ML19347A389

App 1 to State Univ of Ny at Buffalo Final Hazards Summary Rept,Revision 2

ML19347A389
Person / Time
Site:	University of Buffalo
Issue date:	09/23/1963
From:	NEW YORK, STATE UNIV. OF, BUFFALO, NY
To:
References
NUDOCS 8104080573
Download: ML19347A389 (54)

Text

.

APP 2 MIX I A.

Physics

_1.

Gtondy State:

The coro physics computctions for the steady etcto condition were perforced in part by using hand cott.putation techniques, and in part by use of the PDQ machine code.(15). Constants for both these methods of cor.:putations were derived by use of the method of Deutsch (17).

This technique for derivirg: core constants has been verified by Dcuccch through a series of computations of coras such as Yan*cae and HS Savannrh which allow comparison of computed and measured l1 l

resulte. The techniqua parmits competstion of three group constants I

for use in 22Q machine computations, or for hand calculations of a

" Smeared Core." The group energy futervals are:

First grcup,10 m y to 100 Kev Epitherasi group.100 I'.ev to thermal cut-off Thermal group, from tharuc1 cut-off to acro energy i.

A paramatic study was undertaken using hand computations in order to optimizo rod diameter, rod spacing, cicd material, etc.

The formula used in these computations is as follows (constants were prepared by the aforementioned technique):

e.mg.o

,,)f E t &

l f g + flf J.

=

x...

Mch can be modified to the form i

u.

,a

u..

l %,

{ l & O'*% h{i s' (*!PT }{ l t YL.,**)

z

.k f

it i

I 8104o.8057A i

where:

fast fission factor C

=

7' neutron yield pcv fiosion

=

2 buckling D

=

f, age to 100 Kov

=

• /.1

= age from 100 Kev to thermal cut-off L

thermal diffusion icngth

=

resonance cacape probability p

=

absorption a

a

'~

f fission

=

s1 removal

=

1 fast energy group

=

l 2.

epithermal enargy group

=

thermal energy group 3

=

As a result of the optimization phase the reference core previously described was selected for more detailed computations.

Physics parameters associated with the reference cora are shown in

,4 Table A-1.

It ic noted in Table A that the reference core in a cold-clean condition with all rods removed has a k 1.092. A value

=

~

of 2.47 is used for the neutrons released per fission for the reason that Deutsch used the value in the development of his technique.

TABLE A-1 Physics Parameters Neutron temparcture, er (*K) 0.0525 (609)

Disadvantago factors: ifoderator 1.367 J

Cladding 1.184 5

Thormal absorption cross-section, ca,g 0.19 1

-106-

,il_

-.. ~ - _ - _. -.., _ - - -. - - - _. - _...

!t l

Thermal utili::ation, f 0.955 J=

Fest fission factor, C 1.0496 2

Acc, cm :

<.'. f as t,

30.73 n;;,cpithermal 17.57 Resonance esec.pc probability, n 0.767 i

Thermal diffusion area L, ca 1.178 i

2 l

2 2

Eicration area, E, cm 45.39 Rcficctor savings, J cm (redial) 7.739 Buckling, cu-2: vidth 0.003225 length 0.002555 height 0.001683 e tal 0.007493 1

'=

2 2 B L 0.00881 2

3 4-0.23

'1

}-

B [%,

0.1317 2

PB 0.101 r

(1 +L3) (t,3,g ) (1 + p3 -[2) 1.357

'22 2

2 y

Neutrons por fission 2.47 i

ko; 1.491

!<cgg 1.092 k gg with 36 assemblics, appro::imately 1.122 e

Neutron lifetice, sec.

t slowing doun tit:a 0.54 x 10**

2 thermal diffusion tira 1.5'J x 10-5 total 2.062 x 10-5 i =

Effectivo delayed neutron frz.ction Eeff 0.0076 A core with a square horizontal cross section was considered and the bucklino was adjusted to yield a k of unity. From this computatica was obtained. Thus, for a minimum critical nass of 251.5 kg of UO2 a square lattico configuration 17.6 fuel assemblies would be required for criticality. Sinco no partial fuel aasc=blics will bo prcvided,

~

it is evident thst a square configuration containing the required critical acss cannot be assembled, cad the resaltant configuration will ba less than optimum. It is, therafore, expected that the critical configuration will consist of a 5 by 4 core with one corner l -

missing; i.e., a loading of 272 kg.

In order to verify the cocquestional technique, calculations were also mode for the SPE2T oxide core and the results were compared

-107-

.. ~

.... --..m

,1

(

favorably to the values s stred at h?23.

Threc Group cons unta ucra genarated for use in PDQ calculations. The catal fuel cler.cnt bo:ces, the metal in the rod

.i guides, the rods thc=selves, the water between fuel cic= cat boxes, w

']

and the water within the rod guid(.c were treated as separate regions J

and constants prepared accordingly. The fuel, zircaloy cladding, and

}

water inside tha boxes were homogenized and constants were generated for the resultcnt homogencous ccdium. For computational purposes, 1

all six rods ucre sacumed to be control safety rods. A nu=ber of PLQ cases were computed. Table A-2 indicates results obtained from

,]

the various PDQ cases.

t

]a TABLE A-2 Results of PDO Coenutetions

, 'll Change Compared f4' Cese 4 Condition konc in h M) with Case #

,==

~

1 Cold, Cican, Rods out, H O Temperature, 1000 F 1.077 2

2 Cold, clean, Rods In, H O Temperature, 1000 F 0.764

- 31.3 1

2

~

3 Cold, C1can, 'tJ" Shaped Core, Rods out, H O Temp., 1000 F 1.013 6.4 1

j 2

4 Cold, Clean, one Element in "U", Rods out, H O Temp.,

- 1 2

1000 7, 1.051

+ 3.0 3

5 Cold, Clean, Central Element Removed, Rods out, H2O j

Temperature, 100* 7.

1.058 1.9 1

.]

6 Hot, Clean, Rods Out. H O 2

C

-5 Temperature, 140 7 1.065 1.2 1

y 7

Cold, Clean, Single Cont. ol Bod Inserted H O Temp., 100070.987 9.0 1

2 Cold, Clasn, Rods out,1Y. Void O

0 in H 0, H O Temp., 103 F 1.068 0.9 1

2 2

9 Cold, Clean, unds Cut. Thermal Column in Placa B0 2

Tomperature, 100' F 1.091

+ 1.4 1

=.

-108-L

__..e-

.om e

1 A hot-cict.n rods out case was run to give en indication of the icothermal teapcrature coefficient. Conctcats vero prepared for this case on the basis of a uniform temperature of 140* F uhich is 40 F higher than the cold cican case. Examination of the results shows an isothermal tecperaturo coefficient of -3 x 10~0

~

4y delta h/h*/ F or 3.9 cents / F.

This comparcs to a measured value of approximately 0.7 cents /* F for the SPERT oxide core. The large

^%

difference is primarily explained by the fact that the APR is drier than the SP2nT core and hence quite undermoderated. A case was run

~

with voter density of 99% in order to obtain an estimate of the void

!. E coefficient. Results in Table A-2 indicate a void coefficient of s

0.97. delta h/k/7. void or $1.10/% void; wherear, the measured void 7

coefficient for the SPZPC 0::ide Core was 39 cents /% void, i

Sevaral cascs vore run to evaluate fuel worth in certain

~

icttice positions for purposes of analyzing certain fuel handling I

accidents. A "U" shaped core with assemblias 3, 3, C, and C4 3

4 3

1.013. If an assemoly placed (Figure 19 ) removed has a h

=

into the opt 1=um location in the U, the resultant core has a 1.051, giving a value for the assembly of 3.8% delta k/k in k

=

reactivity. A configuration with the central assembly removed was lt l[

also exacined. The computational lattice was set up for only half w

l; a core, using a line of cymmetry betveca rows 3 cnd 4.

This cou-figuration, therefore, actually had half an element removed from D 3

and half an elenant from D, and resultad in a h of 1.050

Thus, 4

~

the fuel worth of the central element in 1.9% delta k/k in j,

reactivity.

-109-

+ - - -

2.

Transient:

=

There are several rather simple foar.ulao w' ich can be used a

n to estic:ste the pulso characteristics, following a step input of reactivity. For exc:nplc ( 18 ):

3. _

2 <?.

Iy ll Eb f.$ "

' -=

2 l

]

where px is the excess reactivity above prompt critical 1.-

E is the energy in tccacuatt-seconds b is a constaat of proporcionality The constant b, equals the compensating reactivity. In the caso of

~

the UO core, the corapenscting or shut-down sacchanism is provided 2

t, by the Doppler effect.

8

-J

'd Then b

=

l

~

where.fis the Doppler coefficient c.nd e is the heat capacity of UO

,I 2

.],

Thus E. 2 3.C

.s From the in-hour equation

-=

1*

1 T

=

1 i

.k i

where 1* =. neutron generation time, seconds

'I1,3 -

2i sechle reactor period, seconds

=

'E Also 15 2

lI=

P.aa:c = P

+

--2b 1*

b 0

] --

= P

+ 1/2 8O b.

o

.v.

1 1~1 E

,0 47 1

-110-1I 1-

+ -

I If the pulso is initiated froc e low power, cs it will be. P is negligible.

E Then: P max =

4 T.

9, The following performances hcvc been calculated for the developmental pulse and the design pulsc:

TAtLE l.-3 _

I Pulse Computations Developmentcl Pulse Design Pulse

}..

Pulse Energy, Ei-seconds 39.5 69 g

It::icum Power, IH 1930 9,340 9jg Pulse Period, milliseconds 4.975 2.375 Pulsa Uidth ct half m:ximum, milliseconds 17.5 8.36

]I Input 2cactivity Recuired, o=

% delta h/h 1.17 1.63 Input accctivity (dollars) 1.546 2.142 9I Doppler Coefficient, 5

,j~

delta h/ C = 10 2.7 2.7 Doppler coefficient, cent /* C 0.359 0.356 Eccc Capacity of UO2 q

mewauste-seconds /* C 0.1297 0.1381 i-2 Temperature C ('F)

GOO (1471) 1650 (3000) 2" Maximum UO The above technique was used to cocpute pulsa characteristics s

of the SP32T 0xide Core. Results compared favorably with those j

o acasured in the SPERT tests, verifying the calculational technique.

The accuracy with which the pulse rod can be positioned initially will, in part, determine the cccuracy with which the pulse can be predicted and the repeatsbility of the pulsos. One sees that El f'l P1 (91)2 s.

and

'I E2

. 2 P2 (p2)'

'3 The positioning accuracy of a standard drive is better 1,

Ii than 0.1% of full stroke or 0.024".

For the design pulse, 1.63%

l

-111=

(.

Jh*

delta h/h excess vill be inserted. If the full rod vere worth this much, the position accuracy smuld ccan an uncertaanty of.00163%

L=

delta k/k or 0.2 cents; houever, rod Ho. 5 has a calculated maximum worth of 0.2337 delta k/h/in. Therefore, the uncertcinty trith which L

the rod can be positioned leads to a reactivity uncertainty of i

.74 cents.Tablo A-4 shows the.ncertainties of power and energy for 40 and 90 megawatt-second pulses, i

)

TABLE A-4 Pulse Accuracies 3csis :

Basis :

l" Total Rod Uorth Averegcd Ihx. Incremen::a1 Rod Worth 1.637. delta k/k/24 inches 0.235% dolta k/k/ inch l

Developtiental Dasign Pulse Developmental Design Pulso 0==

Pulso Pulso Power (ni) 1980 t 14 9340 1 32 1980 i 50 9340 110 Energy (ar-sec) 39.5 1 0.1 89 1 0.2 39.5 1 0.5 89 1 0.5 B.

Reactivity Effects I

1.

Lona Term Operation:

a_

A machine calculation (19) was used to determine the multiplication factor as a function of core burnup. A number of simplifying assumptions were made in the development of the machine

' ~

code used to analyze this problam; however, it is felt that the results obtained. are sufficiently accurate for examination of a i

research reactor core where the fuel configuration is not fixed.

O g

Tha multiplication factor versus operating time is plotted in b

Pigure Al. The core has a calculated burnup of 11,800 megawatt days /tonna of UO ; however, it would not be possible to continue 2

b

-112-m

j, pulcing operations to such a burnup. For the reference four by five core, an c:cccas reactiv..;y of 1.C37 is required to initiate a F

A-pulse of 90 meumiatt-second energy reicese; therefore, from i

Figure A-1, a burnup ;! 3400 meccx. :-de/s (7,800 cecavatt-dcys/ tonne)

L is the upper lit i.t for the reference core used in the pulsing mode.

9 i

At 7,800 oceanstt-days /conne, considered the usoful life of the 6=

core for pulsina, there will bc 10,300 grars of U-235 remaining, 9

I-and a total of 1,5G0 grams of Plutonium-239 vill hcvc been generated in the core. f.to buildup of Plutonium-239 could have two distinct b.e effects on the core characteristics: It could chcage the kinetics I

c2 the core by offecting S c change in the delayed net.cron fraction; o

c.nd it could chanac the shutdown machanism by effecting a change I-in the Doppler coefficient.

p The changa in 3 ucs c::sm'ned by weighting the egg

,'=

l Plutoniur-239 cad Uranium-135 p's (20) in proporcion to the per-5?.

centage of fissions occurring du the respective isotopes throughout (S

l the core. The results of this weighting process are shown in l

l1 -

Figure A-2, indicating a change of p,gg frota.007595 at zero burn-1 up to 0.00695 at burcup of'7,000 magawatt-days /conne. The change le l2 in $,;y could result in approscisataly an 07, change in period for a JII lJ given reactivity.

i It should be pointed out that the change in S,gg is l'.

probably Icss than tha uncertair.ty of the initial computation of R

Segg (20); however, since a change in 3,gg does occur, periodic j_

recalibration of tha shia safety roda vill be required.

lb oo

. a 113-a w

m v

m w-w-

e-ra 7-

,g-yv-+-

-+

1

!cm.

l.j,

The Dopplar coefficicat of reactivity arises principally through the effect of temperature on the reconance aLaorp;; ion cross section. The assumption was made that a chaage in fuel temperature

~

docs not directiv affect absorption in the U-235 and Pu-239 resonanccc. The number of U-230 stous in the core does not chanac o

j, cppreciably as a function of burnup. Thus, the main component of the Dopplc: coefficient remains unchan;cd, and in this somewhat simplified approach, the Doppler coefficient is not a function of core life. IQ:acurements of power coefficient have been made in the Yankee core (21), ( 22) cs a funccion of burnup. Results from these measurements indicato that the pouer coefficient increased approx-imately 10% by the time the core lifeti=c reached 6400 effective full 3

l" power hours. 'lho power coefficient was defined as the reactivity defc. per megawatt with zero power c::isting at the isothermal temperatura of 514 F and full power conditions being measured at-3 ll,

an average water temperature of 514 F.

The power coefficienc is

)

defint i as:

0" 29 dS O T fg 3

x W

=

3P 3 T gg

&P e

9 uhcre: P

= reactivier b

= Pouer

.*M T gg = Effective temperature of fuel e

U

= Staristical weight The statistical weight decreases slightly as a function G Teff T5ms, the product of -l 'T gg of core lifetime.

x a a 3y increased in the Yankee core as a function of core 'aife. The factor, l

l

-114-

\\

1 i

i i

s I

i j

!I 0

4

(

l i

1 Q

J O

J.

. n fi

~10 f

k' l

6 6.

.O y

. : G,'

g OQt 1

l Us..,

29 T l

I o

i d

I

-.m i

M l

D E '. - Q.

t Q

t

.7

• 8 4

s v.

j/.

l

!o 1 J

.r:u :.-

3 o3 4fa:

MM M Og i

Ov ve NO C l

w C-

[

6 i

i i

O t *' *l-i

• )

t Li l

g C

e f

3 b

g i

f CD s

l j

D

'o

• * * * = = -

I.......,'e iO I

t I

j j

.0 I

t l

t j

e e

?f 4

i d

i i

O i

/,-

l lo 4

o 1

e N

,w l

WM i

I i

>D t

0 C

t'

=vx i

.[I l

g O

O 1

O e

i e

3 I

l I

~

M

-13

g..

o N

O o.

O u

q o

O i

~

i a

a a

a

[

~

lin; I

a A.1

?

t 1

a 1

g i

t C

ll j

I S

I i

./.

i i

O i

i

{

i i

i>

+

=

i l

i I

l

!,/

1 i

i i

i l

I l

O t

j O

t 1

I i

i i

l O.

~.

h i

l i

4 l

t i

l I

l s

i i

l o

l t

4 i

'1-o I

.j i

O l

j M

I.

G

+

e 3I f,

y i

l m

i I

l*

I i

j_

v C

8 i

O

,j

?.

CG t

'O

-]

.l L,.

3 a

i i

ji s

i I

i i

i O

I I

-}

O.).

l s_

}

t i

tu I

i i,/

i

.,)

'O t

ji 1

O o

. 'l l l

O i

l 1

I i

j io i

e

O i

3

~3 Tj I

i i

c.

j=

3

,i e

g i

4 l

l in us e j

I s

if i

i io c:

--t 10

>3 j"

l/

I' I

V o

/

I l

)

t'

,8 4

'1

'g l

5 i

c3 g

' O 4,

i j

/; I I

i l

O l

'o i

I

/!

'=

l l

t i

}

f I

i O

o 8

i 1

O i

f l

,Ed I

5 3

l 3

i c.

.OUP l-t i

o

l I

9h l

i s]w x u.

I 1

1 l

./

-fI i

eh g' 6 g

n o

o o

O O

3 O

P V

O C.i 9

h Q

9 U

t.)

s.

.i) 04 s

s

,e

,s s

s e

u o

a o

t,E 1g A-2 i

.~,

.v

I

>-. "' a x -

1.: c..z: cu;c to i.:c~.c.;c beccur.,c t is c zua:;;1oc c,e fy a

-am.

palict contact, ;clie c ccicir.3, c.;c.; however, it is hslicvad

^' ',E thct since n

inc cc:cs na e function of

,.2. n..

s.

p.

cora life, the La;oler coefficicc:: dcc: not dccecc.;c c a function

.I of core 1120.

.'..y incraccc in :c.c Oopple ccafficienc vill m:he

.1, the c;stsa? tion thr.: i; doc.; no: vtc./ vi;h corc lifc consc vctivo.

2.

nnen en:'

'.m crir.-

'ai:,-

1

':ha c:g:c.:sica is che rce.ctivity effccc of Zanon cs a 4-.

3 function of cisc after c crtup,ti. h no Xcnon peccent initicily, Ig is givea (23) ay:

. ).. Tr~i t-

/ *f'/ ~i..

r n

/

• A I 1 ' 2 7 e.

.3^

' ~!

~ C:

.'t

.i 3

e,

4

. I t:

.! A c d ~ f.-

/~x - :,\\g \\.e j ' L..

~ ~ '

J 1I IIacrC sc i e: ' ' - ) ~ i *D,

c...: czut'.i'ariua a

D-155 cc~eca;rceiaa 4-b-b t

f

., %, 4

• c.u cqui.:...a,us

. 5 a.

. -Aa A

a

,e concentrction

,l E

M 4

d, s",

thc effective %c dccr.y constant m

ciuc af ct cts.: un. in seconds u

2.80 x 10-5 At 32,3

=

-l

2.. ::,,.-S

.w sce.

,sx

=

I

3. s,. n 10-18 2

cc

=

1, 7.'

= 0.2775 :c 10 ' n/ca'/sc.:

.e,'.. =

0. ",r2 w.

I 7 = 0.1344

~i e

-i ri-

P O

OO 1

l l

l O

I t

4-1 1

0N 1

i 2

-j O

O.

p 1

O h

I 3-m O.

O O

3 O

2 8

\\

i t

u n

N 1

O

~

.1 t

O o

>l_

I

. 7 i

i v

g i

i 5

1_

,i._.,

8 >1 a:

J 2

E8 1

Oc

-l g0 i-i o

I N

g 7I_

I J

i s

,E o"

o jB Ni ea j

\\ N g

t

.2_

-g zzzz.8888g88 g8 8888 s

s.

e

~

(me) Auous3AN sea-as

~l s

I6 '

h. l,!_

~

A-3

m i

,m

~

~-

I 4

4 i

~

0

~

4 is_

. ?.I h

_m_

nW 6

l,t l

i'*

l it' n

3 Im 2

,e 3

I P

~

U 8

T I i 2

R

~

A

>I c

T S

R

~

mI f

n

.I4 IL Ii

• I

[

A

~

E 4

T 2

F E

MI E TR i

sU 0

vG mIm 2

I g

P F

- t t;i*&

U D

O L

I S

f U

G tk_

xI 6

N I

e I L.

O 8

E N

V E

E X

L, y,

wE g

2

~

~

g 1

j O

d.

i 4

w

-=

r.

3I e.

c

~

a e.m

~

~

S o

i R

c U

O

~

l I

2_

E mI t

t T

I om O

l y, e, a

)

2 g

E i

g 8

t.

y g

e, S.

A 3,

2 s>4$8

= &4wa:

g a

i

. m

>e*=

Nl i'

l

I M i i

I M I MI I

't I

(M i i

i i

t I -

1 I

Im l

l i

i f

1 i

'-- ~

d--

'i -

• 1^ -b-E

-}

t.S

~ ~ =-

-l L--

---

t-s t

e.

{

6 s

s 8

-_.L.--..'...--...

t g--

y l

l l

l t

I 6

t.3 j

- -;-- g g

t a

o d'/,,,__ d:.r,..,_.,

,;;. _ ---- p

--f-----------t---

--t--

l i

1.2 l

t l

i I

I

[

EOUILIBRIUM l' EVE.', I a 1.11.q% ',

4.. _. _.I I

.._..t

+

....;-_..I 3.

l i

1 i

i e

I l

l i

__j... _..;

go g

4_... _.p ___

1 l

}...

_-.4

_.q_....._

t, i

I i

L i

___.4-__...4 s

. p.._.

I...-. _....... _

-]

i i

I 4

I s

1

..a. _.

. _...,.. _ _ _... _ _ _.____4.

,y i

n r

g

_ i....

l 1

p i

gA

-I--

-+-----i-

~~---

~~~;----

m i

4

..__ I _ __ _ A___._; _

...._ j._.

• .3 l

I 4

>.2

---

?-

l I

4..

___l.._..

{,e s

3 i

E I

i O

t 2

3 4

5 6

7 8

8 80 II 82 13 34 lb 16 17 18 19 20 28 22 TIME-HOURS XENON POISONING vsTIME AFTER SHUTDOWN FIGURE-

• - ' * ' ' " - = * - - -

t

- - - - -. - - - - - -, - = * - - - - - - - ~ ~ ~ ~

i l

Utilizing the above deta, Figure A-4 uns constructed.

From 9

this, the equilibrium xenon is seen to bc 1.19%.

The follouing equation (2)) yicids the reactivity contribution of xenon as a function of time after shutdown (with equilibrium xcnon present at shutdown):

1

.)

f

)

x:

FUI* b;; j,. - l o (,c-k t-S )

• 4-

-ky + jl

t

',tydo S

~7

-T C e2 where t = tino in seconds after shutdctm. Pisure A-5 depicts the behavior of xcaon after shutdown.

It is seen that peak xenon occurs three hours after shutdown and is 1.25% delta k/k. No difficulty is expected in over-riding xenon.

The equilibrium level of Samarium-149 poisoning is 9

5 independent of the core thermal flux and was calculated to be 0.83% delta k/h.

3.

Control Itod Worth:

One can deduce the total worth of the five safety-control rods, and of the pulse rod, from the results of the machine comput-i l_I acions listed in Table A2. As shown, the effective multiplication factor for the cold-clean-rods out condition is 1.077 and that for the cold-clean-rods in condition is 0.764 Thus, the total rod worth is seen to be 31.3% delta k/k. N worths of the individual rods were deduced by apportionity the total rod wrth as the squarc of the neutron flux in the various rod locations. The flux values were obtained from the PDQ computations. The relative flux and worth of the individual rods are listed for each of the shim-.

safat'/ rods, and for the pulse rod, in Table A5 h location of each rod is shown in Figure A-6

-116-h

lm TABLE A-5 Uorth of_ Shica Safety v.ods I

D f ($)

• /. delta k/h I

1.00 1.00 4.65 3.54 L

II 1.23 1.57 7.04 5.34 III 1.53 2.34 10.82 0.21 IV 1.23 1.51 7.04 5.34 V

1.00 1.00 4.65 3.54

!. ]3 VI 1.23 1.51 7.04 5.34 As seen from Tchle A5 the No. 3 shim safety rod is teorth 8.2% delta k/h. A machine computation was run with rod No. 3 inserted I

to validate the method of proporcioning rod worth. TableA2 indicates a multiplication factor of 0.907 for the core in this case, yielding a

'l

[a-worth of 9*/, delta k/h for rod No. 3.

It is felt that these results lN verify the ucchod of proportioning rod worth used to compute the

[~

values shown in Table A5 k

Differential and integral worth were computed for each of the rods on the basis that the worth of a rod varies as the cosine I

sc,uared. Intcaral valuas for each of the shim safety rods are shotm on Figure A-6 The values reported have been computed for a typical

!~

reference configuration.. The flexibility of core permits of a number of rod configurations which would result in different values from the tabulated figures.

'4 4

ens em 9

eI m S

-121-b

-I t

fll I

i

-l l

f I

~

I I

l s

t

,I r

I h

I ROD 22 8

J n

l f

j l

'I lf 22

[

J-1 7

-]

~

!: /

ll

-g l

/

l t

- - -.aco

._2, m.m

/.

/-

\\

L

.J-

I

/:

/

s

!,1

/

/

~

!:g

/

/

aco:, r,r 3

i

/

I

)

i

/!/i /

g l-y

/\\/ /'

/

g i,

!///

ff I

i j

N-0

'I B..,lf ossr M M uon*4,,ynMCHgg 8

34 30 38 20 22 2.

INTEGRAL R00 WORTH FIGURE.-

l

,l _

s-

'C Flux Detemination

~

1.

Steady Stato:

The ' results of the machino computations woro used to datormino the fluxos at various locations in the reforonco coro. Tho 13 average thermal noutrou flux in tho fuel was computed to ho 0.277 x 10

~1 nout-cm' -sec at 2 Mw power using tha rotations between power, flux and

~~'

loading. Tho group averaged fluxos provided by cho PDQ computations were normalized to the computed 2 Mw flux and absolute fluxos at discreet points woro established from the FDQ results.

Figuro A7 chows fluxon plotted across the center Eno of the coro. The flux drops to zoro at a distance of 5 in. from the edge of the coro, duo to the boundary conditions used in the PDQ calculations.

l

~

12 l

The maximum thermal flux in the fuel regions is slightly over 7 x 10

~

2

-1 neut-cm -soc, and occurs ac::r tho water gaps created by the removal of the shim safety rods from the rod guidos. It is intoresting to nota r

that the thermal flux in the reflector packing area, the area in which l

experiments are likely to be placed, exceeds 10 3,,yg,,-2,,,,-1, gg,

~

l points out one of the interesting features of the coro. While the flux l

~

in the fuct is relatively low giving a low value for equilibrium Xenon, the useful flux is comparable to that provided with a place type core.

Figsra A8 shows the f1'ux plotted along the line of reflector poaking

~

adjacent to the six accombly side of the coro. Figuro A9 shows the flux plotted along the line of refloctor posking adjacent to the fivo

.m assembly side of the coro. Once again, both those figuros indicato tha high, useful thermal flux available in the reflector locations.

W e.ms

-123-e y

m c...e 1

I I

i~

l i

I i

iM i l

3M iM I 1

I I

iG I l

l

./

i l

i 4

i 4

i 2.5 7

I REFLECT 2.0

-COR4-l FAST CORE; BOUNDT.iff EPITI:ZRi.ML COUI@ARY t

_/

. i... -...

{

g lf I

't

i

- - ' - - ~

'a e

I.O r--

f 9

^

PT x

\\

rj 4

s e'

i I

J TIUni.iAl,

~~

O.5 j-f--

\\-

\\

RO D-l

{

F

]

R OJ

~~

FUEL FUEL FUEL O

2a 24 2G IG 12 8

4 0

4 8

12 16 20 E4 28 32 3G 40

+ + - - + _

DISTANCE FRO.'.1

[

l t

FLUX TRAVERSE ACROSS CORE & REFLECTOR i

FIGURE'-

)!

)!

w i

acroccroa jl I

8.2 bl i

i 2 _.

Ii 1l a_

2 l_

3 il I

1 03 l2_

c i

o.s FAST

.g

^N l

x j_

ru.m

,I N,

- s

}

l

.c

'r'I

\\~

o 8'

4 as sa i

jl oisrawet raou {@iimcw rnou"come (cu) 1 3

l-FLUX IN REFLECTOR

.l FIGURE-

-8.. -..

A

~

RZ/ LECT 3

I

~c5 e-l t2 i

i II 7TZi6,:AL i

~~~

11.

(-

l 1.0 r-R2FLECT g

0.9 1

{

o R

\\

\\

\\

I l

11

\\l f

0.7

~

0.6 f

rn..-

\\

IJ

-'/

A~~

l\\-

0.5 j

EPITHERf.:AL 0.4

}

~

/

I 03 lg i

I n

l 6

)l 9 "#

1

~

Ei O

g

\\

' ).

~

30 20 to

+

0 10 20 30 DISTANCE FROM Q, (C.;'

l s AT I lN C H ( C C.V CORE i

FLUX IN REFLZCTOR FIGURE-A-9 E

7 lE g5 As previously mentioned, a machine computation was cado with a central assembly missing. Figures A10 and All show the flux plotted J

through this water hole in the contor of the core. It is scen that a useful 13 2

thermal flux execoding 3.0 x 10 neutrons /cm -soc is availablo for in-pile irradiation experiments.

Figurca A12 and A13 show fluxes plotted in a "U" shaped 13 cavity on one side of the coro. Usoful fluxes of groacer than 2.5 x 10 neut-cm - sec'1 can be obtained in such an irradiation space.

~

2 Transient Estimatos of tha hecgratst. noutron fluxos during a

,.I 40 Mw-sce pulse were mado for pocicions of peak thermal flux in the water holo created by removal of a central asscably and at the loca-tion of peak flux in the reflector. The integrated flux is givca by:

E

$Ridt: 2 f Q r) df so i

b wherc 'Dn = time to peak power, socs.

'}-

Po = Power at ti=e T = o, He

]-

f = flux at 1 Mw

\\

Tg = period of pulso I

It was assumed that power rose from 10 M2 to the peak power with a constant 3

period, i.e., the chango in period in the region of the peck power was 4~

noglected, h contribution to the integrated flux by power 1cos than

-l 10 Hw was also neg1ceted. h time to reach peak power from 10 Mw was computed to be 26.4 esoc. for a period of 4.975 usec. Table A6 succar-1

1 ises the integrated and peak flux values for a 40 Mw-ase pulse for the position of -h fles in the reflector and in the waterhole.

to I

~

-127-

--l 6

5 4

5 2

i l

I Ig i

t

.g~

L I

1 i

l l

l h

Yf D

/

o t

i l

E l

l F

i 1

3.5 j

(

ruu=z i s

t i

4 i

3.0 i

i

{

l l

"~

I l

J_I 1

i i

i i

{

j 2.5 l a_

j sl i

t dl

{

k l

l FAST

' J-2.0

\\

l-1 zm:-:saux

.I I

'~

g

]

,J -

1 I

lb.

i 7

lJ_

l.0 g:

l 1l WATERHO'LE

+

)-

A-05 g

1 4

!-j

'g Fl[EL g

0 a-I 2

3 4

5 6

7 DISTANCE FRQ'. 6 (C:'.)

q FLUX IN VIATERHOLE ATCENTER OF CORZ

FIGURE.-

!J-ll

'j _

r A-10 m-

_w w

gty g

g g

i g

i 1 M i M i i

i i

IWimI IMl IM M

1 i.

3.5

~ ~~

l l--

~ - - - ~ ~ ~

1--

i l

[ T lER t.i AL-t 3.0

~~

- ~ ~ ~ ~-~

~' - - ~ ~ - - - -

t l

A it f -

25

~~ --

4

.t I,td W

r 2.0

~ ~ ' - -

< /,- - ~ - ---

l CIT M

_..I _

Fnsy h

ill I9

~ ' --;;r%

.["

,;,1,. _,,,- a,.- *

-Y E5YM3 ;../.L '

k l

)

LO j-V.'Kr'EllMOLE _.

ff Y!KfERMOLE i

e 05 e

FUli L 4

M j

C O

~ - ~ "

- =

--2 3

4 5

=

-~

i 4

3 2

i

+

0 1

os unct rnou ( tcui FLUX IN Y!ATERHOLE AT CENTER OF CO;1E FIGURE-J 4

= = e -c s

-e

-,.9-

-,,,me e

oc +-

+m==-*.e**-

e m+

-ee.,

.+ use-w _

_,em e

=

<-en

• =ee>.

era e eep-w,

4_

g THERMAL.

l

. i

a -

l 2.2 l

c j

I 2.0 j --

i 1.8 l

I a

p 6

O l --

1. 6 l

i

]e_

i.4 i

s I

/

1.2

-[

l l

/

l

\\

s

- - ~ ;-----'

l.O s

i i

,I FAST l

j N_

r 0,8 EPITH MAL j

l t

l ~~

i I,

O.6

~

j u-suusvunen i

s O.4 l-I i

i O.2 j

i j

i_

0 I

2 3

4 5

6 7

a DISTANCE FROM { CM).

FLU $ IN.U-SHAPED CAVITY FIGURE-I!

A-12

a. -

,,,s.--.

a

-,,---..--v-,

,v-.

-n---e

.~we>.

e - -,,,

1 l_

n j

I i

2.4 j

l l

l i FAST i

k j f

2.2

~

^

I o

t i

I I

I E PITH E R.'.'.AL I

j 2.0 l

I i

! THERndAL i

1.8

{

.t 1

l l

j i

l

/

I I

1.6

+

i

,I i

i l

i l

1 1

'/

1 i

t-j i

i yN:

'4 i

1 i

k5 if

)

1. 2 a

3 i

4 f.

j t

i.

I 1

t I

'l d

~

U g

{i i

p i

9 9

j

- fij 5

1.0

[

I

/

{

I f

0.8

(

I I

j l

i

}'

N

]_i l_

O.S s

i s

e q

2 l

l i

o.4

}-

[f g\\

l I

g a.2 CAVITY FUEL j-6 6

t t

l

.ii o

0 2

4 6

10 12 14 13 IS 20 22 24 o

p-DISTANCE. ALONG k, FROM EDGE OF CORE (CM)

Il FLUX. IN U-SHAPED CAVITY reus-I b-A-13 o

TABLE A6 Integrated Fluxos for a 40 Mw-coc Pulco REFLECTOR Fast 1.96 x 10 i

Epithormal 1.816 x 10 Thormal 1.10 x 1014 f

14 MATERBOLE Fast 1.73 x 10 10 Epithermal 1.59 x 10 10 h rmal 3.64 x 10 l

the integrated gamma dose for the position of maximum thermal neutron flux in the reflector was cosaputed ir a similar =aanar.

N gamma j

dosa at the chosen reflector position flor 10 Hw power was extrapolated from measurementa made at the BSF ( 24 ).

N integrated gamma dose j

7 was competed to be 2.19 x 10 1 and the peak dose rate, 1.6 x 10 R/br.

l lI l

lI l

I I

I y

I

-132-lI G __ -

L.

P.ac.t Transfer end Strece Anc bcic 1.

Steady Str.te Ucet Trensfer Anelysis:

?

The ueximuci ~stcacy secte power capability of the Advanced l'ulse neactor, coupled uith the existirc 1200 gpca cooling system at the University of Buffalo is 2.3 uegauatts.*

a The power output of the core in Beu/hr is determined by:

f q = - t,. e t I

2 I.c

[y g A,h Where:

g pool water temperature. *F e

=

I t,

maximum surface temperature, "F

=

L/2 (hot spot location), fraction of fuel length a

=

3 coolant flow rate, ft /hr w

=

3 specific heat of coolcat, Btu /ft c

=

F A,

heat transfer surface crea, it

=

h film coefficient, Btu /hr - ft2.0

=

7 hot channel factor for coolant temperature rise F

=

oe i

F0 hot spot factor for ff.La teuperature difference

=

The maximum surface temperature is set ec.ual to the saturation temperature at the hot spot. The hot spot factors used for this

?

core are F

=

2.6 and P 3g G

4.0.

W e assumes ekt au fuel

=

assembly variations and unfevorable flow and flux distributicas occur simultaneously, which is an unlikely occurrence, thereby giving a conservativa estimate.

• All "woop" holes in the grid plete, which provided for coolant flow between adjacent MER-type fuel elopents, will be plugged for operation with this oore.

~

-1M-

_I

(a). Ilot W oe F.'etor (1).

Fuel Loedinn:

H The fuel essembly specification allows en individual fuel pin to vary 27 in loading. This results in 27.

higher heat generation, thereby affecting the fluid teuperature rise end film temperature difference directly. Therefore, a factor of 1.02 will be used.

(2).

Variation in Fuel Pin Spacing:

The nomical fuel pin diameter is 0.47" with c

a maximum diameter of 0.474" and the tolerance on the inside box dimension is *.005".

Therefore, the varistic,. in the flow area and velocity is 2.8% from the nominal. The temperature rise I.l through the assembly is inversely proportional to the flow area I

and velocity. Thus, the ratio of temperature rise in a nominal and minimum assembly is :

l A

V

/:. t nom nem at A

V f

nou 1.023 (1.028) = 1.057

=

l-Yne film coefficient of heat trcnsfer is inversely proportional t-f-

I l

to the cube root of the hydraulic radius, or equivalent diameter; hence, the film tea cratura vcries accordingly:

I o

/d 9/3

-[0.02491/3 f-u l

1.012

=

6"*

Ls i

d

( 0.0241/

(3). Flow Disentytion:

A factor of 1.06 will be used for fluid temp.

erature rise and film temperature difference for flow distribution.

.m.

,,._e-,,

.g

,-e

- ~ - -

~

(

(4). Ecct Tr.ansSi Correintion:

%I The formula used to determine the heat transfer coefficient correlates all of the experiucatal date with a scatter of appro::imately 207, about the correlation line. Therefore, a factor of 1.2 is applied to the film temperature difference. This doca not affect the fluid temperature rise.

(5).

Plenum Effect:

The flow leaving the fuel assemblies goes through the lower plenum and into the primary piping underneath.

The hottest fuel assembly is approximately centered over the primary piping and no affect will be felt by the hottest fuel l'

g assembly. Therefore, the flow reduction factor due to the plenum S-effect is 1.0.

(6). Power Level:

.o Assuming that the control system maintains the I

reactor uithin 1.05 times the nominal power, and that a 7% sensing l.

instrument error exists, a reactor power level of 1.12 times nominal 4

full power would be realized during operation.

1 (7). Flou neduction:

lJ l-Screm devices are assumed not to shut down the le i ',

reactor until 90% of the nominal flow is reached. Therefore, the l <

factor for fluid temperature rise is 1.10 and for film temperature rise is 1.00.

(8). Flux Distribution:

The reselts of the PDQ computations yield flux distributions which give a hot channel variation of apprM=mtely 1.75 and a hot spot variation of approximately 2.5.

-135a

-m

1 p

(9). Ilot Si>ot 7.a.ctor Sumary:

.J,

The hot spot factor for coolant temperature rise is:

Ff F

F""

hot channel factor due

=

i

=

~ l' C to flux distribution i

~

product of factors relating f

=

• SC to coolant tcuperature rise.

I The hot spot factor for film temperature difference is:

P F i9 F2= hot spot factor due to

=

2, g

flux distribution j

fO product of factors relating

=

d-to film temperature difference.

8 t

E Fuel Loading 1.02 1.02 5

Fuci Pin Spacing 1.01 1.06

~

Flow Distribution 1.06 1.06 Film Correlation 1.20

[

Plenum Effect 1.00 1.00 L-Scram Setting 1.05 1.05 Instrument Error 1.07 1.07 Flow Reduction 1.08 1.10

~

.A f

1.59 1.42

=

=

l Therefore, 8

' U" 1.75 (1.42) 2.49 F

=

=

g 3

2.,(1.,,)

3.,0

=

=

l As previously mentioned P was; assumed to be 2.6 and F was g

6 assumed to be 4.0.

(b). Filai cooKI.cient_

The film coefficient is determined by:

I 1-0.023 IS Ed (P }

h

=

r D,uf I

where the fluid film properties are avaluated at the average of the surface and bulk fluid temperature.

I_

136 t

(c). Ssmic Calcul.,.t!.on

)

For a procently availabic 1200 gym pump capacity in the Duffalo core and a no boiling restriction on the new Advanced Pulse Test Reactor, the fuel assembly inlet velocity during steady state operation is:

if, = 600.000 y

=

1*07 f 8 1

A 62 (30) (6.9) 2 00 (144)

The velocity through the fuel section is:

g

_.m Ve 1.9 (1.07) 3.55 fps

=

=

The pressure drop through a fuel assembly is:

'1*-

+f 2 (= IC P

=

g gVg 1

2g tihere Vg= assembly ir.let velocity lap assembly 0.51 V c =

= 0.766 pai

=

y g'

The frictional and dynamic losses between the fuel assembly

~s 2

entrance and the hot spot f.s estimated to be 0.3 Vg ; therefore,

~

P 23(62) 0.3 (1.87)2 62 b.s.

=

g 9.9

.45 9.45 psig 24.7 5 psia

=

=

=

(tsst =

238. M0 F) 3.D (3600 0.025) 62 -

h 0.023

=

(2.3) l 1400 Beu/hr - ft2, og h =

,E 23a.36 - 100

["E 02 (2.6) 4 0.6 x 1F 185 (1400) 6 7.85 x 30 Beu/hr 2.3 magauetts q =

=

-l'17-i u_

1 It is, therefere, concluded that cite: making a series of very conservative assumptions, the AM when coupled with the existing

~

Buffalo cooling systeu is capabic of 2.3 megawatts without nucleate boiling.

(d). Fuel Center Temperetu g The fuel center temperature for the 2 megcwatt steady state operating level is determined by:

~

+ At

+ Ac

+ 4 t,p + At t,

= t h0 g

The temperature rise across the film is:

0 9.100 32.7 'F At

=

=

=

2n r E 2

2 2(3,14)

'2) 1130 2

ilhere:

Q = heat generated in fuel pia - Deu/hr 2=

outer radius of cladding - it r

active length of fuel pia - it 1

=

average film heat transfer coefficient h =

l at 2 seegewatt operation - Stu/hr ft2oy

~

The temperature rise across the eladding is determined by:

!2'1) 0 "cled 2rrk 1

~

there:

neat generation in fuel pin, Stu/hr Q

=

thermal conductivity of eladding

-3 _

K =

ustarial, stu/hr - ft 'F active leasth of fuel pia - ft 1 =

r, = 1.m.r r -

of.

as - ft ester radius of eladeias - ft

<1-

=

-134-L

l

,,100 0.235

.5 o7

.3 I* "cled

• (3.14) 0.2 (2) " 0.2 15

=

The temperature rise across the helium gap between the outer edge of the fuel and the inner surface of the cladding is obtained by:

I ct O z, r

=

7 g 1(

Sep 27r IJhere:

heat generated in fuel pin - Etu/hr Q

=

__ 9,100 (0.00425) g43o y 6.28 (0.215) 2 (0.1) rg= inner radius of cladding - ft Ar= clearance between outer edge of fuel and inner cladding surface - ft be " "

" N"Y 'I

~

I""

1. ~ I" l

1 active length of fuel pia - ft

=

The temperature rise from the center of the fuel pia to its outer edge is determined by:

l

" _ O 0 " gen harL kg Q = heat generated in fuel pia - Ecu/hr 1

active length of fuel pia - ft

=

g=

thernal ooeductivity of fuel - Etu/br - ft 'F X

1 A " gen " 4(3 (2)

• II J

The fuel center temperature is:

100 + 32.7 + 7.5 + 143 +181 = 464' F ea =

3 1,,.

n-,

--,---,e-

.n+---

,--r-,

,,, -,., - - - -,.,,,.,,,. - - -., - -, - - - -.,. - ~ - - -. - -, -, - - - - -,, - - - - - _ _ - - - - - - - - - - - -

J The stecdy state tenocreture disi;ribution for ?. cegavett operation is cpproximated by Figure A-14.

The heet transfer paremeters for 2 mesewatt steady state conditions are listed in Teble A-7 l

~~

Tchle A-7 6

2 1.2 x 10 Btu /hr - ft Burnour Ucat Flux

=

140,000 Btu /hr - ft Maxisme Heat Flux

=

37,000 Pau/hr - it Avern8e Heat Flux

=

• ~

' 600,000 f/hr Coolant Flow Este

=

11'.3 F Average delta t Cors

=

Average delta e Film

= 32.7 'F 1

2 o

1230 Btu /hr - ft

,/J.,

h at hot spot F

=

2.0 Beu/hr - ft2,o Assumed f

=

~

464 F 11aximem Temperature UO2

=

= 349 F Average Temperature UO2 144' F Maximum Temperature Er

=

136* F Average Temperature Zr

=

2 T ansient Heat Transfer Analysis:

1

~

Transient heat transfer characteristics are analysed below for several cases of power escursions.

The time dependent tauperature distribution in a fuel l

{-

l pin for the Advanced Pulse Reactor was obtained using the one l

diuensional heat conduction code ERAT-1. This eode was obtained i

from Mr. Richard Wagner of the Phillips Petroleum Company and was j.

~

the one utilised for the analysis of the SPEEr core. The cases

[~

f l.

investigated were;-

R

^

)_

.r v, e i. ;&i

% :.. n.

' - *n l

[.

-139-A-L_

m

--......_,,,-_,,-s

I dg 3-4l

)-

400

-l

\\

,f

(

j_

300 t

1 s

y J

if 7-200 i

1 e

l HEUUM SAP N

pg a 00 O

.I

.2 RAD E DISTANCE-INQES AMt STEApf STATE TEMPERATURE DISTRIOUTION AT 2 MW

.j_

FIGURE-1

..a 4_

9 Ic.

1 Forced Convection - 40 Di-sec energy pulse 2

Forced Convection - 90 Ma-sec energy pulse 0

3.

Natural Couvection - 40 me-sec energy pulse 4.

Natural Convection - 90 Mi-sec energy pulse The time dependent power input for the 40 me-second and 90 Mi-second energy levels, was bas:ed on the. following parameters:

10.4 g/cc Density UO

=

2

/

2.30'asec (90'% -sec) t =

L

'I=

4.93 meec (40 Ma-sec)

Fuel pin Diameter!= 0.47 inch 0.D.

Fuel Pin Iangth = 24 inches 25 Pins / assembly 30 h aembly/ Core a

p= 0.0076 1~

l Doppler coefficient = 2.7 x 10-5 delta k/*C Heat capacity UO

= 0.13 mt-sec/'C (40 Mi-sec) 2 1

= 0.130 Br-sec/*C (90 Mi-sec)

J-The nonaalized radial pouer distribution in the fuel pin is shoun l^

in Figure A-17 with the maximum occurring at the outer ed e of the 6

j-fuel. This is typical for this type of core as indicated in

,j _

reference (1). The conductance between the fuel pellet and the inner surface of the cladding material was assumed to be 2000

)

Btu /hr - ft

• F (16). This condustance was incorporated as an l

equivalent thermal conductivity for the 3.5 di minimum gap be-1

~

}

tween the fuel and e1 Mag.'. ThisMik,'ideemservative results l'

3

%,e-since the toleranses on the gap are 3.5-5 d 1s with an average of 4.25 alls. The fi'.m eoefficient at the outer boundary of the pin l,

1,

-141-

!)':

r

-r-

--l woo

..s-1 3

sooo i

ra

,l rs I

c. -

=

f i

.o

-g y-v.

y I

+ x..

m-Il POWER INPUT-40 MW-EC, MLSE Hl nevns-I I

n-u A-15

~;l-

.c.~.. -.....

l 1-1 Lg m

l a_

A L

wm

\\

.y s

l j

5 r.

g T

-g

t I

..g i

O O TIME-MSi;C 10 20 POWR BRAT-90 MW-SEC PULSE

!]

, l._

,g

> i __

I n..

l

/

i

,,a

/

I 1

l.10

- - - - ~~ - ~ '

-~

-~

[

i i

t s_

L I

i i.

I s_

I i

l

\\

i

]-

I l

i m

g l

l 1.05 J

j i

i i

8 i

i'

}

I l

I l

[

l i

}l

'gOUTER EDGE l

OF FUEL l

l~

J l

[

o_

-1.00 i

O

.I 2

.3

.4

.5

.6 s

l1 RADIAL DISTANCE-CM f~

lE FUEL-PIN RADIAL POWER DISTRIBUTION 040RMALIZED)

H u FIGURE-

~

m I

E I!.,

f' I

s h.

'm s

M n

ease emme

, M i

0 M

5 l

0

,I 2

W W

l M

00 0

,f 2

W

,(

_g I

00 N

i 5

1 i

M

/

2 I

O M

U 7

0 T 0A I

0E

/w_C EF

- M E-1 H

C R

IF U I

I C

C G

- M I

I M

I

-s 0

0 M

J 5

I

- M t

c E

l

)

Rn Uo T r M

ART EPA ME R I

To

, M O

x g

5 l

• 3 eiW Eg t

_ M I

yb.

i ii1

.i i

_7__________

.i I

i

.I i

1 1

1 1

1

,i I

i i

bl5 it l

.}

'i i

43 f

i i

g t

Q 3

1 e

5 i

Ol N

r l

l f'

.vg

= _,.

..e_ _ _

/

(

l 0

500 1000 1500 2000 250(

I TEt0PERATURE-t oRat ron 7 THERMAL CONDUCTMTY-UO2 I

FIGURE-I

. g

.10

~

.o9 b

~

o

.0 a

~_

i\\

^l lIdk

2_

i X

.oa 3

-I I

i Hl

.o s J_

\\.

J r..

1

,g3

.n N

i E.04 I

fi o_

y N

.03 E

,E s'

• A

/

E a

a_

m 4

t.

5.01

'l

[j

.a_

p o

o m

2000 20 TD.:PERATURE-t 2_

1 THERMAL DIFFUSMTY OF 002 & l' m_

m_

A-20

..r..

a-m u.

l

\\=

u

-r-E E

ob r

I t E o

.F" il

=~

(>

Ih P"

e

, "E n

T

~I z u

<r-e 9

w q,

ik g

ti e

40 W*

t$

m 4>

I-y5 1

g, o

e i,

4W'6 gg o

5

"-- ' d u

p e.

db g

.E U

u g

"a o

a

$o UE W I u

OW g 3 LI E

--l 9 LE 5

o eh_

o o d k ilw a6 on 4

o

- w*

i 4>

tb

,, e i I

<-.a s

.I 8

=

g-

,ws a

E o

.I in.

d l W

O

- z-

-.x y Y

9=

A-21

"F (repreacnting a was tchen..s a constant 1130 Btu /hr - ft cooling flou race of 1200 gpm) for forced convection, and as a

unction of the cladding outer surface temperature (h = 100 + 1.4 T,)

O for natural convection uhcre T, is the surface temperature in F.

No change in the film coefficient was made at the initiation of boilin3 The thermal conductivity and specific heat of the fuel

~-

and cladding are temperature dependent quantities as listed below (1):

=

~9 2

cal t-

.0.507 + 1.54 x 10 1.43 x 10' T + 4.95 x 10 T

j g

T cm-sec 0C g

UO2 0.56 + 4.36 x 10 T - 1.83 x 10~7 C81

}

T CUO g

2

>I'

~

cal-l g

o,034 l

er cm-sec OC 1

-4 cal 0.43 + 2.3 x 10 T

C

=

la_

zr W oc i

Uhere T

=

C The properties are graphically presented for UO in Figures A-10 and A-19 together with the average heat capacity and average thermal l

conductivity for various fuel tecperature increases. The thermal l

l diffusivity for UO and Zircaloy is shown in Figure A-20.

2 The t e arure distribution in the fuel pin for the j.

t.dvanced Pulsc

..or was obtained using the HEAT-1 code and tir.

i

I.

I cima dependent energy input shown in Figures A-15 and A-16 to3 ether l

3 vith the normalized radial energy distribution indicated in Figure A-17.

In the an.slysis, a flux hot spot factor of 2.5 tas used.

i 5

-149-i i

D 0

i.

The fuci pin configuration is shoun in Figure A-21 uith the selected ucsh points and regions. Syametry conditions are assumed at the inside boundary (center of the fuci pin) and convection heat trans-for at the outer boundary. The center fuel temperature and its

.a

~

variation uith time is shoun in Figure A-22 for natural convection.

4 These results indicate, as would be expected, that the mn::icum q

center fuel temperature is independent of the film coefficient used k

i at the outer boundary of the fuel pin. The maximum fuel temperature 1

6 does not occur at the center because of the radial energy distri-l*

\\

l bution assuned in these calculations.

lE

,4E The results for noa-boiling conditions also indicate the h

approximate cool-down time for the fuel pin after a pulse as listed I

below:

a 1

lj 30 seconds for 90 Mi-sec and forced convection l'

' ~

24 seconds for 4013i-sec cnd forced convection

,i 75 seconds for 90 Ik-sec and natural convection j

aE 60 seconds for 4012,-se: and natural convection j'g

}

Cind colting conditions cennot Mr.ur since the total energy in the j

l I

90 Ili-second pulse will result in en equilibrium temperature, under I;

I

~

ediabatic conditions, which is belou the melting point of the l

i Zircaloy-2 cladding (3365' F) (25).

1 3.

Str;su Analysia:

Of prime importance is the maximum temperature gradient across the cladding wall during a power excursion since it v8.11 indicate whether or not the possibility of cladding rupture due to thermal stress exists.

-15 0-

.I

0 e0

- 1

~

S.

~

I

l,I 2

i

' ;! I.

i' I

=

i'IiI Ij>

R

.I.

.i 9gi~

O

~

T

{I C

A lIF

,li

l' l lI A

.C T

C E O E

T!

i

. +

d*'

1 S S P M S 0

I.

j

l

1{M' i 5. O

f.

l, I

0t7 i:

! !i ilU'

~,:'

31

!il; i X 9l 2,U

. i i A).

l g

=. =. L I

s(s.

E TlF E

R E

R U

R E.

b T

U Z

R T

T U

A R

A T

E O

R A

P

~

E R

P : i E M

O.

P 1

E

.s l

C i

M

' j P

E T

i i.

'i W

fiI[

n L.

F ilN f r

E p

T O

g R

t F N E

• s TI U

O f

R.

u t

A T N E s R

I N T A

N o

i O C R E

.li N-TU T E E C I

P L a

A I

i A W 1

E S

I 1

i G-F O E U l

U R

N A C V

T F ID U

E D-K

-j

/

C L

E.

L T

A E A P G ".

'l U

L A

' U UlG l

E

[j I

^ lF Ckl'-i U

Nl I.

pht i

T T F

A A

~

M.

lI, R N U

I 7

q l,M

- /

I P

U F

s,

/

I U W T

T f

P

~

'/

G i

N I

T L.

l.

l 1

.l' j

r 0

'I!l j.

r

.I

[i j

'l l*

I

+

i!

i

~

~

j

~

~

/

~

j j

.C

~

E

~

S f -

~

0E

~

0M X

0 c

C 1

C 0

o 0

O

.1 y hohw&V 0

6 a

4 s

2 1

l YU

The thornal stresses at the inner and outer surfaces of che cladding vore determined by:

~

k

[j,b'-a' (f

= Ed(Tu - T_)

2b

^

hb a

2 (1-V)

In b/a 2

f

= E " (Tp - T,)

(, 2a in b.

l,~

t.

2 (1 y )

In b/a b' - a' T

e where: E = Young's Modulous

~ '

l c/J

= Coef f. of themal expansion

'y # = Poisson's I.atio i"-

a = Inner Radius of Cladding l

b = Outcr Radius of Cladding Ta = Temperature at Inner Surface of Cladding Tb = Temperature at Outer Surface of Cladding A negativa sign represents compressive stress.

The 81rcaloy cladding temperature variation with time j-is shown in Figure A22 for natural convection. These results indicate the effect the film coefficients have on the temperature distribution in the cladding. Higher cladding temperatures are obtained with the lower film coefficient used in natural convection.

These surface temperatures exceed the water saturation temperature by l

a considerable amount. This actually is not the use since the outer l

I l.,

surface temperature of the cladding will remain close to the saturation temperature of the water during nucleate boiling and only show a sharp temperature rise if burnout conditions are approached. A typical surface temperature rise during nucleate boiling is approxi-j l"-

o mataly 45 F.

The higher surface temperatures shown on Figure A22 l1, i

are obtained because of a limitation on the EEAT-1. Code. This code does not take into account boiling beat transfer, and as a

-152-

,.m....mw

1 I

result the surface temperature will continue to rise after the onset i'

The maximum temperature drop acess the cladding is shown to take place in the early stages of the transient, shortly after I

the peak power during the transient, and just prior to or about the ti: c boiling begins. The maximum thermal stress in the zircaloy cledding for the 40 Mw-sec and 90 Mw-sec energy pulses is shown for thic condition in Table A8 with the corresponding maximum to perature drop across the cladding.

~

Table A8 rnnrgy (W -sec)

Forced Coniection Natural Convection "T

( F)

% (oci) 8b (psi) 6T ( F) 6a (psi) b b(oci) t 40 194

-7,750 4,920 169

-6,900 4,370 90 334 14,200 9,000 358

-14,100 8,950 tioucvor, since boiling was not accounted for in the computations some doubt exists as to whether or not the navi== ter:grature differential across the zircaloy cladding has been attained. Since the maximum thermal stress is dependent on this maximum temperature differential, it is essential that the worst conditions be assumed to establish I

l l

a concervative thermal stress value. This approach will circumvent the prob 1cm of not having considered boilias conditions in the com-l putationa.

The worce condition assumed will be when the outer surface of the clndding is at tsat + 6 tsat (285 F) and the inner surface is accu =cd to remain as for non-boiling conditions. The most severe con-dition will occur in the 90 Mw-sec energy pulse using natural convection Mr.ure A22). This will result in a maximum temperature drop acrosa the cledding of 1035 F with a corresponding maximum

)

-153-

~_

t a

~

cor.:pressive thermal strear of 34,000 poi. Using the 40 Mw-soc cncrgy pulse and natural convection, the maximum temporature drop in the c16dding is 700 F with the corresponding maximum compressive thor =al stress of 24,600 psi. Thase results are indicated on the thermal stress curve, Figure A23. The margin of safety between the thermal stress and the yield strength of hot rolled Zircaloy-2 is shown in Figure A23. The yield strength of Zircaloy-2 in various conditions is shown in Figure A24.

Although the thermal stress reaches the yield strength

,I of zircaloy for the 90 Mw-sec pulse with natural convection under the assumed wrst conditions, it must be remembered that in the test program the pulse energy will be increased in a gradual' During the program, data vill be collected and analyzed manner.

before the next stap is taken. At various times during the program, 1

l_

test pins will be examined for physical changes.

It is felt that the gradual increase in severity of pulses will yield sufficient data to assure the safety of the next stop to be taken.

It must, also, be realized that the actual maximum tcmperature difference across the cladding will be lower a:lan that assumed for the worst condition, since the inner cladding surface temper.ture will be lower than that of the non-boiling case.

l:

~~

Even if the thermal stress for the worst conditions exceeds l

the yield stength of the aircaloy cladding by a moderate amount as shown in Fi. u a23, failure of the chdding will not result.

(If t

I the clad passos through the yield point, a residual stress will exist in the chd and yield will not be reached on subsequent pulses.)

j O

~w-m

~,

\\

~

40,000 N N

1 2 (HOT ROLLED)

YIELD STRENGTH 0 N

N N re N

- I 30,OOO O

-y I

E v.

1 20,000 i

ll y

l

/

l g

THERNAL STRESSES t ~

L 90 MWCEC PULSE / NATURAL CONV.

' ~ " -

2.40 WSEC PULSE / NATURAL CONV.

4 1

S NOEED COW.

[

10,000 a

4. 40 MWSEC PULE / FORCED CONV.

O ASSuuEO wonST CONDITIONS I

D STRESS Ar INCIPIENT BOILING a_

O 500 1000 l4 TEMPERATURE DIFFERENCE ACROSS CLADOING

,F l

THERMAL STRESS VS. TEMPERATURE DIFFERENCE ACROSS CLAD -

FIGURE-f A-n j

..1.-..

~

i 1

i

~~

b.

l

/

4 W

i F-(

g z

a w g. r-l N

l.

lf o

W l

0

-g to 3 m oD3 5

g gi a

...I

/

a.

Q N2 l

i i-

.m t

O e

O

.=

g O

t M

[;

iw %..i m a o

1 e.

O Z9 o

bi O

g y 9

ZC

'l 43

.,u

>9 l-e' l

l O

i 0

N i:

O O

O

~

es y

C o

af W

• e ts.

e 3

i w i;

I d

E 8E S

f

• $N a e

~

y w -

I aEg s._

s L'J l'

=

5

~

q g

-l s.

8 j

o 4

O O.

O s

e 8

g O

N I

-l ISd -SS3W18 I

I REFERENCES J.E. Houghtaling, T.M. Quiglcy nnd A.H. Spano, " Calculation d

~~

1.

and Mensurroent o f the Transient Teraperature in a Low-Enrich-cent UO Fuci Rod During Large Power Excursions," IDO-16773.

L 2

6 E. Crcutz, General Atomics to L.E. Johnson, AEC, 2.

Letter:

opril 5, 1960,

Subject:

AEC Licenso, No. R-38.

i

/

p g

3.

S. Mirchak, et al., " Heat Flux at Burnout," USAEC Report lIg DP-355, February, 1959.

4.

Transactions American Nuclear Society, Vol. 6, No.1, June 1963.

~~

~ I j

5.

Dickerman, Sowa and Skladzien, " Transient In-Pilo Meltdown Experiments on Fast-Reactor-Type Uranium Oxide Fuel Elenents in the Absence of Sodium," ANS, June,1963.

6.

J.A. Norberg, Editor, Quarterly Progress Report, January, February, March, 1959, IDO-16539.

g 7.

AEC, TID-14344, page 19.

8.

J.J. Caldwell, Fuels Development Operational Quarterly Progress j

keport, July, August, September, 1962, hw 74378, Pg. 5.1.

9.

Sutton, " Theory of Atmospheric Diffusion".

10. Silverman, L., " Air and Gas C1 caning for Nuclear Energy

~

Purposes," AMA Archives of Industrial Health.

11. Handbook on Air C1 caning, USAEC.

12. ANL 5453

15. J. Health Physics, Vol. 3 June 1960.

14. Lucklow, Mesler, and Widdoes, MMPP-72-2.

i

15. Reactor Shiciding Design Manual, T. Rockwell III (Editor),

!g ll McGraw Hill Book Co., Inc., 1956.

li 16.

G.G. Biladeau, cc al., "PDQ-An IIH - 704 codo to solve the

~

cwo dimensional Faw-Croup Noutron Diffusion Equations,"

i WAPD-TM-70, (1957).

^

\\

l

17. R.W. Deutsch, "Mothod for Analyzing Low-Enrichment, Light-i I

Water Corcs," Reactor Science ar.J Technology (Journal of Nuc1 car Energy Parts (A/B) Vol.14, No. 4, p.168-179,1961.

18. H. Soodak, Editor, "Roactor Handbook, Vol. III, Part A, 1"aysics", John Wiley di Sons Inc.,1962.

j 4

19. 3. Leavenworth, AMF Atomics Numerical Analysis and Com-

}

putations Report, No. 7527. Titic: "long Term Reactivity."

-157-W

REFERENCES (Cont'd)

~

20. Etherington, Editor, "Nuc1 car Engineering Handbook,"

McCrew-IIill Book Co., Inc.,1958 i

21. C.G. Poncolet, " Analysis of the Reactivity Characteristics of Yankee Core I".

WCAP-6050

22. Nuclear Safety, Vol. 4, No.1, September,1962

23. AMF-ER 7653, "Operatf.on & Maintenanco Manual, Vol. I, N4F Tank-Type Roscarch Reactor Facility Western New York Nuclear Ecscarch Center, December,1960."

L

24. AEC, ANL-5800.

I

25. " Reactor Handbook Vol. I, Mat. trials" Sec. Edit. Inter-science Publichers, Inc., 1960.

I 9_

r_

l i

me_

I i

.'u

-158-

-.~

y_

,o_..

m

.