MHD COMPRESSOR-EXPANDER CONVERSION SYSTEM INTEGRATED WITH A GCR INSIDE A DEPLOYABLE REFLECTOR

8/12/2019 MHD COMPRESSOR-EXPANDER CONVERSION SYSTEM INTEGRATED WITH A GCR INSIDE A DEPLOYABLE REFLECTOR

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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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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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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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- 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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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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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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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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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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Proget toproject



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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


36/115

ProgettoprO)Cl


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


37/115

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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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


39/115

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.


40/115

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


46/115

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


47/115


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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



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.


50/115


51/115

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


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) .


53/115

Pro getto Identificativo Rev Paginaproject document no rev .paoe


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


54/115


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Progetto Identificativo Rev. Pagmaproject . , _ , _ . _ . _ . _ . _ document no rev page


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

8o


56/115


57/115

^'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


58/115


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Pro ge tto Identificativo Rev Paginaproiecl document no rev page


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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Pro ge tto Identificativo Rev Pagmaproject document no rev oaae

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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Prog etto Identificativo Rev PaginaP'OI'Ct unnivno ttun oo nr i7 r.Tr . r. documen t no _ r ev page


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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Pro getto Identificativo Rev Pagmaproject document no rev oaoe


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:


63/115


' ^ " " ' 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


64/115

Pro ge tto Identificativo Rev PagmaP'dject . , _ , _ . , . , document no re v page


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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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)

8o


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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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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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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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Rev Pagmarev page

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

8o


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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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- 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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NUCLEAR M HD CONVERTER RD-12-01-FNPP i 75

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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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.

8o


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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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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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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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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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8/12/2019 MHD COMPRESSOR-EXPANDER CONVERSION SYSTEM INTEGRATED WITH A GCR INSIDE A D

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MHD COMPRESSOR-EXPANDER CONVERSION SYSTEM INTEGRATED WITH A GCR INSIDE A DEPLOYABLE REFLECTOR