C A L C U L A T I O N OF T H E N E U T R O N FLUX DISTRIBUTION IN T H E EBWR CORE SHIELDED BY W A T E R , IRON A N D

C O N C R E T E

WILMA SONIA HEHL

Publicação i E A N . ° S5 Dezembro — 1964

INSTITUTO DE ENERGIA ATÔMICA Caixa Postal 11049 (Pinheiros)

CIDADE UNIVERSITÁRIA "ARMANDO DE S A L L E S OLIVEIRA" SÃO PAULO — BRASIL

CALCULATION OF THE NEUTRON FLUX DISTRIBUTION IN THE

EBWR CORE SHIELDED BY WATER, IRON AUD CONCRETE (*)

Wilma Sonia Hehl

Reactor Engineering Division

Instituto de Energia Atómica

são Paulo9 Brasil

Publicação lEA ns 85

December - I964

[*) Work done in I 9 6 I under the direction of ProfoMoGrotenhuis

of the IINSE of the Argonne National Laboratory - U3AEC -

- UoSoAo

Comissão Nacional de Energia Nuclear

Presidentes Profo Luiz Cintra do Prado

Universidade de São Paulo

Reitors Profo Luiz Antonio da Gama e Silva

Instituto de Energia Atômica

Diretor? Profo Romulo Ribeiro Pieroni

Conselho Técnico-Científico do lEA

Profo Jose Moura Gonçalves ) ) pela USP

Profo Francisco João Humberto Maffei )

Profo Rui Ribeiro Franco ) ) pela CNEN

Profo Theodoreto Holo de Arruda Souto )

Divisões Didático-Científicas5

Divo de Física Nuclear? Prof» Marcello DoSo Santos

DiVo de Engenharia de Reatoress Profo Paulo Saraiva de Toledo

DiVo de Ensino e Pormaçãos Profo Luiz Cintra do Prado

DiVo de Radioquímicas Prof, Fausto Walter de Lima

DiVo de Radiobiologias Prof, Romulo Ribeiro Pieroni

DiVo de Metalurgia Nuclears Prof» Tharcisio D„Souza Santos

DiVo de Engenharia Químicas Profo Pawel Krumholz

SUMlRIO

Neste estudo o reator EBWR foi considerado operando

a 1 0 0 Mw e com uma blindagem de 28^6 cm de água, 1 0 cm de fer

ro e 3 0 0 cm de concreto» Uma esfera de igual volume ao do ca­

roço, de 7 5 cm de raio, foi escolhida como a melhor geometria.

Os cálculos dos fluxos rápido e térmico foram baaea

dos na teoria de dois grupos, e executados em máquina de cal­

cular de mesa e em um computador digital I B M - 7 0 4 o

O método utilizado é exposto e os resultados obtidos

são apresentados sob forma de tabelas e gráficos,,

SUMMARY

In this study the operation of the EDWR at 1 0 0 Mw

when shielded by 28o6 cm of water, 1 0 cm of iron and 5 0 0 cm of

concrete was consideredo The equal-volume sphere core, with a

radius of 7 5 cm was chosen for the study as indicated by cal£

ulations for the best core geometryo

The fast and thermal neutron flux calculations were

done by two-group analysis. Calculations for the latter were

made both by hand and by computer.

The procedures followed and the calculations made in

connection with the study are explained, and the results are

tabulated and plotted,

RESUME

Dans cette etude on a pris en consideration 1'opera

tion du EBWR à la puissance de 1 0 0 M?/ et avec une protection

par 28 , 6 cm d'eau, 1 0 cm de fer et 3 0 0 cm de bétouo Un coeur

d'égal volume, en sphère, avec un rayon de 7 3 cm, comme indi­

qué par les calcus de la meilleure géométrie, a été choisi pour

la réalisation de cette étude»

Les calculs du flux neutrons rapides et thermiques

ont été effectués par la théorie de deux groupes, autant a

main, comme aussi à l'aide d'un computateur I B M - 7 0 4 »

Les procédés suivis et les calculs faits, pour cet­

te étude, sont expliqués, et les résultats résumés par des ta

bleaux et des graphiques»

QMJsmATim OF THE •iJiEB!iaQi;_Eiax mm&sm$M EBM com swmmB BI wAfEi.« IE«

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shleldaa b y 2Q,6 em o f ' r a t e r j , 1 ® cm teoa m f l l e o . e © . eoq^'

S ims o f T3 em choseB for the s t u d y a s i M i e s t a i Is®?-erf-effila*?'

tioos for t h e b © s t core g e c m e t r j o

saade bo-te b f hand and hj computer,,

& e p r o c e d t i r e s f o l l o r e i , and tSs® e a l e i s l a t i o n s m d e l a

e o a a e e t i o n •ri.tSi t h e s t m d j a r e © s p l a l a e t j a a d t h e r e s i i l t s 13?® t a b u l a t e d and p lo t t ed , , ,

•by 5o-T5 i a c h © s i a cr©ss<=sect i®H aad lAth aa a e t i v e h e i ^ t of h-

.fto A p p s m i m t e l j 2©^ o f tJa@ a s s e A l i e s a r e s p i k e d (AM. 5T81

Addend™), tta e a l c x i l a t i o n s f o r •fee I»©HK>VB1 c i ^ s s » ® e e t i € M fes-

of t h e msi o f th© A r g o m e l a t i o n a l I a f e ® r a t©2j »' OSffiS-?

2 c

the various coiBpoMeats ©f the fuel elements, made in aeeordance

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AERE-I^2l6 - "Bfethods ©f eaXevdatioii for Use in the Besign

of Shields for Power Reaetors"

NM<»SR -2380 » "Application of Past Neutron Removal Theory

to the Calculation of Thewnal Neutron Flux

Distributions Im Reactor Shields"

: Prices Bo To, Go Co Hortoa and Ko To Spinney, "Radiation

Shielding", Interssational Series of Mono -

graphs on Nuclear Eaevg^g Pergamon Press

igave the following value ss

c/ CHg©) = 2 o 9 9 bams

< ( ¥ ) = 5 « 6

C CZr) = 1 . 9 6 9 4

(T CNb) = 2 . 0 © 6 5

o (Ca) = l o 9 7 1 9

^ (Fe) = 1 . 8 6 1 4

Bemovail cross-sections for the fuel elements were then

determined^ using the data Ijadicated in Table 1 » which yielded

values as follows?

Thin Elements

Enriched ¿ 7 = © . 1 1 1 cm~^

Natural r = © . 1 1 1

Thick Elements

Enriched Z'x = © . 1 1 5

Natural T = 0 . 1 1 5

Spikes 21}, = 0O094

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MEMGD 1

lo The f l B X at the first interface was determined^ using a cross" section H^^^ and the formula

6(0) = li. 4- « 1. y/wh*

2 o Using the same formula and a cross"section Z" ^ for the en­tire region from the core center to the second interface^ a cor­responding value of flijx at the latter point -was calculated.

3 a Similarly^ a flxix calculation was made again for the first interface^ this time using a cross-sectio?i .

ko The effect of the imer sphere^ when treated as having a cross-section of on the flux at the second interface was cal­culated.

5 o The valme found from Step h w&s subtracted from the value ob­tained in step 2 to give the correct xmlns of flux at the second interface.

60 For the other succeeding interfaces^ a similar procedure was followed, whereby the effect on the flux at the outer face o,f a shell by the sphere within the shell is taken into account.

7 o The flux at the edge of the core was finally determined by summing up all the contributions of partial fluxes at the inter­faces, considering the corresponding attenxxations.

METHOD 2

lo The flux at the first interface was determined using the fojrmula

6 . 1^1 i

2 , The eoHtrlbution of the flux found from Step 1 to the flux at the edge of the core, considering attenuation, was calculated us­ing the formula

#1

3a The second region (spherical shell) -was taken as a finite slab source and the fltsx at the second interface ealcmlated from the formula

2li

edge of the core was detenniaed using the fornnala

5 . A similar procelure Vas folloij'ed for the other regions, and the flux at the edge ®f the core ims determined by adding a U the contributions of the partial fluxes from eaeh region.

METHOD 3

1 . The core -ms treated as a homogeneous sphere with an average removal cross-section^ ^ 0 . 1 1 0 cm"" and an average source strength q" - T « 5 3c 1 ® n/em^ X see..

2 . Th^the flux at the edge of the core was determined from the formula

X hJU.

Power and source strengths for the various core regions were ealctilated from the curves of Figs. 1 and 2 , which give values as follows;

7 .

TABLE 5

POWER M D SOUKGE STRENGTHS FOR THE VARI0XJS CORE REGIONS

Region Power P. (watts) Sotirce Strength Q. (n/cm^ ^ ^ X see)

1 O o 2 8 l x l 0 ® 1 . 2 7 X l©-"- 2 0.405 1.11 3 0.205 0.52 k 0 . 1 1 1 0.10

The resialts of the calciolations based on the t^ee methods are tabulated below.

TABLE k

^AST NE0TRON FLUX AT THE EDGE OF THE CORE FROM EACH CORE REGION

Region Method 1 Method 2 Method 3 (homogeneous core)

(0 in n/cm^ x see) 1 7 . 7 6 x 1 0 ^ ® T .76 X lo-'- 2 k.jk X 10-'--'- 5 . 3 5 X 10-'--'-5 8 ,32 X lO-'-'- 9.42 X lO-'-'-4 3.90 X 10-^^ 4.20 X 1©- ^

Total 5 .28 X 10 "= 5 .75 X 1©- '= 5.20 X 10" ^

FAST NEUTRON FLiX DISTRIBUTION IN THE RADIAL SHIELD

The flux based on a homogenous core was chosen for these calculations, with the flux distribution throughout the shield being determined from the formula

8.

and the following datas

1 2 T ,5 X 1©

fast neutrons/cm^ x © o i l © em"-"-

Is - 73 cm ^ 1 = 1

©.121 0.129 MA=SE.238©

<= ©.©91 J

The resulting flux at the homdary of each shield is given in Table 5* and the distribution is plotted in Fig. 4.

9 .

SKEELDIKG GOHFIGURATIOW

Dimensions;

1 . Diameter of pressxii*e vessel 8k inches

2 , Inner diameter of reflector 80 inches

5o Outer diameter of core 57»4 inches

4. Thickness of H^O reflector 28.6 cm

5« Thickness of Fe 10 cm

6. Thicskness of concrete 300 cm

Pressure vessel

Core Concrefe

.9

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• A ^ .• 0

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t

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TABIiE 5

2 Fe 10

Concrete 3©© 0 . 1 1 2 2.7© x lO"^

©.168 2.42 X l©""-'

THERHftL. MEUTRON FLUX AT THE EDGE ©F THE C0EE

By use of the formula

and an average thermal neutron flux value of

and likewise values of

(jv M. 9«5 (arbitittry units) ^* ^ l 8 . ® 5 (arbitrary units)

from the reactor core calculations (refer to Figs, 1 and 2 ) , the thermal neutron flux at the edge of the core was ealctilated to be

THERMMi HEjlRQN FL0X DISTRIBIiTI©N IN THE SHIELD

Tiible 6 lists the comstemts liised in the calculation by hand of the thermal neutron distribution.

FAST FLUX AT THE BOHiMRT ©F EACH SHIELD

Material Thickaess Reinoval Cr©£S-section Fliax 0 (cm) (cm" ) (n/em

X see) Core 73 0*11© H^0 28.6 - 1 .98 X l©-'-'-

.0

1 1 ,

TABEE 6

Fe Concrete

0,22 0o64 0,379

© o 2 4 6

0 , 3 ^ 5

00 418

0 . 1 7 8 0

0 . 2 1

G . 1 2 3

The thermal flixx distribution calculation by hand was made using the formula ^ | r. j,.

0

Taking r . 'l "t*; (0) then

Boundary conditionss Each region was taken as infinite! then

. The B^ and values obtained by the above calculations are tabulated below.

T A B L E 7

V A£0E S CSF B ^

Material H^O Fe Concrete

C: AND THE FLUX AT TIE EDGE OF EACH SHIELD MATERIAL B. 'i 0 (n/em x sec)

= 1 . 3 9 5 X 1 0 " ^ ^ 1.41 X 1 0 - ^ ^ 6 . 0 9 X 1 0 " ^ ^

4 5 « 7 6 X l©-"- 3 o 3 0 X lO-"-*- 4 . 9 4 X 1 0 - ^ ®

- 5 . 8 0 X 1 © ^ 5 o 5 2 X 1 0 - ^ ° 5 o 0 8 X 1 0 " ^

The distribution curve is plotted in Fig. 4,

TABLE OF GONSTAMJS FOR THERMAL HEUTROK CALCULATION

Material K D (slope)

12 „

2.

5-

A J^^^ R A ft r r -"' i .'. /íiA f \ a A," Bâ^Cg-Cie

t

S2

i i Õ

Ml -Hill - 1

MA t* ^ V . V l

1 3 .

The mLmes obtained for and B ^ from the determinants are in Table 8»

TABLE 8

VAL0ES OF A^, B^ AHD THE FLUX AT THE EDGE OF EACH SHIELD MATERIAL

Material A^ 0 (n/cm x see) Q 15 1 2 HgO - 7.25 X 10^ 1,397 X 10 2 .29 x 10

Fe 4 1 .08 X 10^ 4 2.32 X l©"'- 4.52 x l©"""® Cencrete - --9.24 x 1©^ 5.©8 x 1©"^

The thermal flux distribution curve for this latter case (taking two regions together and assuming idie first one finite and the second one infinite) is also plotted in Fig. 4.

Neutron Flux Calculation By Computer

The calculations for the thermal neutron flux were done by computer, using IBM-704, Code RE*34, Calculations were made for slab geometry, teOcing the slope of fast neutron distribution. They were etlso made for sphere geometry, taking both the slope of the fast neutron flux and the removal cross-section, (Refer to the attached programs.)

The results are plotted in Fig, 4.

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Fiq 3 CORE LOAD INS

le Mo Grotenirals, "lÄetm-e lotes on Reaetor Shielding", AHL * 6 0 0 0

2o E» Ao Wlnranc, JoMo Iferrerj, "laaards Eimlmtion Report Associated with the Operation of EBIE at 1 0 © MSf, AHL^ - 5 T 8 1 , Addendum

5 o Fo Co Hard-te, To Ao Laiaritisen, DoPo Moon, "Calculation of the HeutroB and Gamma«Raj Mstributlon in EBBK Radial Sibleld

4 o Ao Fo Avery, BoE« Bendall, Jo Butler, KoTo Spinney> "Methods of Calculation for use in the Design of Shields for Power Reactors", AERE=R32l6

BoTo Price, GoCo Horton, KoT» Spinney, "Radiation Shielding" International Series of MonogTafs on Nuclear Energy, Pergamon Press

6 „ DoSo lunean, Ho©.. Whittum, Jr«, "Apilieation of Fast Neutron Removi^ Theory to the Calculation of Thermal Neutron FlUx DiBtributionB in Reactor Shields", NAÄ-SR -258©

7 « MoKo Butier, JoM» Cook, "RE-5 4 , AM IIiä*704 Rfeactör .^elding

8 o Handbook ©f Chemistry and Physics, 5 7 t h Edition

ACKNOWLEDGEMENTS

Tke study and corresponding calculations were .nsade during ittie 1 9 6 1 Spring Term of the Interhatiohal Institute of Nuclear Science and Engineering of the Argonne National Laboratory, in cojinection with ray appointment as Participant in that Term.

I wish t© thank Prof« R«Go Taecker, Director of the IINSE for the arrangentents made to me to allow the furthei^ce of my train* lag in the field of reactor shieldlngo Allow me to thank Professor Ho Grotenhuis, Professor of Reactor Shieldi^, in particular for his most understanding help and guidance, and the IINSE fcir making available the necessary facilities aad also the assistance by many members of the Sts^ of the Argonne National Laboratory.

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