n o n t . o OO O O O ) > O o . i i O M i i i . 0 0 ' o n o n i . o n ' . n n o n i . o n1 1 . 2 5 1 . 0 0 . n n o n i . o n o o n n i > i i n . i i n n i K . n nt b l 5 F t ( ) 0 1 / 0 / ( M I O ' . i H d . i . n o ' ( n i n n l ' n i i1 ' i i 3 n o . u . 1 ' J l . no ' . 1 1 , 5 , - i no i / ^ i i no1 ' . 9 71 0 4 . 1 b ' i b L o o . 1 7 1 . ' 1 . 0 0 . 1 / ' , ) l 0 01 1,1.4 1- 0 4 . 1 / . I ' l l < 0 0 ' . 1 I I O H I 0 0 . 1 11.) 1 t . 0 01 / 3 b 1 I JO ' . 1 H / , L m o . 1 H ' l b l 0 0 > 1 ' ) 1 0 t 0 0I B O ' H O O I O O O ' ^ J O O ' l ' ) / ' , l O O ' l O ' K l t . 1 1 0I H 8 4 F 0 0 ' . 1 ' I H l F t O O ' . 2 0 0 ' I F . I I O ' 2 0 ( , I . F < n O1 9 t , 5 0 4 ' . 2 0 ' . ' J I 0 0 ' . 2 1 2 .11 0 0 ' . 2 1 l o t 0 02 n b O t < 0 0 . 2 1 0 1 1 O O . 2 1 9 3 1 O O 2 2 O . ' t < l l 02 1 9 5 t ^ 0 4 ' . 2 2 5 3 L + 0 0 ' . 2 2 H 3 1 ' O O . 2 2 H ' , . l ' 0 0. '3 1 10 1 D O ' . 2 . l 5 0 t ^ ( 1 0 . 2 3 9 , 1 1 . 0 0 ' . 0 I 1 0 0 L ( I 0O O o n l 11 1) ' . 0 0 1 1 0 1 . 0 0 . o o o o t . 1 1 0 ' . 1 1 0 1 ) 01 . o n n no o o o t l O O ' n o o n i o o ' . O o O O i ' < o O o n o o i . 0 0
b
O O O O F ^1 4 5 H t1 0 b < 11 0 11 / 11 0 / M l1 O ' l O l1 b < ) ) l ll b ' . 2 l -1 b l l l U1 7 10 11 / ' . 111
1 / H i l l1 H .1 i t1 '1 1 1 1. ' ) i n i.' 1 O ' . l.- 1 ' . ( , 1o o o n i
1 4
o n o o tO O O O ln o i i i i in 0 n 111o o n n i1 1 . I l l1 H i . n i1 9 1 1 11') / . '12 0 3 ' i l
2 I ) ' 1 H I2 1 b 1 12 2 .' .' 12 3 l ) ' ) lo n o n in n n n to o n n i1 n l
o n . 1 )4 '
no 'n o 1n o >n o '0 0 0 0 'n o 1n o 0 0 >
no 'n o b f t t I o n < j*m* I (1 t 1
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WD 00123
C o r r e l a t i o n
C o e f f i c i e n t s
F i r s t 9 u e s s p o w e r D e n s i t y d i s t r i but 1 on I
d e n s i t y O i s t r i t i o t i o n
t e i T . p e r a t o r e o i s t r i i m t i o '
F u e i c r o s s s e c t i o n
o p d a t e
p o w e r d e n s i t y d i s t r i pi. t i o.
1- - e f f c t 1 ve
c o n v e t y e n c t-
c n p c I-
I y
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NUCLEAR MHD CONVERTER
Identificativodocument no
RD-12-01-FNPR
Rev Pagmarev page
1 45
^ R A D l U S - ^ 7 . 9 6 C MO R A D I U S - 4 3 . 6 0 C MX R A D I U S - 3 8 . 7 3+ R A D I U S = 3 3 . 1 7 C MA . R A D I U S = 2 6 . 4 5 C M
O R A D I U S = 2 2 . 3 6 C MCD R A D I U S = 8 C M
I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 e ee 4t .Be te .e a i?.ee lee .ee 2*e.ee z^O'et ?i.ae 32e.e
Z A X I S ( C M )
F i p 3. 6 P o w e r d e n s i t y v s . a x i a l c o o r d , f r o m c o r e i n l e t ) a t d i f f e r e n t r a d i a lc o o r d i n a t e s .
E x t e r n a l r e f l e c t o r 1 0 0 % i n and 6 5 % o f t h e f u e l t h r o u g h t h e a n n u l a rd i f f u s e r .
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Proget toprotect
NUCLEAR MHD CONVERTER
Identificativodocument no
RD-12-01-FNPR
Revrev
Pagmapage
4 6
X
--
o
RADlUS-47.96 CMRADIUS43.60 CMRADlUS-38.73RADIUS=33.I7 CMRADIUS=26.45 CMRADIUS=22.36 CMRADlUS=e CM
Z AXIS (CM)
Fig. 3.7 Power density vs . axial coord, (from core inlet) at different radialcoordinates .External reflector out and 65% of the fuel through the annular diffuser.
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M O 0 0 1 2 3
1 0
8 -
t (H)
5 -
T
2T -8
T -
10
t : t imem: UF6 Overall Plant/Core Mass ratio
Fig. 3.9 Reactor life vs. UF6 Overall Plant/Core Mass ratio.
Reactor operated at full power level continuously.
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Proget topcoieci
NUCLEAR MHD CONVERTER
Identificativooocument no
RD-12-0 : -FNPP
Rev Paginarev page
1 49
"If";" -
~ - n ^ -
1 t '- -1 -
_-
, - - ^- -
- - -n r-
- - - V -
t
\
\\
11
1k 1
11
|
'11
V
~-^
1
11
11
11 ,1
1
'
1
' i1 11 ^
'
>I
,
1
11
1. _,--< '
11
1, 1
'J-
j
^-'
1
1i
1
Mr
45
Fig. 3.10 Reactivity vs . time (UF6 mass ratio = 5) .
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Pro getto Identificativo Rev Paginaproject document no rev .paoe
NUCLEAR MHD CONVERTER RD-12-01-FNPR 1 50
WORK'INB FLUID CHARACTERISTICS
4.1 Symb ols, Terms and Abbreviations
n
ni
rei
NumDer o-f particles pe r unit volume
0 Collision c o r s section
V Particl e velocity
(\jn Nurioer ot neutral molecules pe r unit volume
0 heiombination coe++ici ent
T Temperature
ne Number o+ electrons pe r unit volume
Number of ions oer unit volume
NumDer o-f primarv electrons D sr unit volume
Tnermalization time between electrons ana
ion =
Quantity in tne e. pres sion fo'' thermal izat ion
time
t Eoltzmann s constant
m Electron mass
A Ion mass in amu
M Ion mass
e EiBctron charge
r Quantity in the e'ioression -for coulomb
collisions
eo Energy ot primary electrons
Tp TemDerature oi primary electrons
So
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Progetto Identificativo Rev. Pagmaproject . , _ , _ . _ . _ . _ . _ document no rev page
NUCLEAR MHD CONVERTER RD-12-01-FNPR 1 52
4.2 Phase I
This phase provided a qualitative assessment of the types of
primary reaction s considered as the most import ant, and the
evaluation of the relevant cross-section s, using current
literature data and theoretical models.
The Production of Primary Electrons
Wnenever 235U unaergoe s a fission reaction a number of ionizing
agents sre generated. Fission fragments are the most imoortant as
they aosorb arouna 80/. of the energy rele asee. Tne energy balance
of a fission reaction is illustrated in TABLE 1 (oata Are
essentially similar for thermal or fast fission reactions ana for
th e two uranium isotooes)CI].
TABLE 1
1. Fission Fragment s 165 MeV
2. Prompt gamma rays (bremmstrahlung) 7 MeV
3. Delayed gamma rays (discrete spect rum) 6 MeV
4. fi+ and (i- rays 7 MeV
5. Neutrons 5 MeV
6. Neutrino s 10 MeV
TOTAL 200 MeV
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^'of," 'aentificativo R ^^ PagmaNUCLEAR MHD CONVERTER document no R D - 1 2 - 0 1 - F N P R '* ' l '^^^*
These pr imary io ni za t io ns sre mo stly maae up oy "s t ri p p in g " an
ele ct r on wi th out moaifym g the molecular or a tomic s t ru ct ur e of
t h e t a rg e t .
4.3 Phase I I
Tnis Phase aaaressea tne study of the rate eauations in tne
reactor core, provioing an ap or oM ma te analytical solution, and
Identifying tne critical p arameters.
Tne Froouction of Seconaary Electrons
The orimary electrons give rise to processes sucn as elastic and
inelastic scattering (excitation of bo nding electro ns in the
molecule), secondary ionization, and recombination.
Elastic scattering is low at energie s greater than 10
eV and can be almost neglected in most case s. The
inelastic scatte ring, on the other hand, is a very important
reaction channel since it absorbs around 2/3 of the primary
electron energy. This value is difficult to be computed or
measured. It depends on the energy and on the struct ure of the
molecules: data available in literature give a ratio between
ionization and inelastic collision cross sections of 0.2 - 0.5
C3]. These reactions are part of the gas thermalization and
heating proc ess.
So
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NUCLEAR MHD CONVERTER RD-12-01-FNPR 1 55
Recombination
The neutralization prooability of the ionized system is
related to the product of the electronic density , the
ionic density, ana the density of a third element essential
for energy ana momentum conservation C4 ]. This third element may
be either a neutral atom or an ion, or even an electro n. Tne
higher mobility of the electrons maKes tne following the
preferred recompination process in our case :
ne t ne + ni ne ni
Tnis parameter is extremely' sensitive to the density ana
temperature of the system.
The rate of recombination can be expressed by the following
relation:
dn/dt = - 'xn
whe re a = lOe-ZSn/T''-= , n is the electron (or ion) dens ity per
cm- and T is the temperature expressed in eV.
Note the depend ence upon n- (the coefficien t is linearly
related to n ) , which reminds that recombination is a three-body
process [5j.
sQ
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NUCLEAR MHD CONVERTER RD-12-01-FNPR i 57
The dependence on T is very strong because the electron velocity
IS the other hey parameter to the problem , both when calculating
the cross-section and when successively calculating the
average on the velocity distribution, necessary to determine the
probability per second of the proce ss.
Simplified Rate Equation
The effects of recomoination and ionization may be combined into
a rate eouation for the electronic part of the system:
dn/dt = nO v>Ng - an^
Supstituting tne numerical values into tne aoove eouation
yields:
dn/ dt = n 3.10el3 TJT - lOe-25 n-/T*-=
Ng was assumed to be 5.10e20 molecules per cm-.
Let us now suppose to be under steady state conditions
(hence neglecting dn /d t ) .
This assumption requires that a unique equilibrium temperature
exists, at least among the various ionized species, and that the
time to reach such conditions is much shorter than the time
during which the gas remains in the reactor core. In fact.
So
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NUCLEAR MHD CONVERTER RD-12-01-FNPR 1 58
electrons arouna 500 eV, electron s of a few eVs (secondary), and
ions at almost the same temperature of the gas coexist curing a
first phase.
however, as we snail see better afterwards, tne condition s in tne
reactor core lead to extremely short thermalization times
compared with the transit time of the gas, and hence, in spite of
the simple approac h, this first evaluation may be consiaered
quite realistic.
Let us now introduce the energy balance, that is determinea by
tne distribution of the ionization and thermalization energies:
ynoSOO = n(T+I) = ncT+10) = vZ.B-lOeZl
where v-'l is the part of energy involved in ionizatio n p roce sses
and I IS assumea to oe eaual to 10 eV, a value typical of most
atoms and molecules.
The rate eo uation, once inserted into th e balance eouatio n.
gives:
T=' '=.(T+10J = 165v => T = 2.8y=-''=
Similarly, the implicit value of the electronic density
can be found:
n = 6-10e5(2.G-10e20y-n)=-'
o
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NUCLEAR MHD CONVERTER RD-12-01-FNPR i 59
which yields approximately
n = 2.6-10e20y
It should be noted that the recombinatio n process is
active, above all, at low t emperatures. However, the
process temperature is o et er mm eo critically througn
the parameter y. The con ventional thermal region
(T 4000 C) IS indicated by values of y less than lOe-2.
Tneref ore, the critical parameter that must be
calculated is the actual distribut ion of energ y between the
ionization and thermalization processes or, if one prefers, the
electron equilibrium temperature.
Thermalization Times
Whet remains to be seen is whether the secondary electrons, which
still have sufficien tly high energy , of the order of 2-3 eV, can
thermalize tand hence recombine/ rapidly or not.
The electron-ion thermalization time decreases with the
temperature according to the following relationship C53:
Tei = (tT)-''=
where 6 is given by [5] as:
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' ^ " " ' NUCLEAR MHD CONVERTER ' " * " ' ^ " ' " RD- 12-0 1-FN PR ' " 1 ' eO
3 m ^ ' - 1 6 3 2 A
8 ( 2 T T ) > '= e * l o g r
where m is the electron mass, e the electron charge, A the ion
mass in a.m.u., and logP a parameter which varies slightly with
density and temperat ure (it is related to the smallest collision
parameter in a Coulomb interaction;. In tne case of U F D . tne
value of
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NUCLEAR M HD CONVERTER RD-12-01-FNPR 1 61
Complete Rate Eauations
The complete rate eauations tafe actually into account only a
few of the numerous possible reactions in the system. On the
basis of the cross-section experimental data and of the analysis
reported in the previous paragraphs, we selected the reactions
which were consiaered as the most significant for the
purpose of this stuoy.
reaction s such as the multiple ionization of atoms or molecules
have been neglected. In otner words, only UFi, UFit (with i=0,6;
ana F- type systems are considered and possible states such as
UFi-, UFi+t, etc. ar e neglected.
Under this assumption, there ar e 16 unknown parameters in tne
problem:
ni =UFi/cm' ( 7 variables ) ,
ni+=UFi-t-/cm~ ( 7 vari ao les ',
nf = F/cm',
nf2 = FZ/cm',
nf- = F-/cm' (3 variables),
m addition to n that represents, as before, the number of free
electrons. Therefore IS equations are required to solve the
system as a function of three basic input paramet ers: Ng (gas
density in the reactor) , no (number of primary electrons) and the
average primary radiation energy eo = 500 eV.
The rate equations provide 17 relations, one for each variable;
the energy balance yields the missing condition (system
neutrality is implicit in the rate equations).
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NUCLEAR MHD CONVERTER RD -12-01-FNPR 1 62
Method of Solution
Before proceeding, it is necessary to discuss some assumptions
that should be introduced in a numerical approach to tne
evaluation of ionization levels and gas composition in the
cavity.
1) The system is homogeneous.
This IS a good appro;; imati on given the parameters of
the reactor and the properties of the system being examinee.
In fact, the mass transfer rates are very small m comparison
with two significant fluid parameters, tne tnermal
transfer rate and the speed of sound; in addition, the
thermalization processes tate place on small space
scales, of the oraer of a few cms. Hence, tnere is no use in
introaucing the convection terms into the rate eauation s. and
considering the unknowns as a function of position.
2) The system is under steady state conditio ns.
This assumption is undoubtedly true when considering the
thermalization time scale (lOe-9 s), and allows the rate
equations to be simplified considerably by neglecting the time
dependence of the variables.
3) Cross-section values.
In our approach, there are 46 cross- sectio ns (which are strongly
energy dependent) constituting a set of input parameters to the
problem. They are not variables but physical quantit ies that can
be experimentally measured. In any case, these parameters are not
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Identificativodocument no
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1 64
1) gas density is uniform during tne transit time in tne
channel;
2) a uniform distribution of fission reactions provides a
uniform background of primary electron s (500 eV;;
3) as a first approa ch, the secondary soecies are supposed to
derive essentially from the ionization of UF6. Therefore, tne
maximum level of cnarge density cannot overcome gas aensitv.
Tne conseauences of tnis statement will oe oiscusseo later:
4; tne loss of electr ons is ascripea to tnree-ooav
recomoination:
5; since tne local neutrality conoition is well verifieo
because of tne very short Deo ve length comoared with plasma
dimensi ons, it is assumed ne=ni for secondary charge s.
Even a simplified approach reouires to solve the system giving
the thermal exchange rates among tne ionized soecies . Since
charge density is variable, the energy balance must be couoleo to
the rate eouation for electron production:
dTp
no
dt
noTp - neTs noTp - neTi
ree Tpei
tl;
dTs
ne
dt
noTp - neTs neTs - neTi
Tee Tsei
(2)
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NUCLEAR M H D CONVERTER RD-1 2-01-FNPR 1 6 5
Oil noip - neii nets - neii
ne = ^^^^ * _ ^
at Toei Tsei
one a e \ p ( - I / T p ; e x p ( - I / Ts ;
= Not no
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NUCLEAR M HD CONVERTER RD-12-01-FNPR 1 67
dTi m t5Ng R m Tp R
= - [Tp - - Ts - -( ;--= (Ts-Ti)-] u>
dt M yTo -= ('j M Ts (1
oR aNg(l-R) expt-I/Tp; exD (-I/Ts) oNg^R-
= C (j f R] - (S;
at I T D ' ~ T51 ~ Ts -
The assumption of a uniform aensitv oistrio ution. reiatea
to the rather flat profile of gas density during tne transit
in tne chan nel, allows one to neglect tne contribution of tne
terms Vg.gra atT) ana Vg.graatn; in com parison witn tne time
oerivatives. Tnerefore, an elementary volume of fluia is
modified in its properties oefore aopreciap le deplacement
takes place. As a consequence, tne integration in time is
equivalent to follow the space evolution, with the variaoie
Change x=Vg.t. It turns out that a non-uniform source of
primary electro ns can be included m the mod el, unoer tne
condition that the induced gradient s still verify the inequality
Vg.grad(T)>NaT/at ana Vg.graa(n;^^dn/dt. For instance, in the
presence of a step distributio n of the fission sour ce in
a length xo, it is sufficient to introdu ce, in the solution
of the system, the condition no=0 for t^xo/Vg. Alternatively,
the system can oe solved in the space variable by
introducing dx=Vg. dt. In gene ral, it is not strictly
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required that gas velocity and density ar e uniform ano
constant; it is sufficient that significant variations of Vg
and density occur in a time longer than the time required to
reach a stationary state for Tp, Ts , Ti , and R.
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NUCLEAR MHD CONVERTER RD-12-01-FNPR l 69
t.^ References
CI] Gladstone, Nuclear Reactor Tneory , Fergamon Press, 1964.
C2] Ziegler J.P., Stopping Power and Ranges in Elemental
Matter , Fergamon Press, 1977 - 1981.
C3] Golant V.E. , Zilinskij A.P. , Sacharov I.E., Osnovy fiziki
olasmy ( Fundamentals of Plasma Physics ) , MIR, Moscow, It .
transl. 1963.
C4] Zeidovicn ano R aizer, Fhysics of Shoc^ Wave and hign
Temperature hvoroovnamic Phenome na . Acaoemic Press, New
York , I'v&fi.
C5] Spitzer L., Physics of Fully Ionized Gase s , Inters cience,
New York, 1956.
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NUCLEAR MHD CONVERTER RD -12-01-FNPR 1 70
5 ELECTRICAL COND UCTIVITY EFFECTS
5.1 Symbols, Terms and Abbreviations
Electrical conductivity
Mc Mass of the superconducting coil
Pg Power generated by the ht-iD channel
oc Conouctor mean density
po Permeability of free space
J Current density
L Channel length
D Channel diameter
u Gas velocity
B Magnetic field strength
Ms Mass of the magnet structure
o Density of the structural material
st Working stress level of the structural
material
TI Gas temperature at the compressor inlet
0 Neutron flux along the duct
0o Neutron flux at the entrance of the duct
d Diameter of the entrance section of the duct
X Axial coordinate along the ductUe Electron velocity
Ui Ion velocity
E Total electric field
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Identificativodocument no
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1 72
Ti
a,b
no
i
nf
t
T
I-
a-
Temperature of ions
Coefficients in the rate equations
Number of primary electrons per unit volume
Ratio of no to Ng
Number of primary electrons per fission
Number of fissions per unit volume
Time
Time constant
Attacnment energy
Coefficient in the attachment equation
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5.Z Channel Charact eristics and Conduct ivity
To proceed further in the analysis, it is necessary to combine
conductivit y calculat ions with actual cnannel (ano nozzle;
characteristics. In fact, the results of the former depeno
directly on the latter, as channel and nozzle lengths, along with
the density distributio n of the gas flowing through them, are
required to solve the rate equatio ns (l)-(4; or (5)-(8) given in
section 4.4. Furthermore, the same characteristics influence the
distrib ution s of residual fission neutron s and gamma rays
available in the duct which, in turn, provid e the source of
primary electrons to be introduced in the rate eauatio ns. On the
other hand, the channel operating charact eristics ar e largely
dependent on the conouctivity levels assumed m tne analysis. For
this reason, a parametric approach has been aoooted, and the
generator perfo rmance has been estimated for two levels of
con duct ivi ty , nam ely (r=10 and (r=100 (iim;~^. The n ozz le ano
channel configurations arising from this process have been tested
to verify if they were consistent with the conduct ivity levels
resulting from the rate equations. Channel performance has been
evaluated under the following assumptions:
- Faraday configurat ion of the generator electrodes with a load
factor of 0.9;
- Straight channel with a constant aperture angle of 7*;
- Nozzle inlet temperature and pressure of 2300 K and 15 M Pa,
respectively;
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NUCLEAR MHD CONVERTER RD-12-01-FNPR 1 74
- Cnannel t'iow rate o-f 1000 Kg/s:
A 1-D tnermal--fiuia moael ot tne cnannel ana nozzle aucts has
Deen aoootea in tne analysis. For eacn o-f the two reference
levels OT conoLCtiVItv, a numoer o-f cnannel con-figurations nave
been comoareo as a -first aooroach oy using the soeci-fic ma ss
relation given DV Rosa in Clj tor a cnannel o-f length L and
oiameter D:
Mc lo oc L 1 1
F'Q UO J D F-g TTtrU'B -'*
where pc is tne conouctor mean Density and J is the current
densitv. Tnis relation gives tne mass o-f a suoerconauctin g coii
oer unit o-f oeneratec oower. In tne conaitions o-f the analysis ,
tne mass ot tne structure reauirea to noid the coil together
should be comoaraoie witn tne coil mass given by Ea. ^1> A lower
limit -for tne -former can be estimated witn the -following
relation:
M s = - j d v (2)
S t J ).'0
o
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wnere p is the density and st is the wo r H n g stress level o-f the
structural materi al. Tnis relation too is derived -from [IJ; tne
stru ctur e unit m ass -for a saadle coil is e;;Dectea to be witnin a
-factor 2 o-f tne val ue given by Ea. (2;.
In aaaition to tne two levels o-f conducti vity mentionea above,
the con-f igurations that have oeen investigatea ar s -featurea oy
Oi-f-ferent values o-f tne inlet M acn num oer ana ina uct ion t'lela o-f
the generator duct. The parameters assumeo in tne analysis enaole
to e-;tract o ower in the 110-15 0 MwJe ran ge, limiting the inauction
-fiela strengtn at reasona ole values (6 T at m o s t K ooserving the
constra ints on the length to diameter ratio imoosea oy heat ana
pressur e losses, ana oD taining a speci-fic mass u ro m Ea. i in
the ran ge o-f 10e -2- 10e -3 Kg/klve. Tnis range is in the reacn o-f
both re-ference level s o-f con ouct ivi tv: how eve r, a aecrease o-f cr
must be o-f-fset oy a co rre spo nai ng var iati on o-f otner terms in Ea.
ii). In partic ular, tne values ot u ana B are assumea as
independent parameters , while L/D and Fg ar e aeri ved -from tne
cal cul ati ons . It is evioent that a higher level o-f conou ctiv ity
ma^es it possibl e to attain the desired range of power aensity
with lower val ues o-f B and, esp eci all y, o-f u (and, hence , o-f the
Mach numoer at the generator inlet). This latter condition
appears to be o-f special importance, as a lower gas velocity in
the channel means a shorter nozzl e be-fore the chann el. On the
other hand, the distanc e between the generator and the reactor
cav ity ha s a strong in-fluence on the actual level o-f
conduct ivity. The results show that, i-f one pursues a high oower
o
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NUCLEAR M HD CONVERTER RD -12-01-FNPR 1 75
density condition (that is, essent ially, a high value o-f (ru2) ,
the system should work at a high conductivity , low velocity
condition, rather than the opposite.
It should be pointed out that sucn influen ce is not connected
with the effect of the field on the reactor core, which is
negligible, oue to the different order of magnitude of the
fission ion gyro radius in comoarison with their mean free patn.
In fact, tne nozzle length turns out to be of critical importance
because of the snaro decrease of residual fission and gamma
densities as a function of the distance from the reactor outlet.
Finally, a few consiaerations aoout the parameters adootea in the
analysis.
Tne value of nozzle inlet temper ature (2300 K) has been partly
assumed on the basis of material requirements, by analogy with
conventional MHD converters, and partly to maintain an adeauate
level of cycle efficiency with a high heat rejection temperature
(Tl=600-900 K, Tl being the compressor inlet temperature), as a
space-based system is expected to reouire. W i t h m this range of
Tl and with the other cycle parameters indicated m this section,
efficiency may vary between 0.12 ano 0.36, It should be stressed
that cycle efficiency is heavily mf lu en ce a by heat rejection
temperature and regenerator performance; both characteristics
should be ultimately selected on the basis of minimum system
mass, rather than maximum efficiency.
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NUCLEAR M HD CONVERTER RD-12-01-FNPR i 77
The nozzle inlet pressure (15 MFa^ is eaual to the average
operating pressure of the reactor , which was derived on the
basis of an average reactor temperature and density of 20 00 K and
0.3 g/cm-, respectively, Tne latter is the result of a
preliminary estimate of criticity. The same calculations gave the
cavity diameter (1 m) assumed in the neutron analy sis.
The flow rate of 1000 kg/s results from the power output to be
generated by the converter, assumed in the range 120-150 MWe
gross and 20- 30 MWe net. The latter is actually a lower limit
applicable to the highest rejection temperature assumea in the
calculat ions: the net output increases to 60-8 0 Mw when Tl is
lowered to 600 >-.
Tne temperature of the gas at the reactor inlet U 7 7 0 \ ) has been
obtained t hrough a preliminary an alysis of the working cycle, and
it IS typical of regenera tive Brayton cycles operating between
the temperature levels mentioned above. The same analysis gave
the referenc e value of 277 MW for the thermal power provided by
the reactor.
5.3 Fission and Gamma Density in the Channel
The fission and gamma power densities m the M HD expansion
channel must be estimated to solve the rate equations ana
evaluate the conductivity levels.
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Fission rower Density
Tne fission power aensity calculatio ns nave oeen carriea out D V
means of tne following approximations:
1. Preliminary evaluation witn a simpiifiea metnoa ^see he-f. L I J .
pag. 2 9 0 ) ,
2, SOuID- 360 L 3 ] Diffusion calculat ions witn a s i mon fi eo
two-aimensionai t -Z geometry ana walls faoricatea from AlZu 3
or BeO,
In oraer to e stimate tne power aensit v, tne auct nas oeen
oiviaeo into a f inite numoer of re gion s w itn aif-fe^ent u'b
aensitv (see Fig. 5.1 ana Fig. 5.1' .
For eacn region , tne fission macroscopic cross sections na^e
oeen oerivea from tne core cross sections calcuiateo aur-ing
Tasi- 1. reauceo oy tne appropriate density factors.
Tne neutron fiu;- level insiae tne fiMD cnannel nas oeen
calcuiateo as transmission tnrougn a cvlinaricai ouct.
Freiiminarv evaluation . Tne neutron flu;;es at tne inlet of tne
nozzle have oeen derivea from the nuclear analysis of Tas^ 1.
The effect of wall material reflections ana wor^lng fluia
absorptions have been neglected.
The uncoil I ded flui-'es along the duc t hav e been cal cui ate o
with the formula:
d2
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NUCLEAR MHD CONVERTER RD-12-01-FNPR i 79
where 0o is the flux at the entrance of tne nozzle, d is tne
diameter of the entrance section of the nozzle, and L is the
distance between the entrance of the nozzle ana tne point wnere
the flux IS calculated.
The results iheV/cm^s; are reportea in Tap. 5.1.
D iffusion Calculations. In oraer to estimate tne influence of
wail material ana tnlc^ness on fission power aensit y. a secona
analysis of tne MriD channel has been carriea out bv tne
50LIID-360 diffusion code, using the R-Z geometry to model tne
Power C onversion Unit (gas reactor + nozzl e and MriD channel) , and
the cross sections derived from Task 1,.
The configuration extends radially to m cl u a e tne mcvaDle
reflector and axially from the core midplan e to 1200 cm in the
cnannel (see Fig. 5, 2) ,
As to the spatial discre tizat ion, 114 axial ana 37 radial
meshes have oeen used.
The ouct nas been divided into 9 regions witn different UF6
oensi t ies c a m e o out f rom Fig , 5 .3.
The nozzle ana channel walls have been assumed to be faoricatea
from A1203 or BeO, For each material, two values of wall
thickness have been examined: 3 cm and 6 cm. The adoption of a
two-dimensional model doesn't account for the presence of the
electrodes. However, it shouldn't be unreasonable to assume an
electrod e wall consisting of thin electro des mounted on thick
insulating blocks: furthermore, the electrodes themselves might
So
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NUCLEAR M HD CONVERTER RD -12-01-FNPR 1 80
be fabricated from zirconia based materials, ana zirconium
possesses favourable properties being a low capture cross-section
material, which would allow to exploit the potential of a
moderating layer.
As previously mentioned, the calculation s have been carried
out by using the cross section data from Task 1. collapsed
to a 5 group structure.
Tne fission power for each region is snown m Fig. 5.4. Tne
results of the cases e;>aminea ar e reoortea in Tab. 5.2.
Gamma Power Density
Tne gamma fluxes in tne M HD channel have been calcuiateo by
the MERCURE IV point kernel code C4 ].
The gamma source, consisting of fission gamma, is located in the
core.
Build-up factors have been used in the MERCURE calculation.
The geometry of the analyzed configuration is shown in
Fig. 5,1,
The core has been divided into 3 regions and the duct into 6
regions with different UF6 density.
Region-wise UF6 D ensities in the duct have been carried out
from Fig, 5,3,
The nozzle ana channel walls are assumed to be fabricated from
A1203 material, but they have not been taken into account for
streaming calculations.
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Tne calculatio ns have been performeo by using the BIF GZ
library cross section data from Ref. [5 ],
The results are reported in Table 5,3.
5.-i Condu ctivi ty Calc ulat ions
A Felation for Conductivity
Owing to the rang e of gas transit time in the channel ( 10
ms) and to the very small Deb ye length compared with th e
dimensions of plasm a, tne motion of both charged species can oe
described by neglecting the convecti ve De rivatives of the
velocities and assuming the neutrality conaition ne=ni .
Therefore, the velocities Ue and Ui are given by C6]
eE kTe graa(n)
Ue = - (1)
mVet mVet n
eE kTi grad(n)
Ui = (2)
MVit MVit n
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O T B - =
where the symbols have been previou sly defin ed. The internal
field IS obtained by eauating the flu,;e5 of ions ana
electrons, m accoraance with the neutrality condition. It turns
out that in the absence of an external field, the current is
zero. The internal field is given by
Di-De graa(n)
pe+pi n
where Dj=kTj/mjVjt is the diffusion coefficient and pj=e/mjVjt
is the mobility. T herefore, current density becomes
e=n
J = en(Ui-Ue)= e=n(t.ie-t-pi >Eo = Eo (4)
mVet
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NUCLEAR MHD CONVERTER RD-12-01-FNPR i 83
wnere the mobility of ions nas been neglected, because of the
very small mass ratio. By using the same notation s, the
conductivity is given by
e-RTs- '
(T = (5;
mCcTs^(l-R)-^R/t>
l+3.10e-4Ts=
Sa
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NUCLEAR M HD CONVERTER RD-12-01-FNPR 1 84
IS verified. In case of total ionization (R=l), the
cond ucti vity is simply equal to 10e2Ts ''= , If Ts~1 0 eV, a degree
of ionizat ion of 107. is sufficient to gi ve (r=3.10e3 (ftm) .
Numerical Results and Discussion
The system of Equatio ns (5)-(B) derived in section 4.4 has been
solved bv the Runge-Kutta fourth order method. The initial
conaitions are Tp=500 eV. Ts=l eV, Ti=0.5 eV and R=0. Tnev
correspond to typical mean values: however, the stationary
values don t deoend on the initial conditio ns. The a and b
parameters m Ea.(8) ar e chosen on the basis of data available
m literature, namely a=10e-6 and b=10e-2 2 (cgs units). Tne
value of b is probably more realistic than tnat given previously:
in any case, an overestimation of the recombination rate gives
the lowest limit of achiev able ionization . The ionization
potenzial of UF6 is =-15 eV. The thermali zation coefficient
IS 10e4 (cgs units). The initial rate of primary electro ns /3
IS relateo to the number of fissions i.e fl=5n f/Ng,
where represents the number of 500 eV electrons per fission,
whose value has been estimated at 4.10e5. Figures 5.5-5,7
show the time evolution of temperatures and degree of
ionization at different initial gas de nsit ies. It has been
assumed fi=10 e-2, that corresponds to nf=2.5elO-8Ng,
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NUCLEAR M HD CONVERTER RD-12-01-FNPR i 86
fission react ions , plavs a relevant role. If an initial rate h
of lOe-3 and an initial density of 3.10el8 molecule s/cm are
assumed, the stationary values become Tp=21 eV, Ts=Ti=2 .4 eV ana
R=0.01, I.e. (T =2. 10 e2 (sim) insteaa of 3.10e3, if the initial
valu e of (5 IS lOe-2,
The distributio n of fission rate in the cnannel is very
important in order to maintain suitable condi tions for MriD
conversion. In fact, if the ionization source stops at a time
to (eauivalent to a sharp cut in the spatial distribution at
xo=Vg.to), tne furtner evolution of the ionization rate R is
given by
dR bNa'-R-
dt Ts'' =
the secondary electrons being too cold to sustain the ionization
level. This equation can be integrated by assuming as initial
values those determined, in the stationary state, by the fission
source. Thus, the time evolution is represented by
R=Ro/(l+t/T) ''=, where T=Ts''''=/2b (RoNg) .
By introducing the data of Fig. 5.6, R is reduced by a factor 10
in 0.05 ps. It results that m the absence of a ionization
source, the conductivity drops quickly to unsuitable values.
Tne time benavior of temperature s ana ionization .rate
greatly simplifies the analysis of the fuel chemical composition,
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NUCLEAR MHD CONVERTER RD-12-01-FNPR l 87
with special regard to the formation of negative ions and to the
contribution to ionization of the species arising from UF6
dissociation . D issociation is important from the point of view
of the effective neutral densitv. Reminding the results snown
in Fig, 5.8, an increase of neutral density due to dissociation
does not aiiect dramatically the relevant parameters. On the
contrary, if the initial densitv is 5,10el7 molecules/cm~, as
it could be expected curing the gas expansion in the MriD channel,
a growth of a factor 7, due to dissociation and subsequent
ionization, could lead to an improvement of the final degree
of ionization and tempera tures, whose values should
approximat e those of Ng=3,5 ,10el8 molecules/cm^ (see Fig, 5.6/.
However, according to the measurements of Compton C7 ], the
thresholds for the formation of UFn+ type ions by electron
impact ionization ar e respect ively 14 eV for UFS-f, 18 eV for
UF4+, 22 eV for UF3+, 26 eV for UF2+, 32 eV for UF+ and 4 0 eV for
U+ . Since the stationary temperature of secondary electrons and
ions IS in the range of 5 eV, relevant contribut ions can be
only expected from UF6 and UF5.
The influence of the formation of negative ions on the
conductivit y can be estimated by simple argumen ts. The affinity
potential is around 5 eV with a cross section of 3 A= C7D
(the behavior is similar for UF 6- and F - ) . By averaging over a
M axwell distribut ion, the contribution of attachment in
Eq.(8) can be expressed as
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