CF-53-9-84 by Jon Morrow

F r c a %TaderWa,Director

Beactor Technology eomists of two aemsters of f o r W e o w s e i n s t r u c -

tion, followed by ten weeks given t o r e a c t o r design s t u d i e s .

These

s t u d i e s provide each s t u d e n t as1. sTprsrtunity of applying t o a s p e c i f i c

t o include mi3 of the ~ m i o u sengineering professions and s c i e n t i f i c f i e l d s i n much t h e

p a t t e r n found i n a ty-picetl reactor p r o j e c t .

T h i s report is based on the s t u Q made! by its authors w h i l e !

they were students i n the 19521-33 session of ORSORTe the report prepared in t a n weeks.

spent,

WEZB

made and

Obarious%y those weeke were diligently

Even so it woviLd be zanroeasr>nab%e to expect t h a t %he studs

repasted hem i s either definitive or free of defect i n Judgemmt.

The

f a c u l t y and many, perhaps all of the studenks m e comineed that the p r o j e c t w e l l serve& i t s peaagog3ca2. purpose,

received f ~ o its a consultant, E.. â&#x201A;Ź3, Ham.

-3

The report i s published

This group wishes t o excress i t s appreciation t o the members of the CRSORT f a c u l t y who presented the i n f o r m a t i o n which served as the technical background f o r %his study.

a l l members o f %he Oak Ridge ANP group

Thanks are also extended to foy their invaluable

assistance, p a t i e n t consul%ation and e o r d i a l h o s p i t a l i t y . For hPs gaidance and assistance. t h i s g m u p expresses i t s appreciation t o the group a dvisor , E, R , Nann.

Particular thanks

are also extended t o If. F. Poppeirdiek who n:ade the f l o w experiment possib7.e and to A, I I . Fox foy Of'

the reactor.

his guldmce

Q~I

tbE

nucle81" aepeets

Pwe

39 39 40

Faw 1

Typical. keff vs. Uranium Mass Curve

Cheracteristic Self-shielding Factors

Thermal U t i l i z a t i o n Curves f o r C y l i n d r i c a l

19 20

fie1 Tubes Nuclear Approximation of the Screwball.

Ga?ms Heating Uist r i b u t i o n

Over-all Heat Transfer C o e f f i c i e n t vs.

NaOD V e i o c i t y

. NaOD

Ternperatui,e Varfijltions Thuou@~t h e Core

Reflector Powep. Absorption Curve

Photograph o f the Flow Experiment iipparatus

Shield Weight C u ~ v e

1.4

C r i t i c a l Detezminarzt

Ne013 Heat T r a n s f e i - C o e f f i c i e n t vs Velocity

INTTtODUCTION The objective of t h i s p r o j e c t was t o apply the t h e o r e t i c a l

information psesented a t ORSORT to the d e s i g n o f

reflector-

moderated, c i r c u l a t i n g f u e l , aircraft r e a c t o r . . The seope of t h e i n v e s t i g a t i o n was l i m i t e d primarily t o

an analytical evaluation, although a minor f l o w experiment was perf omed Thfs design study has been l i m i t e d to the r e a c t o r ;

propulsion system has not been considered.

the

I1 SrnmRY A preliminary f e a s i b i l i t y skvtdy o f a 200 MW r e f l e c t o r moderated,

circulating fuel

atrcraf'c, r e a c t o r i s presented

The Screwball

' core

configuration as p r e s e n t l y conceived c o n s i s t s o f : 1) A spherical s h e l l beryllfum r e f l e c t o r

2) APE type f l u o r i d e f u e l i n h e l i c a l tubes arranged i n annular form

3) NaOD moderator and r e f l e c t o r coolant I n an attempt t o j u s t i f y t h e use

o f fuel tubes, an experimental

i n v e s t i g a t i o n o f the flow i n a model h e l i c a l Lube was conducted. The r e a c t o r a n a l y s i s was conducted on a Luo group, t h r e e region basis.

Tne nuclear c r o s s s e c t i o n s were a p p r o p r i a t e l y weighted and

judiciously appllied s o t h a t t h e r e s u l t s compared favorably with t h e multi-group machine c a l c u l a t i o n s

The r e a c t o r presented i s believed t o he conservative and appears t o be f e a s i b l e .

'The fundamental l i m i t a t i o n i s t h e 1250째F maximum. w a l l

temperature toc prevent, excessive NaOD corrosion.

Large NaOD f l a w i-abes

and m p l e flow guidanw: are require6 t o minimize corrosion.

If t h e

c o r r o s i o n limit can be r a f s e d , Vne use of NaOD as moderator and coolant has grea'ter p o t e n t i a l

Helical fuel tubes a m recommended t o reduce the u n c e r h i n t i e s of

unstable flow i n high power-density r e a c t o r s ,

!he engineering

complexities introduced by t h e i T use are just,i f i e d f o r c o n t r o l l e d flow

The r e a c t o r descrfbed i n t h i s r e p o r t w i l l be c a l l e d t h e PsScrewba31.tt ( t h e F i r e b a l l with a new t w i s t ) .

III GEHhTAL PLANT DESIGN 3 J . General Description The Screwball i s a sphesical., r e f l e c t o r moderated. c i r c u l a t i n g fuel reactor.

The f u e l e n t e r s t h e core a% t h e north pole ant3 flows

downmrd through six 3.5 inch I .De inconel t u b e s ,

Five of these tubes

a r e wrapped i n a variable p i t c h helfx t o f o n a spherical annulus of f u e l and t h e s i x t h tube passes through t h e centavr o f t h e sphere forming

a h e l i x of smaller diameter.

See F i g w e s 1 and 2.

In returning t h e

f u e l flows over Hair cooled %ubes i n t h e primary h e a t exchanger which is wrapped i n a s p h e r i c a l annulus surrounding the beryllium r e f l e c t o r .

The beryllfum r e f l e e t o r has t h e form o f a s p h e r i c a l s h e l l with h o l e s a t t h e north and south poles f o r e n t r y of t h e f u e l tubes.

Sodium deuteroxide

flows downward through the s p h e r i c a l c a v i t y f n t h e beryllium and surrounds t h e h e 1 tubes, hence functioning as a moderator t8island". The NaOD r e t u r n s t o t h e top through 0,23 inch dfmeter h o l e s d r i l l e d i n t h e r e f l e c t o r and through a s p h e r i c a l cavity o u t s i d e %he r e f l e c t o r thereby removing t h e h e a t produced in %he r e f l e c t o r ,

The NaOD then passes through

a h e a t exchanger and i s pumped hack through the core, The intermediate heak transfer medium, NaF, r e t u r n i n g from t h e propulsion system passes through the sodium deuterox5.de h e a t exehanger and then through the primmy h e a t axchanger,

This system uses only one

intermediate h e a t t r a n s f e r medium and eliminates t h e n e c e s s i t y o f a d d i t i o n a l r a d i a t o r s f o r subcooling n p o r t i o n o f t h e EaK as proposed f o r the Fireball.

However,

control. system

required which will keep the

r e t u r n HaK temperature constan%, If -the te-tperature rises, the NuOD w i l l

be i n s u f f i c i e n t l y cooled and exeesslve eorrosion nay r e s u l t ,

-9-

A t return

I 4 f

a t

u.9

FUEL IN

temperatures below 900째F., t h e fuel w i l l fyeeze i n t h e primat-y h e a t T*dith i t s idi.:rent s i m p l i c i t y , the use o f a s i n g l e t r a n s f e r

exchanger,

inedjum warrants furtiiier i n v e s t i g a t i o n ,

Figu-e 1 i s a rh-awing o f t h e

Scrwdmll system, and a t a b u l a t i o n o f design d a t a i s contained i n t h e Appendix 1,

3.2 Design Philosophy A byief survey o f NEPA, erJP, R, K . Ferguson, and Technical Advisory Board r e p o r t s indicated t h a t homogeneous r e a c t o r s held the g r e a t e s t p o t e n t i a l f o r e f f i c i e n t nuclear propelled f l i g h t .

Since l i t t l e information

i s a v a i l a b l e on a combined hydroxide of l i t h i m and sodium ( t h e rnost obvious candidate f o r a high temperature homogeneous r e a c t o r f u e l ) t h e c i r e u l a t i n g f u e l type r e a c t o r was chosen as an intermediate s t e p between f i x e d fuel elements and the homogeneous type f u e l .

The l a r g e h e a t t r a n s f e r s u r f a c e

r e q u i r e d i n fixed f u e l reactors i s removed from t h e

COTE

in c i r c u l a t i n g

f u e l r e a c t o r s and t h e p o t e n t i a l s i m p l i c i t y o f homogeneous r e a c t o r s i s retained

Thc moderating propest2es o f t h e uranium b e a r i n g

fused sal t s

are generally p o o r , but employing t h i c k , e f f i c i e n t r e f l e c t o r s enables t h e construction of a small high power reactor.

Waving chosen a r e f l e c t o r moderated, c i r c u l a t i n g f u e l tyye i e a c t o r ,

a more d e t a i l e d i n v e s t i g a t i o n vas f n i t i a t d on t h e Fireball as described i n Reference 2,

I n v e s t i g a t i o n o f t h e F f r e b a l l design parameters yielded t h e

following f i v e problems which appeared t o warrant basic design changes o r modificatfons:

1, El& 2

power d e n s i t y

Questionable fuel f l o w p a t t e r n s

3 - P o s s i b i l i t y o f pl-essure surges

Cooling t h e Be "island"

Self-shielding i n t h e f u e l

The Screwball e l i m i n a t e s o r reduces t h e magnitude of each o f t h e s e problems except presswe surges.

To achieve these ends compromises

i n s i m p l i c i t y and r e a c t o r s i z e have been made;

however, t h e increase i n

s h i e l d weipht over the 22.5 inch core is less t h a n 10%.

I t is believed

t h a t t h i s reactor has a real p o t e n t i a l f o r aircraft a p p l i c a t i o n , and as such warrants f u r t h e r i n v e s t i g a t i o n , The c o n t r o l l a b i l i t y of a high power d e n s i t y r e a c t c r has been n e i t h e r

proven n o r disproven,

E. R. Mann states t h a t c o n t r o l l i n g a r e a c t o r i n which

t h e f'uel temperature rise i n t h e core exceeds 2000째F. p e r second w i l l be d i f f l c u l t and somewhat doubtful.. To be more conservative: a power d e n s i t y

o f 3.5 KW/m (1O7O0F. per second) bas been chosen f o r t h i s r e a c t o r .

W i t h such r a p i d i n c r e a s e s i n fuel temperature only short l i v e d flow i n s t a b i l i t i e s o r eddies can be t o l e r a t e d i n t h e fuel.

Tke use o f f u e l

tubes i n t h e Screwball has greatly reduced t h e u n c e r t a i n t y o f s u s t a i n e d i n s t a b i l i t i e s fn %he fuel region.

A b r i e f q u a l i t i v e experkent v a r i r y i n g

s t a b l e florcr through h e l f c a l pipes i s described i n Section 6 * 3 *

Pressure surges result from r a p i d d e n s i t y changes due t o temperature varTations which occur i n eddies of lengthy d u r a t i o n , o r froxi t h e instantaneous i n t r o d u c t i o n o f a c o l d s l u g o f fuel.

A s t e p decrease i n

temperature i s d i f f i c u l t to v i s u a l f a e i n a c i r c u l a t i n g fuel r e a c t o r . Pressure surge c a l c u l a t i o n s have been made on t h e Fireball assuming stagnant fuel i n t h e core and a s t e p f n c r e a s e i n

k of 1% throughout t h e core.

These assu=flptions are both conservatfve s i n c e n e i t h e r condition i s l i k e l y t o QCCW

i n the reactor.

Based on t h e s e assumptions t h e r e s u l t i n g pressure

-13-

surge i s not expected t o exceed 150 p s i . .

A s a r e s u l t o f the more

tortuous expansion path out o f t h e cope, pressure surges i n t h e Screwball alee expected i o be l a r g e r .

However, Yne f u e l tubes i n t h e

Screwball w i l l withstand preasures o f 200 p s i and no d i f f i c u l t y from t h i s phenomenon i s a n t i c i p a t e d e The bery-llium c e n t r a l "island" i n t h e F i r e b a l l r e a c t o r r e q u i r e s cooling t o remove attenuation.

tine

h e a t generated by neutron moderation and gamma r a y

The density of h e a t generation i s 100 t o 200 watts/cc, and

it; removal w i l l r e q u i r e a l a r g e number o f c o o l a n t tubes.

The beryllium

has been replaced in t h e Screwball by a c i r c u l a t i n g r?islandltof NaOD. However, the problem o f NaOD corrosion has been introduced.

As i n d i c a t e d

in Section 6 . 2 2 , no stagnant o r low v e l o c i t y laycrs i n NaOD can be t o l e r a t e d next t o t h e h o t fluel tubes or containing s h e l l . The s e l f - s h i e l d i n g e f f e c t , as described i n Section 5 * 2 , for the

3.5 i n c h diameter tubes o f t h e Screwbal-l should be l e s s severe tnan f o r t h e s p h e r i c a l f u e l annulus i n tine Ffreball.

-1L-

IV MATE3iAL3 4.1 The proposed fueel f o r the Screwball is a fused s a l t containing 50 mole p e r c e n t

N S , l+7'mole p e r c e n t ZrFltt and 3 mole percent enriched

uF4. This fuel I s similar

t o t h a t proposed f o r the AXE and was chosen

f e a+ailetbh on its because eomfderable i~I?orma%fora p h y s i c a l and chemical p r o p e r t i e s .

To relax t h e l i m i t a t i o n on t h e

temperature o f t h e r e t u r n i n g NaK (Section 3 2 1 , a f u e l with a lower melting p o i n t xould be desirable,

Inconel will be used as the &el

containing

material e

L,2 R e f l e c t o r The r e f l e c t o r has two functions; moderation and s h i e l d i n g . a good moderator,

Be i s

Its a o d e r a t i n g r a t i o 1s 159 compared t o 170 f o r carbon.

In a d d i t i o n , it s e r v e s as an excellent s h i e l d due t o i t s high atomic d e n s i t y and small age,

The fast neutron leakage f o r a given r e f l e c t o r

t h i c k n e s s is much smaller f o r beryllfum than far substances such as NaOD,

BeC, g r a p h i t e and Be0 aggregate

(Reference 2, Figure 7)

Hence?

beryllium has been chosen for t h e Screwball reflector. lo 3 Moderator

A f l u i d moderator with a low vapor pressure a t elevated temperature

was desi;.ed,

Their high vapor pressures eliminated the possibility o f

using l i g h t o r heavy water.

Hydroxides were

then considered.

The d i f f h s i o n l e n g t h of a hydroxide is v e r y small r e l a t i v e t o i t s age,

Heme, a hydroxide i n t h e core o f the Screwball would serve 8s a

s i n k f o r f a s t neutrons r a t h e r % h a as a moderator,

Deuteroddes do not

have this undesirable nuclear property and should e x h i b i t sfiljlar physical

-15-

arid corrosive p r o p e r t i e s . both were considered.

Therefore, 1,iOD

FJaOD and combinations o f

The double i s o t o p i c separation eliminated LiOD

f r o m s e r i o u s consideration; NaOD was chosen f o r t h e core moderator. NaOD a l s o serves as t h e coolant f o r t h e r e f l e c t m .

It 3.s a b e t t e r

moderator than sodium (the proposed Fireball m f l e c t o r coolant) s o t h a t

t h e Screwball r e f l e c t o r should be a more e f f e c t i v e s h i e l d .

However, t h e

macroscopic- cross s e c t i o n f o r thermal neutrons i s l a r g e r f o r NaOD than for sodium.

The s l i g h t d i f f e r e n c e i n absorption does n o t warrant cohsidering

t h e additional. complexity o f a s e p a r a t e s o d h r ~system f o r t h e Serevball, B M I has made R survey o f containinE materials f o r NaOH a t elevated temperatures (Reference 23)

Graphite, s i l v e r and n i c k e l were

the most s a t i s f a c t o r y o f t h e materials t e s t e d ,

Nickel was chosen f o r the

Screwball on t h e basis of ease o f c l a d d i n g and e l e c t r o p l a t i n g and t o l e r a b l e neutron c r o s s section.

The corrosion mechanism o f MaOH

on nickel i s

reported i n Refemnce

The r e a c t i o n equilibrium i s temperature s e n s i t i v e resnl.ting i n

mass t r a n s f e r of n i c k e l from h o t r e g i o n s t o adjacent c o l d e r suyfaces, The corrosion can be suppressed by hydmgen pressure over %he NaOH.

The

corrosion mechanism f o r N&D

i s expected t o be similar t o

t h a t f o r NaOH, but t h e degree and %exnperatzlre dependance o f the corrosion

are unknown.

For %'lis skudy, t h e temperature

l i m i t a t i o n f o r NaOD

comosiop"I o f n i c k e l i s assiuned t h e same as f o r NaOH.

According t o Reference 3, corrosion o f n i c k e l by stagnant NaOH i s ,

1) n o t nci%icable at LOOQOF 2 ) small a t 1250째F and would be tolerable f o r a i r c r a f t applications

3 ) excessive a t 1500째F A l h f t i n g wall temperature o f 125PF and a deuterium gas pressure i n t h e AiaOD expansion t a n k of two t o three atmospheres are proposed f o r t h i s r e a c t o r .

4 ,L+ Intermediate lieat Transfer Medium A near e u t e c t i c a l l o y

of sodium and potassium, 56 welpht percent

1% and +!,A weiqht pel-cent K , has been chosen as t h e i n t e m e d i a t e heat

transfer. medium.

n;S

i s typical nf l i q u i d metals, %his a l l o y has e x c e l l e n t

beat transfer. p r o p e r t i e s and a l s o has a low m e l t i n g point (66째F).

The

main disadvantage o f NaX i s t h e induced r a d i a t i o n r e s u l t i n g from neutron

bombardment i n t h e primary heat exchanger.

A.5 Fabrication The proposed methods f o r f a b r i c a t f n g t h e primary h e a t exchanger,

p u q x and beryllium ?=eflector are t h e stme as those desci-fbed i n Reference 2,

N f will be substitutei! for chromium i n t h e reflector,

Bending t h e fuel1 tubes 2s p w s i b l e (Reference 51, with the u s e

of a cernet i n t e r n a l mandrel,

The HaOD h e a t exchanger i s standard, welded s h e l l and tube construction a

The e n t i r e system will be welded,

Reference 6 states t h a t welds

i n nickel f o r 100U째F NaOH c o r m s i o n t e s t s were rnade with no unusual t i i f ficulLy

Inconel. weldLi-ig presents no m a g o r cc+mplfcations

The fabrication sequence has not been f u l l y considered i n t h e layout of ysgWe 1

flodifications :nay be requi-ed t o f a c i l i t a t e assembly o f parts *

-17-

V REACTOR

PHYSICS

5.1 @-Sections The cross sections tzscd f o r nuclear c a l c u l a t i o n s i n t h i s r e p o r t a r e based on c u r r e n t ABP d a t a . 5.2 :elf-shielding

The a p p l i c a t i o n of d i f f u s i o n LheoTy i.n Reactor design, yields a t b e s t only a reasonable approxtmstion o f the micfeas c h a r a c t e r i s t i c s o f homogeneous systems.

The Screwball i.; a heteropenenus m a c t o r which has

been homogenized f o r the purpose o f e % e d i t i n g t h e nuclear c a l c u l a t i o n s . This f a c t makes it necessary t o correct t h e d i f f u s i o n equa%iom by 1nCroducing a parmeter commonly r e f e r r e d t o as t h e s e l f - s h i e l d i n g f a c t o r ,

F. T h i s

factor accounts for t h e l o c a l depression of the neutron f l u x wi3hin t h e f u e l reglon, which i n t,urm results i n decreased thermal u t i l i z a t i o n o f t h e fuel.

Tho major disadvantages r e s u l t from self-shielding, F i r s t , more f u e l i s reqliired than f a r a homoqcneous r e a c t o r of the sa'ie pFoportions:

second, t h e negative temperat1lre c o e f f i e i e n t i s n o t as l a r g e ,

and

As seen i n

FXgwt 3, a smaller change i n keff r e s u l t s from t h e removal o f an equal mass o f uranium f o r a r e a c t o r with a greater uranium investment,

Pigare 4 d e p i c t s esti.natcd values of F vs. fuel tube d i a m t e l - afu

various r e a c t o r o p e r a t k g temperature;. t h e n e t k o d s e t f o r t h i n Reference 7.

The c a l c u l a t i o n s were kased on

To apply t h e method one m s t know

Zs and ZL of each constZtuent, the atom%@d e n s i t i e s in t h e f i e 1 tube and f t s diameter, and t h e v a r i a t i o n of f with 2RXb as shovn i n Plgm-eS.

F1-onl t,'siese ita La cal c u l a t e ,

-18-

.....

................ ................................... ............. ~

as a function of

,kt%ra-gy, d~hichi s then used as a multiplying constant

on the mzcroscopic cross s e c t i o n of uranium, The self-shielding factors which were incorporated in the Screwbal.1 e o n f L p a l i o n were

pth = O , s ,

0.8,

believed that -these

figures resulted i n a conservative value f o r t h e c r i t i c a l mass.

T,3 One Group, Two Region, C r i t f c a l i t s C a l c u l a t u A3 a basis f o r Bdvanced zngincering ajnd nuclear calculations, m

estimate of the Screwball c r i t i c a l nauss was necessary.

For t h i s purpose a

one group, t w o r e g i o n calculation was made of Lhe proposed configuration. me general method of ca7culation i s discussed i n Reference 8,

equation 8 31.1

k- 31

â&#x201A;ŹJotez wuation S.31.31 f s i n error i n the f i r s t edition o f Reference 8 The item

should read

The e f f e c t i v e reflector tM.cknsss was eonp-uted f o r ANT Reactor

121 f o r wh9eh the c r i t i c a l m e s s had been cal.culated by the 32 group 1BlI technique.

Assum3 ny the scme effective r e f l e c t o r thickness, Lhe critical

nass was det,emined f o r the proposed Screwball

-22-

For the purpose of

CPOBIS

section weighting both reactors were

f m t and the faat f r a c t i o n to bes equally d i s t r i b u t e d among

o f intermediate reactors is more d i f f i c u l t than for thermal r e a c t o r s ,

The

The approxi-nati on of t h e Screwball used for nucl.eai- cal-culation i s schematically depicted i n F f g w e b . sphere (I) 9

R1__ i s the radius o f the i n n e r

with R2 and R 3 representing the r a d i i of s p h e r i c a l shells

11 and 111. A s applied t o t h i s r e a c t o r , region I i s the moderator, region 11 t h e f u e l bearing medium and region I11 the r e f l e c t o r . The d i f f u s i o n equations which inrere used i n t h e r e a c t o r a n a l y s i s

where s u b s c r i p t s I , i n d i c a t e s f a s t group region I: and where s u b s c r i p t s

indicates thermal group region I , e t c .

The above equations arc

founited

3n the following assmiptions:

(1)There re no f a s t a b s o r p t i o n s i n t h e r e f l e c t o r ( 2 ) There are no s c a t t e r i n g c o l l i s i o n s with the

iiranfvm in t h e h e 1

( 3 ) A l l f a s t a b s o r p t i o n in the fuel region i s due t o urani un

(!+.I The use

"f Ct in pl-ace of

approximation providing

-2 =s

3 Xs

is a valid

<< i

(5) The neutron energy spectrum, from source t o thermal, Can be divided i n t o -two r e p r e s e n t a t i v e energy groups.

(6) Neutrons do n o t leak before the f i r s t c o l l i s i o n . (7) Thc Doppler E f f e c t i s neglected. (8) C r y s t a l effects are neglected.

(9) Kodera t i o n e s s e n t i a l l y takes place i n t h e r e f l e c t o r moderator region

The a p p l i c a b l e boundary conditions for both groups are: (1) Synvnetry o r nonsingularity of f l u x a t the center o f (2) Q u a l f l u x e s a t t h e i-nterfaces

(3) Equal currents at the i n t e r f a c e s .

( 4 ) Fluxes vanish at the e x t r a p o l a t e d boundary. Sol-vlng t h e d i f f u s i o n equations and applying the f i r s t and fourth

boundary c o n d i t i o n s y i e l d s the f ollowj-ng expressions f o r the flm:

The constants in t h e above equations $re defined

(L)

-h

as f o l l o w s :

2 L

?I=

s2 =

-27-

(8)

SA =

5i111,

[LIIIZ L-

-28-

E i g h t equations with e i g h t &noms t h e remaining boundary eonditfons,

r e s u l t from applying

A non-trivial solution for

these equations i s o b h i n e d If the c o e f f i c i e n t s of t h e determinant

(Figwe I&) vanish; t h i s then e s t a b l i s h e s the c r i t i c a l equation.

Tho two eroup cal.culs5fon method r e q u i r e s accurate and

judfciaus application of" n u c l e a r cross s e c t i o n s .

Thermal base 92

values were used f o r determining thermal pou-p Cross s e c t i o n s and

an average over lethargy groups 1 through 26 f o r t h e f a s t group. or2 vs,

curves were plotted f o r RNP reactor 129 and nomalezed

area f r a c t i o n s (Appendix 3 ) determined f o r each lethargy group and region,

These areas are proportional. t o t h e f r a c t i o n of neutrons

i n each group.

The same neutron versus l e t h a r g y d i s t r i b u t i o n was

assumed f o r t h e proposed Screwball r e a c t o r ,

1% i s poss5ble t o solve t h e c r i t i c a l i t y determinant after c a l c u l a t i n g t h e nuclear c o n s t a n t s (L, I), and 2=

from t h e s p e c i f i e d

dimensfons and m a t e r i a l c o n s t i t u e n t s f o r each region.

The c r i t i c a l mass

is obtained by i t e r a t i o n and i s that uranium mass which results i n the aero value o f the determLnant, is

The rnetRod f o r scl-uing the determinant

presented i n Reference 9 * To check t h e va9ftlity of the method o f malysis, a e a l c u l a t i o n

was eonduct;ed on t h e F i r e b a l l Reactcr 12.9; i t s critical. mass as deterrrdned by a 32 g~roupIBM @a]-culation was 23 pounds of U235.

me two

g r w p t h r e e region calculatfon of reactor 129 predicted 23.4 pounds o f

U235 +

T h h i n d i c a t e d e x c e l l e n t c o r r e l a t f o n between analytical methods

and e b o i c e af cross sect50nae

-29-

-:. ..

......

I I _ _

The value of the deterninant varies radically x i t h small change

in wmfm massa The d e t e d n e n t f o r the Screwball was zero f o r two assumed uranium masses, 31+,,8pomds and 49 p o ~ n d s . The c u r v e of

fluoride fuel composition;

2,9 mole percent UFA

47J. mole percent ZrFq 50.0 mole percent N i F Several e f f o r t s t o calculate t h e spatial distribution o f the flux

yielded results of questionable validity,

Very srnal.1 chnngr?s in t h e nucl.ear

c o n s t a t s produce major change;; in the flu.x distribution.

With such a

sensitive rela,tionship no signiffcant mnclusions have been obtained. Based on thc results of t h e

32 group c a l c u l a t i o n s , it is

znticipat,cd that the Screwball will. be approfimatcly 50 percent thermal

If' s o 9

t,hs flux level requiietl to produce

centfmeter per second

280 W is 3 ' 0 1

Wutrsm per squme

5 * 5 Tcm~e-'c"Lture-Coefficieni;o f Reaetivi%x The Screwball has been conceived for p o s s i b l e use i n aircraft.

appHcathns,

It is therefore f m p o s t a n t that its control system be as

simple as posslble.

Since the use of control.. rods i s not anticipated

and t h e de2ayed neutron c o n t r i b u t i o n s t o the f l i x x are attenuated when

%he fuel- is circulating, t h e control o f t h i s reactor can be assur!?ed t o satLsfuctory only if it is provided with a strong negative temperature

c o e f f i c i e n t of r e a c t i v i t y .

This c o e f f i c i e n t i s a function of numerous

nuclear and physical parameters, a few o f t h e more important ones being: (1 ) l i q u i d f u e l expansion

(2) f u e l tube wall expansion

(3) Doppler e f f e c t i n f u e l

( 4 ) moderator expansion ( 5 ) thermal base changes with teaperatuye There are s e v e r a l reaaons why keff i s temperature dependent, t h e n o s t important one being t h e thermal expansion of t h e core m a t e r i a l s . This e f f e c t u s u a l l y r e s u l t s i n r e a c t i v i t y decreases with t e n p e r a t u r e

increase.

If the o v e r - a l l temperature c o e f f i c i e n t i s p o s i t i v e , t h e

continuoils i n c r e a s e nonuseful l i f e .

i n temperature r e l e g a t e s t h e r e a c t o r t o a s h o r t

The r e a c t o r then contains a b u i l t - i n s u i c i d e complex.

A negative c o e f f i c i e n t i s obtained from t h e t h e i m a l expansion o f %he f u e l and i t s loss from the a c t i v e volume.

Moderator expansion, resul.tint~,i n

increased neutron leakaqe, i s a l s o a l a r g e c o n t r i b u t o r toward a negative coefficient.

The Doppler broadening, which f o r enriched fhel could

provide a p o s i t i v e component o f t h e temperature c o e f f i c i e n t , has n o t been considered i n

t h i s report.

I n t h T s connection, it i s believed t h a t

a d d i t i o n o f $38

â&#x20AC;&#x153;0

Doppler e f f e c t ;

t h e p r i c e i s a g r e a t e r f u e l inves-knent.

t h e enriched fuel may possibly cancel o r overcome t h e

The c a l c u l a t i o n s therms3 reactor.

trier-e

conducted on t h e b a s i s o f a two group

Although t h e Screwball has been estimated t o be 50

percent thermal, it i s believed t h a t a reasonable e s t i - m t e o f t h e temperature c o e f f i c i e n t was obtained,

It was a l s o assumed t h a t t h e product

ofâ&#x20AC;&#x2DC; t h e resonance escape p r o b a b i l i t y and t h e f a s t f i s s i o n f a c t o r

t o unity.

rere equal

This steady s t a t e equation i s

temperature dependent as a result

o f temperature variation of core peometry, m a t e r i a l d e n s i t i e s and energy d i s t r i b u t i o n o f the neutrons,

The f r a c t i o n a l . change i n keff whfch

accompanies a u n i t temperature rise i s the temperature coefficient of reactivity.

This q u v l t i t y must be negative f o r stable r e a c t o r operation;

It i s obtained by taking the logarithmfc

der5vatLve o f t h e above equation

w-itih respect to t h e temperature,

The solutdon o f t22i.s equation bused

on t h e m a n

o p e r a t i n g temperature o f

app rofimately 130OoF a d 5nclud2ng cross s e c t i o m appropriately weighted by t h e se3 f-5hk.s I: Inp; fC:tctor ,yielded t h e f o l l o w i n g r e s u l t s :

Tne r a t i o of the noderator t o f u e l c o e f f i c i e n t is two Lo one. Tki,; ratio has ir:ipor'tant bearing on the k i n e t i e behavior of t h e r e a c t o r

bemuse of the relat5onshLp between the tennperaturs response tirae

constants for f b l and moderator regions,

For t h e Screwball these t5me

constan%s a r e approximatefy 1 - 3 and. 3 seconds f o r t h e f u e l and moderator respectively;

the r a t i o o f moderator t>o fuel con:%ant:; is: approximately

-33-

seven.

The combination o f t h e above r a t i o s becomes rriost

when t h e power i n c r e a s e s

u n l e s s t h e mean moderator t e n p e r a t u r e i s kept

constant t h e f u e l may freeze. follovs;

important

The explanation of t h i s phenomenon i s as

an increased moderator temperature reduces t h e rea c t i v i by and

cauSes t h e f u e l texperatwe t o decrease since i t s negative temperature c o e f f i c i e n t compensates f o r this reduction i n r e a c t i v t t y and maintains Since t h e reactor i s without servo-type control r o d s ,

t h e reactor c r i t i c a l .

it ma37 be p o s s i b l e t o f o r e s t a l l t h i s p o s s i b i l i t y by maintaining a constant

mean moderator t e n p e r a t w e .

5.6 Fission Product Handline; The two major f i s s i o n products which a b s o r b neutrons p a r a s i t i c a l l y are Xe135

and

Sm149.

An important advantage o f cfrcul-ating

fuel r e a c t o r s is the p o s s i b i l i t y o f continuously purging X e and o t h e r f i s s i o n product gases from t h e system, thereby appreciably reducing t h e

fuel inventory r e q u i r e d .

Reference 22 proposes bypassing a f r a c t i o n of

t h e primary f u e l stream through a turbo-diffuser unit in which the Xe i s purged with helium.

It has been estimated t h a t f o r an assumed equi.librium

Xe concentration condition of

, about

oe3g

6 percent o f t h e

K primary flow must be con tfnuously passed throuzh t h e s e p a r a t o r . Additional fuel. w i l l be due

.&a&

accor;nt f o r t h e reduction of k,ff

t o absor.p-tion by t h e equilfbriuni Xe,

Samarium poisoning under

= oe6g e Fuel r ~ i l l k have t o be added to t a k e c a r e of the e q u i l i b r i u i Sm abeorptfon.

equiLibi-iwn conditions i s expected t o have EL

-34-

SISI

5.7 Excess Fuel %qui~-ernents

I n accordance with Reference 2, t h e change i n uranium mass required for a given change In keff ( f o r rlpjP c i r c u l a t i n g f l u o r i d e fuel r e a c t o r s i s given by t h e r e l a t i o n :

It viis estimated t h a t z

kerf of

1,021 w i l l be required i f the

reactor i s Go operate a% 100 MU f o r 100 hours.

Background information

SOT calculating t h i s f i p o was obtxined from v a r i o u s ANIâ&#x20AC;&#x2122;, rWX and RIGâ&#x20AC;&#x2122; reports,

A breakdown oP the component

keff is:

Critical

1.QOO

Equilibrium Xe override

Q,OO?

Equil5.bsit.m 4n override

0.006

Fuel d e p l e t i o n

0.006

Excess f o r delayed neutron a t t e n u a t i o n

0 .OO5

Excess f o r instrrur;lentation i n t h e r e f l e c t o r

0,001

k,jy

2,021

The excess reactivit;y required 5s obtained by i n c r e a s i n g t h e

c r i L i c d mass by 3,3 p o u n d s ~ of t h i s , approximately one pound w i l l be used t o shkn t h e system during operation. 5 * 8 Kinetics

The question of i n h e r e n t s % a b i l i t y i s sxtremeLy important With high powered, mobile, c i r c u l a t i n g a e l reactors,

Since high power at

high themodptimic e f f i c h n s y i s required9 a reactor temperature approach5ng the upper permissible lhit is desirable, The extremely r a p i d power

f l u c t u a t i o n possible i n r e a c t o r s of high power d e n s i t y I-1.e m s manual o r even servo-type control inipi-actica,!..

As a r e s u l t cont,rol rods f o r use

during normal reactor operation were no 1; considered f e a s i b l e . The . t r a n s i t t i n e sf t h e fuel till-ough t h e i-eactcxr i s a f r a c t i o n o f a second,

As a pesu.t.t, t h e delayed neutmn contributinns t o t h e f l u x

are attenuated when t h e file1 i s circulaked

Nomally , t h e delayed neutrons

play 8.n iniportant 1,ol.e i n conventional r e a c t o r s ; t h e i r a t t e n u a t i o n raises

a l e g i t i m a t e worry regardin,?t h e s t a b i l i t y o f t h e Screwball

There aye two a s p e c t s t o fnl?emnL s t a b i l i t y , (1) s t a t i c , which

means t h a t an increase i n jxactor â&#x20AC;&#x2DC;cej-:iperature causes Lhe r e a c t i v i t y Lo

decrease, and (2), d p m i c , i>!hich mans t h a t t h e o s c i l l a t i o n s i n r e a c t o r

power are ir2rte:rentl.y dam;ted

A5 indica-bod under Section 5.5 t h e Screwball

has been eal.culated t o have a strong iiegeitive tempc:!-ature c o e f f i c i e n t .

Current d a t a and t h e o r e t i c a l s t u d i e s i n d i c a t e t h a t the r a p i d c.i-rculation o f the f u e l i t s e l f provides oscillations

powerful- damping f a c t o r f o r power

with periods compzrabhe Lo the t r a n s i t tkoe o f t h e fuel.

through t h e r e a c t o r .

ThTs damping f a c t o r i s presumed t o compensate f o r

t h e d-elayed ncutron a t t e n w t i o n

Evidence sup1mrting t h i s statement

# e t f o r t h under References 1 0 , 11, and 1.2; it

c i r c u l a t i n g fuea-

reacttyir

is indicated that -the

equation (tritIiou.t r e l i a n c e on c!eI.ayed

neutrons o r

control rod^^,, ha8 no antic 1-ealistic c o n ~ l . - t l o2 r ~

(I) constant power ex-traction ( 2 ) l a r g e temperature and power excursions where t h e

steady s t a t e power. i s four times dzsigii power f o r a l l times

-35-

( 3 ) sudden p o s i t i v e excursions of the power Lo ten tines design power, t

It would seen t h a t a properly designed c i r c u l r t i n g f u e l reactor is no nurse w i t h r e s p e c t t o c l a q ~ f n go s c i l l a t i o n s than one i n which none of the delayed neutrons are a t t e n u a t e d ,

5.9 Controls

The underlying c o n t ~ o lphilosophy f o r this reactor i s t h e %aster-s1ave''

?elationship

reactor the slave.

uhere the power p l a n t

is the master and the

In o t h e r words, Yine power extracted from t h e reactor

is d e k m i n e d solely by the demand of the propulsion sys-tera. The Screwball e o n t m l systert 9s basically depenclcnt upon i t s

large negative fuel terqxsature cbefficient. shim control i s obtafned

lis s%a%edin Section 5.7,

So:, a d d i t i o n o f enriched fael;

scheme to accomplish this is set f o r t h in Reference 1 3 .

possible basic

There are no%

expected t o be con-Grol rQds in tht: reaetor fuel and moderator regions.

Cqnsideration should be given t o the possibility o f a v a r i a b l e h y p ~ s son thc Xe s e p a r a t o r Lo provide f i n o adjustments i n r e a c t i v i t y between brteh a d d i t i o n s of eiiriehx3 fuel$3 ia:iortant

advantags o f the c i r c u l a t i n g rUcl reactor Fowerplant

conbination, I s t h a t p r e l h i n a r y mal.ys5.s o f c o n t r o l a b i l i t y of a loosely c5upJ.ed system e m be predicted f o r each separate c c q o n e n t ,

e n ~ i n es t a b i l i t y problems can

Reactor and

therefore, be attacked independently since

surges in e i t h e r eonpanant are admitted Lo the other after considerable delay.

A s indicated i n Reference I.& it appear:; that the master-dxme i d e a

can probably be s a t k s f a s t o y i f y reduced t o practice.

5.10 S t a r t UP A p o s s i b l e proccdure f o r s t a r t i n g %he reactor i s as follows: (1-1 Heat t h c fiiroridc J extarsl;ri sye;t&m

ada

to a m m tcsmgerature

emmea

1300% in rn

~UCKL

(2) Using an external heat source, heat the NaK and NaOD,

(3) Bring

t h e f u e l , a t c o r r e c t concentration,

-to 15000F.

( I + ) Install a strong polonium-beryllium sourcc: in the r e f l e c t o r (perhaps by n i x h g molten polonium with the beryllium in a sepayate r e f l e c t o r tube)

(5) Transfer t h e f u e l into the heated r e a c t o r system.

(6) Allow the s u b c r i t i c a l f u e l t o c o o l ,

11%

a b o a t 1300Â°F, with

t h e moderator tempesatuvo close1.y c o n t r o l led by t h e NaK

the core should

be c i - i i i c a l ,

The r e a c t o r should now be ready t o supply h e a t to t h e propulsion system,

ike

ovent that the tetlperatuizc o f t h e moderator cun n o t be

p r e c i s e l y controlled, it may be p o s s i b l e to vary t h e h e i p h t o f t h o moderator level in the core znd thereby s f f e c t a reasondL1c [legsee of

control f o r s t a r t up.

5.19. S i u t Down Driving a r e a c t o r s u b c r i t i c a l ariien at idle, power without tâ&#x20AC;&#x2122;ne

use of s a f e t y r o d s mzy not be a p r a c t i c a l possibility, The p r a c t i c a b i l i t y

of draining t h e flml froi:i t h e core was given l e n y t l y consideration.

This

was e-iiminated on the ground-; that t h e add i ttonal m i ht, higher r a d i e t i o n

levels and manifold e n g i n c s r i n g complzxities would be t h i s sys tea.

-38-

assocdatlsd t&th

To drive the reactor subcritical a ahut down rod in the reflector appears to be neee~isary. This rod will be completely withdrawn from t h e

reactor during normal operation;

t o drive the r e a c t o r s u b c r l t i e a l it will

be irnserteit In %he refleetor either manually or automatically.

not. expected to unduly penalize the s h i e l d o r reactor design.

-39-

This rod ie

Nickel inconel ;hell

5 . 17e r c f l e c t o ; . arid c2n estimated q u a n t i t y of NaOD and Ri for* cooling. W , S o F;imer9s method (Reference 16) was used with modifications suggested by F. 11, Abern::f.h:r ABshunptiQm

< m d SA. H . Fox.

inherent fri %he mth& m e :

The % t r a i : h t ahead" theory o f g m a absorptlon applies, i a e . , eompton s c a t t e r i n g deprtdes t h e photon i n energy but does n o t change i t s d i r e c t i o n .

Plo reffrac-tioii I;al..es place

c , The

equivalent

a t boundaries.

source power d e n s i t y i s uniform o v e r t h e

source annulus.

d, The fission r a t e i s unifam. Assumptions used f o r -the Screwball: a. The l'amulus" o f

fuel tubes may be replaced by

homogeneous annulus of the s m e thickness. b. The g m a spectsum may be i d e a l i z e d as a source

c o n s i s t i n g o f 1 ~ e gemmas v mly.

( A more accurate treatment

would be t o use sources cf 1, 2, and 3 Me-u gacmas with t h e

source s t r e n g t h s a d j u s t e d according t o the n m b e r of gammas

between 0 and 1,5, l . 5 and 2.5, and 2.5 and i n f i n i t e &lev

energy. } c , T h e use o f

for b o t h energy deposition probobil.ity

and a t t e n u a t i o n f a c t o r s , r a t h e r khan u;fng p and a build;up factor fm- a t t e n u a t i o n , w i l l not resd-t i n s e r i o u s eri-ors ,.

(The proper

build-up factors for t h e SCrebJball configuration w e not known

This assumption will cause an e r r o r such khat t h e c o o l i n g tubes

will be placed c l o s e r than necessal-y

Accurate r e s u l t s can

o n l y be obtained throirgh t h e use o f c r i t i c a l experiments o r

actual mockups d

For ealculnt,ions in t h e source r e g i o n , gmms's

which t r a v e r s e t h e i s l a n d must be considered,

Therefore; f o r

f o r t h e i s l a n d (0,117 inchesm1)

these eaJ.@ulations, t h e

was assumed equal t o t h a t f o r tize source r e g i o n ( 11-1th,.soul-ce region (

absorber hrive t h e sane

q>he:-ical axnul_us) where the soux-ce and

P(r) = POT

0,152 inches'-').

I n t e g r a t i n g by p a r t s and -usins Reference 17.

d 63 d

(1)

Close t o %hc source region,

subscripts;

an i n f i n i t e

s l a b source is as.;umd,

refers t o laycr(s) of t h e slab

refers t o t h e source

i.e.,

FzizVner f r o m t h e source region, a s u r f a c e source i s used t o

calculats t h e a t t c n u a t i o n p

(Ei

)Ro

I n the wIslandn, t h e slab Source should be used for a t t e n u a t i o n near t h e fuel amxilus, and t h e surface system at greater distnace,

At the

ceiiter of t h e island, spherical s p u a e t r y reduces the fornula t o s 3 " " O

A f i c t l t i o u s surface source which yields reasonable h e a t i n g results i n the ifIsland'gi s obtained by matching t h e power absorption at

I,AA-i

from tfie source.

I n the r e f l e c t o r r e g i o n , %e slab source is used f o r about

1/2

...... ~....................

h; then

it i s matched t o a surface source on the o u t s i d e of t h e

1 nickel

Fqua.tion (6) may be modified by rep]-acing t h e

inconel s h e l l .

functions by E

f u n c t i o n s , thus c o r r e c t i n s the non-isotropic

emission from t h e surface source?. The second te-m i n the parenthesis

i s a?ways n e g l i g i b l e and may be deleted. Equation (6) thus becomes:

> Ro

The gamma heating ca1cu.l.at i o n s appear i n Appendix 6 By p l o t t i n g . 4 y2 ~ P ( r ) vs

and paphical1.y integratj-ng, "ine

percentage o f the f i s s i o n energy emitted i n gamma r a y s and ncut,mns whj.ch is absorbed i n t'nc r e a c t o r i s determined f o r each region,

8.8%

Island

Fuel

51, .4&

Ni-Inconel s h e l l

Ref1ec t o r ApproxBmately 300

11(w

3 09% 32.98

leak

out of the reactor.

Figure 7 shows t h e spatial d i s t r i b u t i o n o f heat absorption in the r e a c t o r . 6,2,2

I n t e r n a l Heat Transfer Due to t h e complex flow passage f o r t h e NaOD, an exact

p r e d i c t i o n or anzlysis o f t h e NaOD v e l o c i t i e s in t h e core i s impossible. Hence, t h e f o l lowing simplified method has Seen used f o r determining t h e requlred NaQD flow rate,

Sfnce corrosfo-rm and enqfneering d a t a are

n o t a v a i l a b l c f o r NaOD, NaOH has been i i s e d in the engfnee-fnp a n a l y s i s ,

The thermal conductivity o f NaOH I s small (6,72 Dixi/hr ft "F.

a t 1100oF.)

.......

-4s-

Drawing # 23193

eompared with liqufci metals atld is appmx%mat,ely half t h e thermal conductivity o f t h e f u e l .

Hence. a l a r g e f r a c t i o n o f t h e temperature

d i f f e r e n c e between t h e f u e l and hydroxide may occus i n t h e NaOD f i l m f o r low v e l o c i t i e s To estimate more i n t e l l i g e n t l y t h e f l o w r a t e which r e s u l t s

i n a Pabe wall temperature n o t exceeding 12500F. a c a l c u l a t i o n was made for a

3-6 inch sw:Gsi&eJimeter f u e l tube w i t h a one inch annulus o f

NaOH surrounding i t .

The f u e l v e l o c i t y was assumed t o be 20 f t / s e c ,

and the NaOH vel-ocity was v a r i e d ,

The v a r i a t i o n of U with VNaOB was

determined and i s shown i n Figure". The NaOD flow a - e a perpendicular t o t h e p o l a r axis was determined a% various l a t i t u f i e s

Then t h e v a r i a t i o n o f VNaCID with p o s i t i o n

in t h e r e a c t o r could be c a l c u l a t e d , a t t h e e q u a t o r i a l plane (V,)

A r e l a t i o n between the NaOD v e l o c i t y

and t h e average v e l o c i t y was found.

Assuming a v e l o c i t y normal t o t h e equator, t h e average U was c a l c u l a t e d and t h e t o t a l ternperature rise of t h e NaOD through t h e core

was estimated.

Since t h e t o t a l texperature r i s e ineludfng Ynat due t o

gama h e a t i n g w8.s small I10

- 200F,),

a l i n e a r temperature r i s e through

t,he reactor was assumed,

A t one inch i n t e r v a l s along the axis, average velocTtfes, h ' s end AT ' 9 were estimated

flux.

'IT'S,

The product o f U and AT gave t h e h e a t

The temperature rise i n t h e NaOD f f h ,

ATl MaOD

, was

calculated

by (3fviciing t h e heat f l u x by hNaODo F f p r e 9 i s a p l o t o f hNaODv s ,

The g m a heat which i s generated i n t h e tube walls w i l l be N ' aOD transfoi-red t o %he NaOD causing an a d d i t T o m 7 tenperattire ;fse AT2"

Rrauing # 23194

The sum of AT1

and t h e NaOD temperature i s t h e outstde tube

.AT,

wall temperature, which inust n o t exceed 1250째F, Figure 10 shows t h e v a r i a t i o n o f fuel mixed mean temperature, tube outsfde 1 ~ 1 temperature 1 and t h e NaOD mixed mean teriperature with p o s i t i o n i n t h e core,

o f 125A째F,

A V, o f 6 f t / s e c , gives a maximum w a l l temperature

This c a l c u l a t i o n e s t a b l i s h e s t h e magnftude o f t h e flow r a t e

based on t h e s i m p l i f i e d flow system,

6,2,3 f l . f l e c t o r Cooling The h e a t eeneratcd i n t h e beryllium r e f l e c t o r is removed by the

passage of NaOD through 0,23 inch diameter coolant tubes.

The

c a l c u l a t i o n o f coolarat tube spacing i s based on t h e f o l l o w i n g assumptions: 1. Neutron flux dBstributfon from t h e two group, t h r e e region c a l c u l a t i o n s were n o t available f o r this c a l c u l a t i o n .

Therefore, t h e h e a t

generation due t o t h e neutron moderation was assumed &qual t o t h e gamma heating.

This assumption agrees with work done on t h e Fireball (Feference

2) * 2 , Each coolant tube sow f s t r e a t e d as a s e p a r a t e annular c e l l ,

3. A mean, uniform power density i s assumed f o r each c e l l . The tubes are arranged i n an e q u i l a t e r a l m3.tFlxa

5 , The tube diameter is 0.2'3 Snches. 6 . The m a x i m u m beryllium temperature will not exceed t h e coolant tube w a l l temperature by more than SOOF. 7 , Eeating from capture g m a s f n the inconel shell is neglected.

8 , &I f l s s f o n product gammas are ernftted i n t h e core, Prom the basic heal; conduction equation it can be shown t h a t

-114"-

-50-

Froin geometric considerations

= k,

/g(11)

s=bJ7-

To determine t h e cooling tube spacing, t h e following i t e r a t i v e method tms used,

1. Assum t h e row spneinc,

2, Calculate u n i t c e l l dLQensions using equation:; (2) and (3) 3. Estirclate l o g , mean power d e n s i t y from figure XI.

4* Prom equations (1) ( 2 ) and (3) which

calculate the value s f o r

50OF.

5. Check t h e c a l c u l a t e d value of

S w i t h t h e assumed row spacing

and i t e r a t e u n t i l equal.

From t h e row spacing and r e f l e c t o r dimensions, t h e tube p i t c h c i r c l e r a d i u s i s determined,

The number o f tubes i n each row i s calculated

from t h e p i t c h c i r c l e cfrcumference and tube spacing.

Non-integral

numbers o f tubes were adjusted t o t h e next h i g h e r i n t e g e r and t h e i r

spacing on t h e p i t c h c i r e l e a l t e r e d accordingly

The results for t h e Screwball r e f l e c t o r are l i s t e d below,

Row

Spacing

0.788 i n

15.69 i n .

1-25

0 e974

16,52

103

1.23

17,63

1.62

13.05

P i t c h C i r c l e Radius

No, o f Tubes

(con fa)

-51-

.............

Pitch CSrcPe Radius

2,32

21.174

4.12

21, .27

I n cal-culating the g a m a h e a t i n g ,

Eo, of Tube6 57 37

was used as t h e

r e s u l t i n g i n more r a p i d a t t e n u a t i o n

attenuatAor? factor ra.ther than p and hence l a r g e r heat generat;ion.

T h e r e f o m , t h e above r e s u l t s should

be conservative.

by-pass annulus. The NaQD veloclty in t h e r e f l e c t o r was detemiined by c a l c u l a t i n g t h e heat f l u x , h e a t t m n s f e r AT, and temperature r i s e of t h e NaOD a t

v a r i o u s assumed velocities,

Calculations were mhde for t h e tube row i n the

highest power density region. A t a v e l o c i t y of' 7 ft/sec, the temperature r i s e o f t h e NaOD i s

156@F, h i;

2600, and the h e a t t r a n s f e r h T 1:; 80째F.

tenperatuse a t the end o f f h e c o o l m t tube o f 1251

This g i v e s a t o t a l

"F: which is

approximately t h e max2mua temperature allowable fj-om a corrosfon standpoint

6 2 4 Primary Hen% Exchanger The primary h e a t exchanger f o r t h e Screwball reactor i s a s p h e r i c a l s h e l l which w i l l m a p around n 53 inch diarneter sphere, s h e l l will be

This

inches t h i c k and w i l l begin and. end on the sphere a t

645' Horth L a t i t u d e and 60'

Smth Latitude, respectively.

Within the

s h e l l t h e f u e l and NE& cooJ.ant w i l l flow comter-currend2y; t h e NaIi flows

-53-

dolisn

within tne tubes i n the h e a t exchanger.

The tubes w i l l be wrapped

i n such a way t h a t t h e r e i s a constant clearance between tubes o f 0.035 inch,

Two spacers p e r foot, o f length o f tubing appear t o be adequate, The fuel v i l l enter at the Sotton of the h e a t exchanger a t

1550'F

and will leave a t t h e top a t 1150째E'.

On the NaiS s i d e the entrance

temperature i s 940OF and the temperature r i s e w i 1 . l be 510째F.

The

v e l o c i t i e s and pressure drops f o r the f u e l and NaK a r e , r e s p e c t i v e l y ,

6.95 f t / s e c , , 36.3 f t / s e e , , 32.9 p s i 2nd 31 p s i .

The m a t e r i a l o f

construction w i l l be inconel-. The primary heat exchanger design f o r t h e Screwball i s based on the method presented i n Reference 19;

a s ~ m a r gof the tal-culations f o r

t h i s exchanger appear i n Appendix 8.

This h e a t exchanger represents a f e a s i b l e d e s i p n and no major a t t e n p t has been made t o optimize it.

It i s a n t i c i p a t e d t h a t t h e fuel

volume i n the h e a t exchanger can be reduced t o approach t h a t o f t h e

Fireball d e s i q and further e f f o r t i n this d%rection i s recommended,

6.2,.5 NaOD Heat Exchanger The NaOD heat exchanger has the form of a i.j.ght, circul-ar

cylfndrical annulus s i x inches t h i c k 2nd 1 5 inches t a l l . ciomward through l / 2 inch 0, D ,

The Malk flow:;

ineonel tubes which have a w a l l

thickness o f 50 m i l s , including an external 10 mil cladding o f nickel. These tubes fqrm a l a t t i c e f n the form o f an e q u i l a t e r a l t r i a n g l e with a minimum clearance o f 0,125 inches between the tubes,

The NzQD flows

across the battnm o f the ~ ~ u f u l u sup , the outside and back down the j.nsj-de of the w-mulus m Tndlceatsd in Figure 1, For t h i f i cd:ula.tIon

pe7Teffat

-5L-

eight

(

o f t h e reactor heat was assumed to bc removed by t h e NnOB.

16 &Rd

The h e a t t r a n s f e r c a l c u l a t i o n s are bssed on r e l a t i o n s presented

Sn Reference 2 0 ,

Two pass, parallel! flow o f NuOD and s i n g l e pass

downward f l o w o f NaK were assurtzcd.

Pressure loss c a l c u l a t i o n s f o r the

f'JaG;D assmed mixed parallel and cross flow.

A zmnample calcul.ation and

t a b u l a t i o n o f design d a t a are contained i n Appendix 9 and Appendix 1,

respectively, The NaOD h e a t exchanger 5s a cqnsemative design; more h e a t t r a n s f e r area i s provided than 2s actually required s i n c e the higher rates

of h e a t t r a n s f e r in cross flow h w e been neglected t o simplify the analysis

4,+3Fuel Flow Emerhcni; A s mentioned i n Section '?,2it i s assumed that t h e flaw patterns

in t h e tubes of constant cross s e c t i o n Ere -nore p r e d i c t a b l e than t h e vgrfable mea passat?@enp1o;ied 4n t h e F i r e b a l l ,

T h i s experiment was

conducted t o verif;y flew s t a b i l i t y i n h e l i c a l tubes.

Figure 12 is a photograph of the apparatus.

The one inch glass

tube i s geometricelly similar t o %he Screwball fuel t u b e s ?

i r r e g u l a r i t i e s were observed,

no flow

The f l u i d is an aniline dye.

il secondayy flow t y p i c a l o f khat generated i n smooth tube bends

was observed;

t h f s added turbulence should fncrease f u e l nixinp:

produce a more uniform v e l o c i t y p r o f i l e and Increase p~asaurakW%?S.

This experfinenti supports t h e assumption of fuel flow stability i n the Screwball,

VII. SHIELDING Figure 13 i s taken from the r e p o r t of the meeting.

1953 S h i e l d i w Board

The s h i e l d c o n s i s t of lead and borated w a t e r .

Lead w a s used

adjacent t o the pressure s h e l l and i n a 20’ shdow s h i e l d which i s incorporated i n those s h i e l d designs requiring s e l e c t i v e reduction of e x t e r n a l dose. The curve8 ehown a r e f o r r e a c t o r core diameters of (Screwball) and 22.5”.

28.5’

Details of the calculations can be found i n the

reference report.

-58

VI11 GOI\JCLUSTONS AND ~ E ~ O ~ ~ N ~ A ~ I O ~ ~ ~

On %he b a s i s of t h e work presented Pn t h i s r e p o r t , t h e Screwball

reactor appears t n be feasible, However, a considerable q u a n t i t y of detafled analysis and experfmerat is required before its p r a c t i c a b i l i t y is WLabliShed,

Based an the work covered by t h e r e p w t , t h e concl-usions and reeomendatfons are:

1) The use of NaOD as a moderatm and r e f l e c t o r coolant, as proposed, h a s great p o % e n t i d i % g ;

however, with the assumed corrosion

limitation on tbbs wall tempera%ure (1250째F), usei-y l a r g e flaw rates and adequate flow guidance are reqarired t o attain marginal performance,

2) The uncertainty about flow i n s t a b i l i t i e s is less severe

h e l i c a l fuel tubes -than in s p h e r i c a l , annular flow passages,

Hence, the

use o f h e l i c a l tubes i s recommended u n t i l s t a b i l i t y in spherical annulif has been conffrmed e x p e r h e n t a l l y .

3 ) For d e s i p pointt operation, preheating the NaK w i t h the moderator h e a t lends I t s e l f t o a s h p l e reactor and propulsion system des5gii

The desirability of this acheme increases

o f fused s a l t fuels is decreased,

is recommended

as the mel ting-point

Further i n v e s t i g a t i o n of NaK preheat

partit.dtilar1.y f o r operation o f f the design point,e

4 ) Although the f u e l v o l m e externa.l.

t o %he core

is l a r g e , by

o p t i n i z i n g t h e p r h w y heat exchanger f o r rninSmura f i e 1 volwie whSle

mafntainfng raasonable pressure drops; t h e fuel volume r e p o r t e d should approach that o f the Fireball, With an exGesnal f u e l volume equal t o t h a t i n t h e Fireball ( 5 , 7 cubic. feet;), the Screwball core w f l I c o n t a b

-59-

33 percent of $he t o t a l f u e l volrme.

' B e h i s h e r delayed ncutron

cancentration i n the core and a more conservative power density make control o f Vne Screwball more practicable than t h e F i r e b a l l

5 ) Despite the l a g e r size and the use o f tubes f o r fuel c o n t a i n e r s , the critical mEs8 of t h e SCrewball (35 pounds

base4 on

cnnservaf,ive sell f-shielding factors) compares favorably with tlhe F i r e b a l l c r i t i c a l mass (30 pounds) as reported f n Reference 1, I n addition, t h c ratio of t o t a l f u e l volume to core v o l m e f o r t h e Screwball may be rediaeed by op%imi.zfnz t h e primary heat exchanger, thus y i e l d i n g a smaller

t o t a l fuel mass f o r %he Screwball

6 ) The NaOD flow p a t t e r n in t h e core i s unknown.

The assumption

t h a t NaOn will flow betimen t h e tubes nay n o t be r e a l h t i c and more poTitive guidance or" flow may be required. 7 ) Support of t h e t h b - w a l l e d f u e l tubes at such close tolewmces

nay be d i f f i c u l t , p a r t i c u l a r l y s i n c e -the thermal expansion p a t t e r n s art?

analytically mipredictable

Any support s tuwcture contactfnz the tubes i n

t h e core p r e s e n t s a p o t e n t i a l NaOD stagnation p o i n t and hcnce, a corrosion

eent2-r.

8) The assumption of quantitatively similar physical and chemical properties f o r NaOD and NaOW i s unfnemded, The major, f m d m a n t a l limitation o f t h e Scrawbal 1. Is "Lie NaOD

csrrosion,

Title

R e f . No.

_ I _

ORfaz 1556, W, B e C o t t r e l . l + "P

Quarterly Progress Report".

f o r period ending Jms 10, 1953.

CF-53-3-210

A P

FmaS

. B.

MBlls

Ref]-ectsr Moderated

Circulating Fuel Reactor For an A i r c r a f t Power. P l a t t f , March 27, 1953.

The lieactor Handbook, PH-3, Technical Information Service ;'AEC NRL-Herno Report No. 130, R , R , Miller, "Fourth Progress Report

on the Thermal P r o p e r t i e s of S o d i u t Hydroxide and L i t h i m f4etaln, iiai-ch 1953.

Conversation v? :i Lao Hemphill

- P-12

Engineer.

TAB-20, D . 3 , Bloom, rfReport o f T r i p to BMI, I n t e r n a t i o n a l

Nickel Company and Pi. 1.T

June 29 to July 3, 15350

P-F10-902, C, â&#x201A;Ź3, MiIXs, I r A n Outlinc;

the General Methods

of Reaetor h a l y s i s used by %he N P Physics Gr.oupl'. 8,

Glasstome and Edlund, "The Elenents of Reactor Theory".

1434-182, 1'. D, Crout, "A Short Method f o r Evaluating Deter-

minants and S o l u t b n s of Systems o f Linear Equations With Real and Complex C o e f f i c i e n t s t f .

la.

GF-53-3-2315 br. K, Ergen, %inetics Muclear 2eacLors", March 30

o f Circulating Fuel

1953.

Y-Fl.5-98, W. I;, Ergen, RPhysies Consideration of Circulating Fuel Reactors", A p r i l 16, 1952,

1 . 1

-61. -

12.

Y-FlO-IQ9, S. Tomoi-; 19Woteon t h e Non-linear Kinetics o f C i r c u l a t i n g Fuel ReactorsI1, Lug

13.

OWL

15, 1.952.

1%3/,,W . 5 , C o t t r e l l , T3eactor Program f o r t h e Plircrzft

XiicLear Propulsion Project", June 2, 1.952 a

14 *

15.

CF-52-9-201,l?r S Farmer, "Cooling Bole Distribution for ~

Reactor Reflectors", Sept. 3, 1952.

Cooling System" 17.

"Tables of Sine

, Cosine and

1940, Vols

ikw York

Exponential I n t e g r a l s " , FJPA,

. I and IT

MT-I, G . Phaezek, Part I, "The Functions P a r t 11, '"Table OWL

1330, *

ql(x) =

of E,(x)"

A. P. Frws 74. E , LaVerne, "Ileat Exchanger Design

Charts". 20.

W. I.].

~ ~ I c A d m s'%at ,

Transmission!!, M c G r a s ~ - l I i l l Book Go.

, Inc

New York and London, 1942.

21.

OML 1.375, IH. F. Poppendiek, and L. D , P a k ~ e r ,W e a t Transfer

i n Pipes With Volume Heat Source Within t h e Fluids", 22.

HKF-109, Karl. Cohen, "Homogeneous Fceactor f o r hkbsonii: Aircx*aft*', Dec. 1 5 , 1950.

23.

B?41--"76, C. 14. Craighead, L, A, Smiith and X. I. JaPfee, f9ScreeningTests on Metals nnd Alloys i n Contact 145th Sodium IiydroxTrle at 1000 and 150O0Fgt,

-62-

X APFETWEES

Appendix 1, Design Data

1) General Power

200 InyL.

Power d e n s i t y

- 2.5

C r j t i c a l mass

Aw/cc

34.8 pounds o f U235

Estimated add;tional f u e l required f o r poisons, burn-up, e t c . ,

3.3 pounds. Estimated (not optimized) t o t a l uranium investment

Temperatxre coefffcient of reactivity

- 2,lx 10"'

- 1.06 x loz5 n/(cm2see) thermal flux - 1,06 x l0l5 n/(cm2see).

- 175 pounds.

/OF.

negative

Estimated â&#x201A;Źast f l u x Estimated

(These are

assuming the r e a c t o r is 5Q percent thermal.) Dimens i o n s :

Pressure s h e l l diameter

- 68,5

in,

fIeight t o o u t s i d e of pressure shell

Flow rates he1

NaOD

M& 2 ) Materials

Fuel

- 1410 pounds/sec.

1890 pounds/see.

2640 pounds/sec.

- 50 snole percent P I S r;7 mole percent ZsFG 3 mole percenk UF k

- 84 i n .

Ihrlerator and reflector coolant,

Reflector

- NaOD

- bery2lfum.

Intermediate h e a t t r a n s f e r medium Structural material

(56 weizht percent Na)

inco~iel-,with n i c k e l p l a t i n g o r cladding when? i t i s i n c o n t a c t with NaOD

3} Core Fuel volutne = 1,880 cubic inches

NaOD volume

7200 cubic inches

Dimensions: Moderator "islandtj diameter = 21 .5 inches

Fuel region outside diameter h e ? tube i n s i d e diameter

= 28.5

inches

3.5 inches

Tube wall thickness = 50 mils o f inconel with 10 m i l n i c k e l cladding

Number o f f u e l tubes = s i x , including c e n t r a l tube Tur-ns i n core = 1 5 Rie7- temperature rise = &0OoF

Maximum file? temperature = 155O0F

Waxirnm NaOD temperature

1000째F

M a x i m u m waJ1 temperature on MaOD s i d e Fuel pressure drop

12540F

10 p s i including e?c3ansion an6 contraction l o s s e s a t tube entrance and e x i t

4 ) Reflector Thickness = 11 inches o f Be and 2 inches o f NaQD

Number o f coo3ing tubes

486

Cooling tube diameter = 0,23 inches Rows of coo1lng tubes

NzOD velocity i n cooling tubes = 3*4 ft/sec

5) Primary heat exchanger Neat removal = 185 14M

Fuel volume = ?,45 cublc f e e t PJaK volune = 7,5L cubic f e e t

Spherfcal s h e l l thEckness

k inches

Tube inside diameter = 3/16 inches

Tube wall thickness = 0,017 inches Plinimwn tube spacing = 0,035 inches

ISumber o f tubes = 5220 Latitude o f entrance header = 45?

Latitude o f ex5t header

Fuel pressme drop

60째

33 p s i

RaK pressure drop = 39 p s i Average tube length = 7,35 feet Equatorial c r o s s k g angle = 30째

E x i t IJaK tenperature = 1t,50QF

Heat t r a n s f e r area = 2280 sqttare f e e t , based on tube outside diameter

6 ) MaOD heat exchanger

Reat removal = 16 Pm

Dimensions y.

Cylindrisa.3 annulus with r a d i i o f 21 snd 27 inches

HeiLTht = 1 5 inches

NaK voliune = 5030 cubic inches NaOD vol-me = 5700 cubic inches Tube outside cliiamcter = 1/2 inch Tube hrall. thickness = 0.050 inches 1.lininiw-i tube spacing (equilateral. t r i a n g u l a r p i t c h ; = 0.125 inches

Number of -tubes = 2675

N&X temperature r i s e

4O0F

NaOD temperature decrease = 20째F

NaK pressure drop

HaOD pressure drop

3 psi = 20 p s i

Is) &ps Type

- mixed

Number

f l o w , sump pmps

- 4 fuel P W ~ ~ S 4 NaOD pumps

Seals

gas s e a l s f o r the f u e l jmnps

e i t h e r gas o r frozen seals for. t h e NaOD p u x p h

p horsepower

8 ) Shield Estimated weight

- undetermined

- imdeterniined

External dose a t 50 f e e t - 10 r/h

9) Total weight Reactor, s h f e l d and Crew compartment s h i e l d %

-66-

= 96,000

pounds

Screwball

6 Tubes

3 1/2 inches Dimetel-.

Be r e f l . ~ c G ~ RaGD r, cooled; core f u e l 30 and MaOD Two %&on,

Note:

37 inch d i a m t e r core, 51 inch diameter reflector

AI..?. the values are k,toms/cc] x 10-2L+ u n l e s s otherwise indicated

Appendix 3 , TWO Group Cross Section I d e i g h a

The foll.owing r e l a t i o n s were the b a s i s f o r weighting t h e cross sections f o r .the two group, three region analysis. The fl-ux i n each l e t h a r g y group was averaged over each reactor

region

Oi=

I-

r e g i on i region

(T)

r2 d r

The fraction o f t h e t o t a l f a s t f l u x

each lethargy group.

($i)

was determined f o r

Then

The values of

qi a r e tabulated

below.

The cross sections f o r Vne f a s t group were obtained by multiplying t h e cross s e c t i o n s i n each l e t h a r g y group by i t s â&#x201A;Ź1-

fraction and s w i n g .

Hodera tor

Core

R e f 1e c t o r

0.0061,

0.0055

0.0019

0 .Ol%

0.0307

0.0081

0.0571

0 A792

0.0260

0.0051

0.0127

0 .0033

0.0802

0 .S.354

0 .OL92

0 09 4-4

0.J-342

o .04s6

0.1128

0.1360

0 .(I571

0.0923

0 .I170

0 s05ii.3

0 .of373

(? .0876

0.0546

0.0646

0.05Etl

0 .O537

3-0

Group

(Con d)

Moderator

Reflector

GL*UP

0 .O.532

0 .C1476

2.1

0.0518

0,0497

0,0:?26

0.0483

0.0312

0 .OL61

0.0277

0 e.01134

0.0262

0 a 0403

i) .0234.

r? .(I398

0 0199

0 *.0392

n .ol_tlp,

0 .O3%1

0 .0170

n ,13372

fi .0163

0.0361

0,0156

0.035cr

0 0149

0.0356

0.0135

0,0355

0 .OX28

0.0353

0 B Ol&

0.0352

Q .9999

9992

1,0000 -- T o t a l

&mnrlix L , Two Group. Three ReEion Data I n p e ~ f o m i r qa critical i t y calculation on the Screwbal.1

reactor, the three r e g i o n s were chosen

%o a p p o x i m a t e

most accuratel-y

ihe a c t u a l r e a c t o r .

The dimensions o f the IAree regtons aye shown i n .Figure 6 . The constituent volumes in each r e n i o n a r e as follows:

Region TI1

El-ement

Reircion

NaOD

5117.10

1936 3

6975.20

Fue 1

4890 .OO

Inconel

2'75.03

Nickel

SleEion

56.14

Beryllium

--0

Totals

5117,lO in3

T o t a l volume o f a l l regions

-70-

71.57.5 in3

75764.6 i n 3

145.77 236.27

%ziL&L% 63492.17 in3

Apmndix 5, Optimization

2, &sPe Ass-: I n order t o e x t r a c t 2C0 f?%!

o f h e a t a t 2,5

of fuel i n t h e r e a c t o r core i s necessary,

Moi/cc, a fixed volume

Usine this volme the system

was o p t i m i ~ e dfror: t h e nuclear and engineering standpoint by varying t h e

number o f tubes an6 t h e tube dimeters. 2

Fs.ctors Considered and Their Associated Parameters ; The self s h i e l d i n g factor F

a. Self Shielding:

i s discussed

i n Section 5 $ 2 . It can be shown that F depends directly. upon the 2 5 m e t e r af %hi: tubc.

b. Pressw-e Surze:

This c r i t e r i o n r e q u i r e s further i n v e s t i g a t i o n .

However, t h c l a r g e r the r a t i o o f c e n t r d flow area t o t h e exit f l o w area t h e more severe thy: problerl will be,

~ 2 - c e n t r a l flow a r e a e x i t flow area

Thus we w i z h t o minimize "L, where

The amount of heat t r a n s f e r r e d , Q, can be

e. Eeat Transfer:

shw-n t o be proportional t o nOe2L

o f l e n g t h , L , and Diameter,

, where

n is the nmber of tubes o f

D, It is desirable t o minimize the h e a t

trensferred t o t h e â&#x201A;Ź M I D . d

PresLjureLoss:

nu& lower than t h a t

major importance

The pressure drop in t h e fuel tubes w i l l be

i n t h e h e a t exchanger, hence this facto:- i s n o t of

The parameter used was AP

J?y

e . fabrication:

An index of fah-.icai?ilitg i s tube length;

the l o n g e r &e tube, t'rie more turns made, and hence g r e a t e r f a b r i c a t i o n

problems

f, Poisons:

Since f o r a fixed diameter t h e t o t a l . tube length

i s constant, thc: r a t i o o f 11oison to fuel adccd i s independent o f t h e

nwiber o f tubes.

Howeve-., t h e poison increases as t h e tube diameter

The pzciinetzr i s ,

decreizses.

cc/

Volwne of fuel

The reactor weight iiicreases w i t h core

g e Core Uiaunzter:

It i,s secn tizat t h e dimie-ber increases

diameter. diameter

Volmie o f inconel

t.itki

decreasing tube

3, .-Table of Lbom Factors f o r Va-rious Conbinations: -

___l__m_ll__-cII-

I n the t a b l e tl-ere ,?re two values given f o r the s e l f - s h i e l d i n g factor

t'nc f i r s t being f o r t h e f a s t neutrons and the second figure

for t h c theimal neutrons. Factor a

. 3cl f - s h i r l d i n g

Symbol 7

b, Prensure su-ge

e . Heat h.7nn;fe.r

d . Pressure l o s s

0 ..46

0.$2

0 .3F

['.R3

0.80

0.78

5.5

3.8

3.5

211

18.5

3.2

2L9

108

92 .IC

f PG? SOnS

' b " r)

0.50

e;. Core diameter

2- 3 9n 6 4 1/2 i n

0.61

e . Fabrication e

2 itl

0 .Ob9

0 .Or5

39 2.2

86 0 .nl,4 2'7

A s a cmp*omise between nuclear and cnzineering considerations,

s i x t,hree and

one-half inch tubes were sel.ected.

-72-

The power absorption was c a l c u l a t e d accoi:ding t o formula ( 3 ) yielding:

r (in1

WEOD

E!zL&.Lirz

P (r)

(~~/in3)

10.69

0.379

0.603

3.438

0,697

0.529

0.840

1.3

0.5~6

0.863

114

0.493,

0.782.

14.3

i? .r,Qo

0.731

h32LIlus :

The power a b m r p t i o n

~ 2 . sc a l c u l a t e d

according

tfi

(

yielding:

1.4-4

0 e 1,oo

14.8

0.329

25 . l 3

0.291

Hickel-Inconel Shell:

-73-

(in)

-P--( r j

FJ(1") /p ( 0 )

(~~/in3)

15.13

0.872

1.387

15 .S9

0.799

1.255

15.25

0.715

1.I 37

?e flect0'1 :

The power absorbed in the r e f l e c t o r

W E ~ Scalculated

equatiom(1,) and (8) and natching the two f o m s a-t

Using this s o u x e th;-ouqhout and ( 8 ) r (in)

I" =

u-iing

17 inches.

t h e power absorption is:

-P(~)/P& (in-11

P (r)

(XW/in')

?.5.25

0.161

0.798

0 .080l,

0.398

0 .0L21L

0.210

0.021!,0

0.119

0. O l Q

0.070/,

0.00862

0.01427

0.00534.

0.026L.

0.00298

0.01L8

0.00213

0.0106

0 .OOlLX-,

0.00695

0.(I0103

0.00508

o.ooog5

0.00.!+71

The power was evaluated using equations

( 4 ) and

(5).

The curves were matched at r = 6 i n , y i e l d i n g a fietLtious source on

0.e

0.0336

0.0747

0e 0337

0.0749

0.0346

0 0791

0,0362

0 .Of305

0.0386

0 .O358

0 .O&L

e so937

0 0,473

0 .105

P (r1/P ( 0 ) 7

0 e 9828

0.131

67,1055

0,168

0.1777

0.21-9

0 -191

0 304

io.69

0.269

0 -428

+ Celculrted from (

itppendlx 7, Core Heat Transfer The following

i,T

a saxiple c a l c u l a t i o n o f thc tube wall

t e ~ q ~ r a t u raet x = 19.

V, (NaOI))

h f e e t per second

1.57 x 4 = 9.&? f e e t p e r second

= 101.2 Ctu/hr.

f t2 O F

from Figwe 8

31+5OF (estimatcd)

Tine t o t a l h e a t t r a n s f e r a r e a c a l c u l a t e d i s 3i:.6

q =

= 1.28

A AT

f t2

x 107 e t u / h r .

The average temperature r i s e of the NaOD I n the core is then obtained. The gamma heat flux from t h c inconel tube i s estimated t o be

5.61 x 104 B t u / l i r .

AT,

f-t2.

1.2OF due t o g m n a heating.

Since the heat a d d i t i o n t o t h e Na0D r e s u l t s i n such a small tenpesature r i s e , the temperature i n c r e a s e through the core was assumed l i n e a r and t h e t e a p e p a t w e kise t o p o i n t x = 19 was 6OF.

t h e t e n p e r a t u r e difference between t h e 13.3013 snd

fuel.

= soy

The h e a t flux i s t h u s ,

UX AT,=

3.65 x

lo5 Etu/

. .

hr f t 2

The t e n p c r a h r e rise through t h e fJaOD i s fomG by dividing the heat fluxes duc

tf2

lieat t r a n s f e r and g a m a h e a t i n g by the l o c a l h e a t trasfer c o e f f i c i e n t

~ O L .NnOD.

Heat -transfer

AT,

.@ding these temperature rises to

+ -

tine

va1.1 terzperature of 1254OF

-76-

215OF

Gm:la heatin? AT2 = 33OF

MaOD tzmperaturre o f 10C)O째F gives a

The design procedure f o r the primary heat exchawer is presented

in Reference 19. The following assumptions were made: 1, P?wnber of tubes = 5220

5. Tube crossing ang1.e at the equstor = 300

Tube bundle thickness

4t'

Applying these assumptions to the c u r v e s Cmd equations in Reference 19, the following results were obtained:

1. For @= 450,

450,

@= Goo,

(I) =

900,

TO%& angle 02 r volution 2 . fie1 volume = 7.45 ft,

4. Fuel pressure Loss;

7&0

90째

~ 6 4 ~

= 33 psi

EaK pressure l o s s = 31 p s i

5. Tube length

?,35 ft,

6. Eleat transfer coeff'icients : Fuel NaK

= 2

3110 Rtu/hl-w ft?3 OF

16,600 Btu/l-i.:.

7 . Log mean temperature difference = I48OF

ft? O F

8 , Calculated heat t r a n s f e r = 198 FM

The heat transfer required for ti?@ prjnar-y h e a t exchanger i s approximately

185 NU, leaving a margin of 13 b%J to a l l o w for inaccuracies in t h e h e a t transfer calculations,

- 77-

1. 9equii-ed heet t r a n s f e r = 16 1114 3.. Flow r a t e s UaOD = 1595 lbs/sec (prelirninaxy

estimate)

General C onf igkzrat ion

NaK

.1-26

WaK Tubes .070 Tctal.

F'J.o~..JVel. o c i t i e s l

0 >336 in?

Qfs

Peat '?ransfer Coefffcientsa

ITah = 133,000 B.Cu/ht,. ft?

F w inconel, 11 =

fL:

= LO80 Btu/hr,

or"

The over-all heat transfer c o e f f i c i e n t for the o u t s i d e tube area

1780 Btulhx ft2 h a t t r a n s f e r arcas:

iirea :*ecluired for

-iS

16 i4ld

? , ~ , * ~ i ~ : ? ~ i ~

43% ft2

Them calculations have been based on t w o p a r a l l e l . flow passes,

Tfie

aclditional heat t r a n z f e r due to cross Cl-ov will compensate f o r the

inaccuracies i n heat t r n n s f e r calculations. P:-*essure Loss Calmfiations :

Slxmary:

Tube I.0ss

0.7 p s i

Entrance l o s s = 0,5

Exit 103;s TO%&

1.2

_ I

?,5

(approxhately 3 p s i )

-0.15

c D E

f F

k? h

k I,

M s

R S

t F

v2 -T -3

,”

c 22

Sub8e r i p t s et

eff f

s L

I1 I2

absorption cope

effective

fission

L e t h W a gPOU2

scattering

total

XI1

112

1111 1112

transport

fast group, region I

Superscripts

therm1 group, region I f a s t grouy, region 11 thermal group, region 13

fast g r o u ~ ,region 111

t h e r m a l . group, region III

P B

I " -

rmlius of circle having area equal to hexagonal c e l l

B -

8,ngl.e between r aazd R angle o f latitnde

A p"-

7 -

r e l m a t i o n leng:th tTIxco9ity

o r gamma absorption c o e f f i c i e n t

variable of integration

distance between F and R

C " demity

s -

sumnation

T -

garma energy deposition cosfficienty

e n t r a c e angle between tubes ad.hinge of constant longitude

poison gmmeer

pressure surge parameter Subscripts

reflector

heat tramfer component