"1 RESEARCH MEMORANDUM

I CALCULATIFS REACTIYITY OF URANYL-FLmBfDE - WATER CRITICALITY EXP-

By Donald Bogart and Leonard Soffer

Lewis Flight Propuleiini XSbrakory -

Cleveland, O b ..

I . .. - I I . . . . .

NATIONAL ADVISORY COMMITTEE I I FOR AERONAUTICS

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M

r

2 mC4" E55L23

For water-modefated reactors with .significant neutron production at epithermal energies, a modLfied"&up method uas fatmuhte-d which con- siders the d e t a i l s of the .@roceases in the epmd region (ref. 6) .

'phe validity of reactor criticality calculatione by groug mew is best tested by apEly3ng these methods to a eet of controlled criti? ~ a l "ts . m e o a l ~ A t a g e critical mass etudles (refs. 7 and 8 ) provide , a n excellent. set of experbnerrts to &e& diffusion-theory groq analysis as itapplies to hydrogen-moderated reactors. These experi- ments ' a r e ideal for analysis, a0 they consist of homogeneous solutione of uranyl fluoride in water enclosed by thin aluminum or sta idem-stee l cy3.indrical.c-a with and without water reflectors. 'phe uranium . is .enriched to contain 93.4 &cent urani~m-235. EI= modified group method of reference '6' I s amlied herein to all the baFe and water- reflected critical -ts reported in.refqnce 7., with the excep- tion of the cadmium-cuvered water-reflected caees. In addition, the re- s u l t s of an extended progmm of critical. experiments in cylindrical Be- -try reported in reference 8 are included in the presen.t"sis. - group forwrlatlon qloyed makes m e of the pecuUezly rapid elowing- down properties of hydrogen and includes the effects of epithezmal ab- sorption and flssion. Iche concept. of reflector savings, calculated by two-grorzp analysis, is employed in eyaleting the criticality of the reflected ex~?mim~&8l assenibliea .

Since the experirraents of reference 7 -re reported, these data have been widely analyzed. Schuake and Morfltt (refs. 9 and 10) in meking safe handling procedures spxeeded in fi3- the experimental data to empirid curves. ~acklin (ref. LL) later inproved the reh- tions in order. to extend the. data beyond the experimental range. Clark (ref. 12) applied .a- one-graup neutron diffusion-m-&l. to tpe -hen- tal . d a t a in order to establish a basis for estimating the nuclear eafety of .sepexation-process equlpent . ,

- . V a r i o u s . investigators, led by G r e u l i n g (ref%. 13 and 14), have at-

tempted to obtain a c c m p d ~ ~ ~ i v e yet simple theary of the hydrogen- moderated reactor. -MUS, B ~ U , Bendt, and (2%f6. 15, U, 17, and 18, reepectively) have &mJyzed the "ntal data with such an object In mind. With individually varying methods, a l l haxe obtained

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' reasonable results. llre present report at-ts to determine how the b modified group method of criticality analy-sis, eqloyed i n HACA am-

lytical reactor studies, predicts the reactivfty of the water reactors of references 7 asd 8.

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energy per collison. This three-anergy-region picture leade t o the fol- lowing cr i t ica l i ty equation (see appendix A for definition of syubole) : #

The flrst term represents the contribution to the neutron gener- ation du= to fissions by thermalized mutrom, wherein the quantlty l/(l+ Lp2) is the probability of a neutran escaping. leakage in slow-

~ n g ao~n to - energies in a of buckling constant- ~ 2 ; pth is the f'r&ctFon of fission rmrtcom absorbed +.hat escape capture in slowing drnm t o thermal energies; 11 1 3. G B ie the probability of

a neutron emaping leakage during thenml diffusion; and IC, is the thermal multiplication constant.

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Evaluation of t h i s integral tern permite a detailed deterzrdnation of-the dlspoaition .of neutrone by leakage, absorption, and slowing with- in the epithennal region. Elmever, it is possible and desirable t0 re- place the integral-tqm by a m e conyenient tenn i m l v l n g quaatitlea W

averaged over the epithermal region. .'!Be a- values are obtafmd by weighting local va lues by the neutron f lux~s in thie epithennal re- gion. The wiatbn of neutron flux with e-gy fs evaluated an the * basis of an appropriate neu*o-n s l ~ - d . o w n model in an in f in i te me-

model has been used, &.me, far the reaqtors ;Indp-F 'coneiderathi, m" Important non- contributlona o c c u r z t ~ t h e epithermal region

dium of the Bame CmIpOsition. In ?he pres&t-.&ing.yjis:tb a@"-ory .-

c age theory. It has been shown i n reference 2 that - 9; ~lls;y be corre-

lated wlth the value of % for a given m e camposition, fnasmuch ae uranium Fs the only absorber whose cross section does not vary Inversely with neutron -city. TIE correaticm of % and for E

range of rmtw core cqos i t lom I s given in reference 2 and is used herein.

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The results of the criticality cslculatione for the bare and water- reflected cyllndrlcal-reactor experiment6 o f refwnces 7 and- 8 are pre- sented in figures I and 2, respectlkly. 'pbe evec t ive multiplication constant X&y as calculated fram eqyatlon (2) is plotted @net the E/U-235 at" ratio R. A distinct& i s made between t4e .d-- and steel-encloeed reactdi of .var ious diameters. In refererice8 7 and 8 , f o r reactors of a given diameter, the core hewt was varied to obtain crit lcall ty f o r solutions of difTerent uranium concentration cmseepond- 1% t o the ordinate R.. The material parsmeters used in cceqeutlng val- ues of Gff for all-values of R . q?e giv& i n $able I.

NAm RM E55Jx3 7

The results f o r the water-reflected reactors are shown in figure 2. There is apparently a mch greater scatter thctn for the bare reactors; however, tu0 important things axe noted: _- .

(1) he almtnum- and steel-contsinar points are separated 0.02 t o 0.03 in AK. Within each group of points. the s c a t t e r is abmt

contained assemblies and abaut an a- value of of I .OW far the steel-contained assemblies. .

"01 about an 8- value of Keff of 0.98 for WnUm-

8 HACA RM E 5 m 3

uncertainty in the critical height measurament may introduce a variation i n of 0.7 percent f o r the flatter reactors, whereas the m e r - taintg in uranium concentration mag introduce a variation in It&' of 0.6 percent for the leaner reactors. The eqerlmen@l errors may there- fare accoullt .for much of the scatter i n the data.

these cmdiguratians, two barn @r@ two reflected. . . I n the following table Mill I 6 redt6 are canqpared with those obtained in this report:

Diameter, %ff Atom Critical Reflector C o n t a i n e r might,. m . mass, thickness, mtefial an

IQ U-235 R ratio' Present R e f . 15 cm

rep& 25.4

.978 1.007 329 .893 19.78 Al 22.4. 25.4 .

.972 1.008 999 1.31 u.43 Al 44.3 38.L

.967 - -981 43.9 8.8 0 S t e e l . 32.3 25.4 0.979 1.005 52.9 7.9 0 Al 34.0

Both methods are i n relst ive agreement in predict.?ng the reactivity of . _

for the r i che r 'of the two lare reactare. F a the two reflected cases, Mills estimates reactivity 8 8 about 1 perch supercritical, a d the present report estimates these as abaut 2 p m e n t subcrfitical. Howaver, the indications a m that use of two-grow reflectar savings, which m e calculated far reactors of spherical gemtry and an l i ed herein t o the eqe r imen td aseemblies, is satis-ctory. The following discussion will indicate that the consistently subcritical predicted reactivFtFes for bare assemblies may be explained by considerations of the extrapo- lat ion length.

the bRre reactors, d both s h o w the 88me trend in unanrr?st-ti= &ff

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The extrapolation length 6, whose calculation is described in ap- . pendix B, is an .ing2ort;ant quantity used in cmuputing the gecnnetric buck- ling for bare reactors. The QuEtntity 6 was 8xbitrarU.y cmputed *am the transpOrt mean free path eduated from w s s ' secti.2~14 at a neutron energy of about 1 Mev. 'phis assumed that 1 Mew was representative of the energy of the leakage neutrop~. It is qyLte.poss1bl.e that a acnae- what higher enera shuld be used with cmreeponding d e r cross sec- tions, leading to a s l i g h t l y bger extrapolation length.

In order t o determine. the effect on the predicted reactivity of a change fn the extrapolation length 6, the criti-ty of all the bare reactars was recmputed with values of 6 increased by 10 percent over

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RACA RM E55L23 9

those used 'for figure 1 (these appear in table I) . Tfie results of these calculations are shown in figure 3. Caparison of figures 1 and 3 indi- cate~ that arbitrarily increaeing the extrapolation afstaace serves to shift the data in a more or less unifarm way, maldng the reactivity pre- actions closer to ~ t y . m t t e r reactors ( ~ g e r ~ t e r s ) as a group are more sensitive to changes in 6. Since they are flat, the axial bucklin is sensitive to changes in the extrapolation L e n g t h . , It is appaxent that no one value of 6 can serve for all the data points.

Clark (ref. 12) has used the Oak Ridge critical mas8 study data to

to 3.5. centimeters, a e e e with the values used herefn. l3e indications are that the choice of 1Mev as a neutron energy to eelect cros~ Bec- tbns for estimating values of 6 fe eatisfactory for hydrogen- moderated critical asseniblles.

r2 PrJ calcnlate ex"8p.olation distances; and his. results, which vary fram 3.0

0

A modified poxq methoa of criticality analysis, emplayed i n m i - ou8 NAW 8nalyt;ical reactor studies, was applied to the experimental configurcttions vhich are p&Ft of the OEhk R i d g e crltical mas8 studies. The calculated reactivities of theee uranyl-fluoride - water critical assemblies were reasonably good far a l l the reflected and most of the bare cores over the errtire range of uranium concentration and core ge- ometry covered by the Oak Ridge -nts. The effects of almulnum and steel containers on the reactivfty of water-reflected assePibUes were Indicated.

Lewis Flight propulsion Laboratory l&tional Advtsory Ccmdttee for Aeronautics.

Cl-, m o , Decder 31, 1955

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APPENDIX A

B2

E

K

&f f

L2

N

'th

Q

R

t

6

x U

F1

P

z

u .

T

fr: 8

w

..+

"

. c

- *

NACA RM E55L23

9

Subscripts :

A

C

F

f cu 0 10

~

M i

r

s

1

z- TR

B th NU

Q

absorption

care

fission

fast-neqtron p u p

intermediate neutron @mtq

reflector

scattering

t o t a l

transport

therIuElne!utrangrorq! -

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12 NACA RM E55LZ3

In the critfcality equation ueed to calculate geff (eq. (2 1 1, the requlrea pammeters fall Into the following categorlea:

The thd paremetera are calculated Froan the* definitions a8 f o l l m :

NACh RM E L 2 3 l3

I = 0.33 4.5 0

3 .o 3 -94 0 F

7 .O 10.0. 687 u-235 3.5 4 .la 0

580 (UP 0.025)

If it is esemed that hydrogen is the only scatterer and that other ab- sorbers obey - l/v uw in the epitherd. region, a s i m p ~ ~ - r e ~ t i o n s ~ p derived in reference 2 may be wed ham:

c

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8 W MY

Figure 6 was used to proulde values of p.t;h for a l l solutions

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“terS

he %at-neutron s ~ n g - h w n length $ wae caoaguted ~ i t h +he

nyl fluoride of different concentnstlons. m e results were averaged method of Marshals (ref. 22, eq. (A-3)) for water and solutions of ulg-

over the U-235 fission spectrum (ref. 23). Be- the UO& used’* the criticality eqeriments was only 93.4 percent enriched i n U-235, Consideration waa given to the’ scattering prop&rtiee of the fluoride asaoclated with U-234 and U-238. The results of t h i s calculation gave L:=25.36 square centimsters for p water. This calculated value forr

to thermal energies of 31.8 square centimefxrs (ref. 24 1. The values for the fluaria solutione were s l d h r l y a4justed by the 68me ratio. A CUrVe’ Of aajuStd Of L2f wiIl6.t 1/R I S preSeZl”d in fiecure 6.

Also included in figure 6. 1s a, curve o f ’ Ti Ebna (L; - quired for all fluoride solutions were read from the curye.

pure water was adjusted. to the-“ vrtlue of slowing-tloun Length

- Ti). values re-

whererand meters, d 6 or a reflector

Since the

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thin reflectors, the mvings can be apprcudmstd by use of the foU- &tion (ref. 2):

Lo 5.85 6 .lB 6.55 7-20 30 6.25

, 6.60 7.00 7.75

The family of curyes of reflect= savings ae;alnst reflect- thick- ness is given in figure 7. .

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All the reflected reactors of reference 7 had a 6-fnch reflectar on top and a &inch reflector cm bottapn. The reactors of reference 8 had

6 inches of water. According t o two-group themy, the saturated reflec- tor savings for water reflectors on lean water-moderated cores should be appro-tew (see ref. 2)

2

6 =I 4-i = -131.8 -t 7.66 = 6.28 cm

which is in exlcellent -anent with the value obtained for R - 999 at t er 30 centimeters. The value of 6 for reflected reactors obtained ‘by Clark (ref. 12) I s around 6 centimeters, which is in good agmenent with

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18 - mCA RME55L23

K4CA RM E55L23 t

The authors of reference 7 break down the experFmsntal - into cu .two types ; a &&millimeter error i n messuring the critical height, and 8 M

a &-percent error in es tbpt ing the uranium concentration. An errocp i n measuring the critical height would be more important for the flat- ter cares; emor in uranium concentration WOuLa be more 3mporknt for the leaner, 'less concentxated cores.

A-1 A-6 8-1 5-5 8-15 8-17 5-19

R

52 -9

43.9 755

174 ll9 329 755

L

1.34 1.14 1.27 1-52 .20 34 .53

0.11 . .06 .lo '

.08

.71

.54

.25 L

0.08 .5!5 .I2 .l6 - 07 .14 -57

rotRl AK, k

0 .I3 61

.22

.24

.78 68

.02

.

.

20 NACA RM E51;23 c

2. Bogart, Donald, aud Soffer, Leonard: Criticality Survey of Hydrox- idee as Coolant Moderatore for Aircraft Nuclear R e a c t o r s . RAW RM E53F30, 1953.

3. McCready, Robert R., Spomer, R o b e r t B., and Valerino, Michael F. : Distribution of Fissionable Material in Thermal Reactors of Bpher- icd GecPraetry for uhifolpl Power Generation. NlGA RM E 2 C U , 1952.

6 - B m , D , aad Vale-, M. F - Sane .mi them Effects Criti- cality Requirements of Water-Moderated ReactorsLTD-2014, Wac- tor Sci. and Tech., vol. 4, no. 3, Sept . 1956, pp. 107-ll4.

8 . Blizard, E. P., ed.: Critical Exprimente. phse. Div., Eiemiannual Bog. Rep. for Period Ending Mar. 10, 1955. OWETL 1926, Ckik Ridge Net- Ub.. mt. 7, 1955. . .

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10. Schuske, C. L., and Morfltt, J. W.: mlrical. Studies of Saue Crit- ical Bss Data, pt. II. Y-829, Carbide and Carbon Chem. Co., Dec. 5 , 1951. . . L . . .

11. Macklin, e- .L- : CylFadrid Reactor f ion^ O f the wa.t;er Enriched Urarryl Fluoride-Water System as a Function of Ccmcentra- tian. Rep. KO. K-905, Carbide and Carbon Chem. Co., MaJr 9, 1952.

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mCA RM Em3 21

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20. Anon.: Neutron Cross Sections: A C c m r p i h t i a n of tbe AM: N e u t r o n Section Advisory -. BNL-170,. Brookhaven Hat. Lab ., Upton (N.Y), WeJr 15, 1952. '

21. Glaestone, sannzel, and Edlund., Milton C. : . T h e m t s of Nuchez k c t o r Theory. D. Van mostrand Co., Inc., 1952.

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22 HculA Rzd E55L23 1

w m I. - MATkRIAL PARAmTERB 8

R

24.4 26.2 26.9 29.9 31.6 43.9 52.9 56.7 58.8 Q.1 62.7 71.5' 73.4 74.0 75.5 86.4 99.5 L19 L23.2 L69 L74 t92. 3 2 l 226 3 9 0 520 529 L99 755 399 0

2.052 1.800 2 -051 1 799 2.050 1.798 2.047 1.796 2.085 1.795 2 .OS. 1.789 2.024- 1.785 2.02l 1.784 2..019 1.783 2.017 1.782 2.035' 1.780 2.007 1.776 2.005 1.775 2.005 1.775 2.003 1.772 1.9Q3. I. 772 1.98U 1.762 1.962 1.753 1.959 1.7SL 1.918 1.726 1.9l4' 1.724 1.898 1.715' 1.874 1.700 1.870 1.697 1.819 1.665 1.796 1 . S O 1.789 1.646

1.516 1.444

0 0

1.669. 1.559

1.395 1 . m

Pt4

0.187 .210 .218 .254 .275 .391 .457 .em .493 .SO6 ,515 .557 .566 ,568 .573 .6l4 .a3 .6% .707 .772 .778 .795' .8l7 .azo .853 .864. .867 .905 .930 .942 .gel

36.81 35.95 3!j .64 34r-73

34.31 32.97 32.50 32.47 32.42 32 .S 32.34 32.31 32.20 32.20 32.20 32.10 32.03 31.98 31.98

31.88 31.86 31.85 31.85 31.82 31.82 31.81 31.80 31.79 31.79 31.79

31. a9

55.25 34.50 34.28 33.49 35.19 32 .L a.84 31.79 31.75 31.72 31.71 31.65 31.61 31.61 31.61 31.60 31.58 31.57 31.57 31.58 51.58 31.59 51.59 31.59 31.60 31.60 31.60 31.61 31.61 3I. 63 31.65

0 .I32 .136 ,149 . E O .153 .193 .223 .236 .243 .250 .257 .308 .3E .317 .322 .337 .382 .446 .460 .607 .623 .679 .767 .7al .966

1.049 1 .OE 1.509 2 1065 2 . m 7.689

- 8, cm - 3.24 3.22 3.15 3.21 3.21 3.21 3.22 3.23 3.23 3.23 3.23 3.24 3.25 3.25 3.25 3.26 3.27 3.27 3.28 3.29. 3.29 3.29 3.50 3.30 3.30 3.50 3.31 3.31 5.32 3.32 3.35 -

8

t

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XACA RM ES5L23 4

P

23

1000 Reactor

600 .

400 '

V T V A aa

diameter, in.

9 10 l2 15 20 30

Open Steel container I 'Solid Aluminum container

4

I

b

P t

&- \

+

.98 1 .oo Effective multiplication factor, ICeff

Figure 1. -.EPfective multiplication factor f o r bare uranyl-flouride - water cylindrical critical aesemblies of references 7 and 8. '

24 NACA RM E55L23 c

L.

Reactor diameter,

i n .

0 6 0 6.5 0 A

7 8

V P

9 LO

V 12 I A 15 1000

800

A

Open Steel container Solld Aluminum container Flags Data from ref. 8 600

400

200

100

80

60

40

201 I I I I I I I 1 f f I .94 .96 .98 1 .oo 1.02 1.04

Effective multiplication factor, K d f

c

c

c

Figure 2. - Effective multiplication .factor for. reflected uranyl-flouride - wetter c y l i ~ r i c & l c r i t i c a l assemblies of reference6 7 and 8 .

1000 [ I I I I I

800. A

600.

400 diameter,

25

V ';I V A

200 . h 4

9 10 12 15 20 30

Open Steel container Solid Aluminum contalner

100

80

60

40

20 .94 -- .96 ' .9a 1.00 1.02 1.04

Effective multiplication factor, Kerf

Figure 3. - Effect of IO-percent increase of ex t rqola t ion distance on effective multiplication factor for bare uranyl- f louride - water cy l indr ica l c r i t i ca l assemblies of references 7 and 8.

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Figure 4 . - U r a n i u m atomic concentration m. function of hydrogen atomic concentration for varloue uranyl-flouride - water eolutions at rwm temperature, calculated from experimental data of reference 7.

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NAGA RM E55L23

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Figure 5. - Noacapture probabiltty for uranyl-flouride - water solutione at room temperature. .

28

r 0

Figure 6. - Mean-square slowing-down distance fpr uranyl-flourT.de - water solutions at room temperature.

r

t

L

. . . .. . -

s L L a

0 4 8 12 16 20 24 28 Reflector thlckness, t, cm

4 b

Figure 7. - Reflector savlngs due t o water reflector for uranyl-flouride - water Bolutlone at room temperature, calculated by two-gxoup theory.

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