ORNL-TM-0203.txt

 
[skipped page] 

MURGATROYD - AN IBM 7090 PROGRAM FOR THE ANALYSIS OF
THE KINETICS OF THE MSRE

I. Introduction

This report is a description of an IBM TO90 program based on a par-
ticular model of the Molten Salt Reactor Experiment. The differential
equations of motion are discussed in Section II; since much of the de=-
rivation has appeared elsewhere,l only the additional derivations nec-
essary in the present problem are included. The fifth-order Runge-Kutta
procedure is a‘standard one which can be found in many numerical analysis

3

textbooks.2 Tts previous successful use in the TO4 program PET- indicated
applicability to the present problem and no revision has as yet been found
either desirable or necessary. The use of the program is discussed in
Section'III, with instructions for the preparation of input data; sample

input forms and output sheets are included.

II. Differential Equations of Motion

A. Power, Fuel and Graphite Temperatures

The reactor model used as the basis of the program is a one=-point,
one=-energy group representation, with up to seven delayed neutron pre-
cursors, which is described by the following set of differential equations:
(all symbols are defined in the Nomenclature; a dot over a symbol denotes

time derivative)

 

: k (1-p)~-1 N
P = S - P + Z ATy (1)
-l
. Si P
r, = 35— "ML ,i=1, N (2)

The effective multiplication constant ké is assumed to be of the form

ok ok
- - e - s e - :
k= 1+4+bt ST (Tp = Tpl) B—Tg ('rg Tgo) . (3)

(The subscript zero denotes the steady state value.)
(&)

N
e
i

fP - wc_P_(tr.'2 - Tl) + h('rg - Tf)

(5)

n
i

(1-f) P - h(Tg - 'I'f)

It is now necessary to specify some connection between the mean fuel

1
The assumption is made that the mean fuel temperature is a weighted mean

of the inlet and outlet; i.e., that

temperature Tf, the inlet temperature T, and the outlet temperature T2.

T, = al) + (1-a) T, ; (6)

the weight a(0 < a < 1) is an input number in the T090 programn.
Further it is assumed that the inlet temperature Tl is a constant.
With the definitions

 

 

s (T, - T, )
. — £ 3 f fo
Yo = = (7)
O
- Sg(Tg - Tgo) :
yg - (l-f) Po ( )

and the initial condition

h(T - T

go go) = (1-T) By : (9)

the following equations may be obtained

. fP_ Weo h(l-—f)Po
fPOyf = f(P - PO) - “S“;"‘ yf<i-_-_—é- + h>+ "--é-g-myg (10)
i h(l-f)Po hfP
(l-f)Poyg = (l-f)(P-PO) - —-"-é'g-'-“-" yg + --é}-- Vg (11)

which, with the definition

x = P[P (12)

may be further transformed to obtain the equations used in Murgatroyd:

L d

 
. 1 h h  1-f |
‘ Vp = %=L [Zl~a§tc ¥ S, } Yp ¥ Sg r g (13)
. © L o, £

Vg = XL -5Vt T8 I s (1)

g f

Similarly equations 1 thru 6 may be transformed with the definitions

 

Cl = I'J'./Po
and 7, = f3i/£
to
k (1-B) -1 N
¢« e |
X = 7 X + .23 %i C, (15)
i=1
c'i = 7, x-AC, , i=1, N. (16)

If the definitions of yp and Vg equations (7) and (8), are introduced

into equation (3) the effective multiplication constant becomes

 

 

 

 

‘ ak_e fP_ ake (1-f )Po
k = 140 +bt=|c=| —=— y.- —_— Y. ; aT7)
e 5Tf Sf f 3Tg Sg g
with the definitions
> ake fP_
e = |5T.| 52 (18)
£r| f
-f )P
W82 = 65:8 (lsfi > (19)
g g
[These are similar to the parameter WNE in reference 1;}
. the equation for the normalized power becomes
( )( ) | :
o c L+6+Dbt)(1 -B) -1 2 2
X = [ ) - (1 - 6)(Wf Ve + Wé yg)} X +123 A, Cy
(20)

The differential equations actually used in the program are the set
20, 16, 13, and 1h4.

 
B. Pressure

The simplified model of the primary fuel salt system is shown in
Fig.III. It is assumed that compression of the gas in the pump bowl
is adiabatic, and that the behavior of the molten salt is adequately

described by the linear equation of state

p(Tp) = p + g%f (Tp = Tpo) - (21)

A force balance on the liquid in the outlet pipe yields the equation

M

r . - 2 .
m: U = A(pc - Pp - 8, u) (22)
in steady state
2
p.(0) = p (o) +a, U . ‘ (23)

The assumption that compression of the gas in the pump bowl is adiabatic

can be stated as

p_ V" = pp(O) [VP(O)]n (24)

oo

P P

if we assume that VP - Vp(o)'<<: Vp(o) and neglect second order terms,

we obtain

nAv
P, = PP(O) [l ~ \7;(%5] . (25)

The change AV? in the pump bowl gas space volume is now assumed
to be equal to the change in volume of the core fuel salt due to the
change in temperature of the core fuel salt during a transient; i.e.,
compression of the molten salt is neglected, as is heating of the ex-

ternal loop. The change in volume AVc is expressed as

ko

-6V, = AV, - I 5

and substituting in (25) we obtain

 
nv

Py = P(0) [l * \7—%5'5—

b

 

0 T

%—- g,%-\(Tf - Tfo)] ‘. (26)

Solving equation (22) for the core pressure we obtain

M
2 T .

Po = Pypta,U + iflfluézfif' U ;
subtracting equation (23), we obtain
pp= b -0 (0)= b -p(0)+a (P-U2)s T 7 ; (27)

p= P, =P, - pp pp f o iflflfiézzf ’

the term pp - pp(c) is due to the compression of gas in the pump bowl, the

term af(U2 - an) is due to the increase in friction losses, and the last

term is the contribution from the inertia of the fluid in the outlet pipe.
In order to proceed, a relation between outlet velocity and fluid

density change is needed. The equation of continuity for the fuel salt

in the core is approximately

‘ A oy
P = - v;—-pO(U-UO), (28)

solving for the velocity U we obtain

_ . .1 % . .
U = U — S Te (29)

and taking time derivatives

Vc o *

= %...59.. T . (30)

U= =

We now substitute equations (29) and (30) into (27); after some re-

arrangement we obtain

 
 

Vv M
_ c 1 O r
Ap = - = 5;. 5%;'["IKE_§;K'Tf t Py (o) —~r-7- )
2 e, i -Vchp-é“ (3)
o f £ ZAUO Py Tf T

With the definitions of y. and X (equations 11 and 16) equation (31) is

transformed into

 

 

Ve Jp s M nA
bp = - Kk o 3. S [um *+2.00) Gy Ve
o T T p
‘ Vv P "
. 1l 93 o
+2Uay<l-—-—--—~c = 9 -—--—y)] (32)
o fvf 2AUO Py Tf Sf f
With the definitions
Lty M
A Py Tf 1 gcA. £
144 g A
dy = - Pp(o) v (o) M,
14 g A
al = 20U af T
T
amd.
Vv P
a = - MKS_. 1_ gQw —
3 2-UO Ps T Sa

we obtain the equation used in the program:

Sp =dl[>'<+d2yf+als’rf(l+d35rf)J (33)

In terms of the dimensional groups of reference 1 and the parameter ng

defined in equation (18), the constants, d,, d,,, and d3 may be written

 

* . e .
It is assumed that T, = .fP/Sr.
 

 

2
. fo \
4 = 2
7oy
a, = W°oc \ L)
2 H 2 (3
= 2 /
a, W /273

C. Effective Delayed Neutron Yields

In order to account for the reduction in delayed neutron production
in the core due to fluid flow, an effective yield is calculated for each
precursor, assuming constant flux and slug flow. The fraction v, of
delayed neutrons of the ith group which are released in the core is

given by(u)

ALt A by
1 1 ¢ 31 e

 

(35)
. e--?\i(tc + tL)

where t, is the core residence time, %i is the decay constant of the

ith precursor and t. is the external loop transit time.

L

III. Organization and Use of the Machine Program

The program is designed for use in parameter studies; therefore the
calculation is separated into two parts, the first of which deals with
the characteristics of the reactor which remain constant for a series
of cases, and the second of which deals with the characteristics which
change from case to case. Input forms are shown in Figures la and Ib;
in the usual procedure the first form would be filled out once to describe
the characteristics of the reactor, and a second form would be filled out
to describe each set of initial conditions and ramp insertions. The in-
put data symbols appearing on the input forms are listed in Tables 3 and kL,
with their definitions, the names given them in the program, and the format
with which they are read from the input tape.

The standard CDPF Monitor input (logical 10) and output (logical 9)

tapes are used; no other tapes are required.
10

Output for a typical case is displayed in Figures Ila and IIb.
Figure IJa is an edit of the input describing the reactor system, with
the calculated effective delayed neutron yields; Figure IIb is the in-
put for a particular case, and the continuations of Figure Ilb show the

time behavior of the reactor. The two columns headed

PCT DK REMOVED BY

FUEL GRAPHITE

show the percent reactivity removed from the system by the temperature
rise of the fuel salt and graphite, respectively. The quantity labeled
"(1/P)(DP/DT)" is calculated from the expression

o = EB(t) - P(t - At) 2
At " P(t) + P(t - At)
and is therefore approximately the inverse period at t - At/2, where At
is the input time step.

Since the frequency of printing is an input number, special provision
has been made for indicating the first power maximum, the first pressure
maximum and the subsequent pressure minimum. ("Meximum" and "minimum"
are to be taken here in the mathematical sense of points of zero first
derivative and negative or positive second derivative, respectively.)

The values labeled "VALUES AT POWER MAXIMUM" are the values at the time
t. when the power has first decreased, and the values at the two previous

3

times, t., and te, as shown in Table 1.

1

Table 1. Power Maximum Indication

Time Power (L/P)(DP/DT)
t, P(tl ) B
*,2
ts B(t,)
%,3
t3 P(t3 )
11

The criterion for printing is
>
P(tl) < P(ta) > P(t3)

and the quantities ai 3 are
2

. ] P(tj) - P(ti) o
i,3 At ’ P(tj) + P(ti) ’

 

 

Similar remarks apply, mutatis mutandis, to the values labeled "VALUES AT
PRESSURE MAXIMUM'" and "VALUES AT PRESSURE MINIMUM."

Acknowledgment

 

Thanks are due P. N. Haubenreich and J. R. Engel, for assistance in
the derivation of the equations and other helpful comments and suggestions;
to M. P. Lietzke, for considerable programming assistance; and to H. A.

MacColl, for preparation of the input forms.

References

 

l. P. R. Kasten, Operational Safety of the Homogeneous Reactor Test,
ORNL~-2088, July 3, 1956.

2. R. G. Stanton, Numerical Methods for Science and Engineering, Prentice=-
Hall, Inc., 1961.

3. S. Jaye and M. P. Lietzke, Power Response Following Reactivity Additions
to the HRT, ORNL CF-58-12-106, Dec. 30, 1950,

 

L. P. R. Kasten, Dynamics of the Homogeneous Reactor Test, ORNL-2072,
June T, 1956.

 
12

Table 2. Nomenclature

Definition

area of outlet pipe, ftz

friction factor, psi/(f“t/sec)2

initial ramp reactivity input

specific heat of fuel salt

fraction of power generated in fuel salt
conversion factor

product of heat transfer coefficient times
wetted area of graphite

effective multiplication constant
prompt neutron lifetime
mass of fluid in outlet pipe, 1lb

ratio of specific heats (CP/CV) for pump
bowl gas

power
core pressure, psi

pump bowl pressure, psi

initial core pressure, psi
initial pump bowl pressure, psi
fuel salt heat capacity
graphite heat capacity

fuel temperature

graphite temperature

time

core residence time

fuel salt inlet temperature

fuel salt outlet temperature

Eguation
22

22

22

24

22
22
23
23

1]
13

Table 2. = Cont'd

Definition

 

outlet speed in pipe, ft/sec

initial gas space volume in pump bovl, ft3
mass flow rate of fuel through core

total delayed neutron yield

yield of ith delayed neutron precursor
latent power due to ith precursor

initial step reactivity input

fuel salt density

Eguation
22

2l

 
Title

14

Table 3. Input for Description of Reactor System

l. Core characteristics

V
c

t
c

 

 

l (1/p0)(30/ an)l

AL
i

B.

1

salt volume, ftB

residence time, sec (if fuel is not circu-
lating, enter zero)

weighting factor for mean temperature

heat transferred from graphite to sale per unit
temperature difference, Mw sec/ F

fraction of power generated in salt
fuel heat capacity, Mw sec/°F
graphite heat capacity, Mw sec/oF

fue% te%perature coefficient of reactivity,
("F)”

graghitf temperature coefficient of reactivity,
("F)"

prompt neutron lifetime, sec

fuel density, lb/f‘b3

fuel expansion coefficient, (OF):';l

delayed neutron precursor decay constants, sec-l

delayed neutron precursor yields

2. External loop characteristics

t

residence time, sec (if fuel is not circulating,
enter zero)

outlet pipe area, ft2
outlet pipe length, ft
steady state outlet velocity, ft/sec

friction factor, psi/(ft/secz)

Fortran Name

 

HPLM

VC

TCORE

ATMX

FRACT
HCAPF

HCAPG

TCOF

FLT

DENSE

FLAM(I)

BETAS(T)

TLPPP

AREA

L3

PLGTH

VEL@X
15

Table 3. Cont'd

Title Fortran Name

 

3. Pump bowl characteristics

Vp(o) initial gas volume, £ VPRS
pp(o) initial pressure, psi | - PPRS
N ratio of specific heat at constant pressure

to specific heat at constant volume for

gas in pump bowl | CP@CV

Title card is read with format 12AG; others with TELO.O.

 
16

Table 4. Input for Individual Cases

 

 

Fortran name Format
Case number ICASE 16, 11AC
Title HPLC }
Symbol Definition
Po initial power, watts PZER(
Tfo initial fuel mean temperature, °F TFO |
Tgo initial graphite mean temperature, °F TGO 6ELO0.0, 2I5
Ak(o) initial step insertion, % STEP
b(o) initial ramp rate, %/sec RATE
ot time step, sec HH
NP@ printout frequency NP@
‘ KST@P number of time steps to be run after
power peak KST¢P
ST¢P TIME total time to run YEND }
| FE10.0, I5
NTC number of ramp rate changes NTC

3 pairs to a card)

time to change ramp rate, sec TC 6EL0.0
new ramp rate, %/sec BNEW
 

 

 

MURGATROYD INPUT |

 

. TITLE FOR SERIES OF CASES

T b
WHHH—HHIH‘IHHHHIHHHIHIHHIHIHlll'llll-ll'liHIHHHHHHHHIHH_L

 

 

 

CORE DATA

 

Ve t a ~h | f . S¢ | Sqg '

OO O O O O O L T T LT T T O T

 

 

 

 

 

 

|lake/an‘ 1 lake/aTgl 21 l‘ ‘31 P | l f' s 73 80
HEERRRER H'HHHlTHHHHHHllh_[HI RENEREREEEEERNEREREEERERERREEENERRREER

DELAYED NEUTRON DATA

 

 

 

 

Ay | N A3 l | e Ns re Az

! 5 71 80

T L T L T L L T T T

B Bs B B, Bs Be | B;

i 21 3 41 71

T O O T O OO T T T T T T T

EXTERMAL LOOP DATA

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

O T T

PUMP EuVIL DATA

L ‘ U as¢ G

ENANNRANNANAANSNNNNNARNN NN NNRARAR NN AN NN AR RNANE

 

 

 

 

 

 

 

 

 

 

Vp (0) Pp (0) n

T T LT T LTI

31

SENANNARANARERNNNARENNNNANNRNNNRRNNNRRRNINRNAEE

 

 

 

 

 

 

'F‘GJ Ia\ INP.UT DESC{Z\B(Q@ QGACT‘o{Z SYSTEM

1
LT
- MURGATROYD INPUT-2

 

CASE NO.
7

A o b PP

CASE TITLE

- ——

8c

 

 

 

TTIT

 

TITTT

IHIIHHIJHIHHH'IH"HHHIIHHHIJIilIIIIHUII[IHIIHIHU

 

Po

Tfo

Tgo

o A.< (0)

by

3t

NPO K STOP

 

TTITITL

 

LTI

mmm

 

HHHH]

 

m'mm

 

 

s'ml

 

 

L

TTIIIIL

 

NRNRNNNEE

 

STOP TIMF’ sec

30]

 

T

 

 

 

 

HHILHLHIHHIIHIHHHIHIIHAHHHHHIIHHHHH

TTTIIT

 

- TIME, sec.

NE‘I RAMP °/o/sec

TIME, sec.

NE\I RAMP °/o/sec

TIME, sec.

NE\I RAMP, "/o/scc'

 

T

[TITTIIIT

T

IIHIHH

TTTIITITS

,HHUH_[.

“TTITTTT

 

IllIIHHH

 

 

3

 

T

T

TITTITIT]

TITTIITIT

LIE Il

 

TTTTT]

 

s o v

T

TTITIIT

 

 

TOTTD

I

TITITTTT]

TTTITTIT]

T

T

L1

HERENNREER

TITIIIL

 

 

 

IO TT

T

TITTIIITT

TTTIITIT]

T

[TTITTITIT]

T

 

TTITITTITI

 

|

 

T

TITITITTI

TTITIITTTL.

 

ERRNER

 

1T

TTTIIITT

 

TP PILedgy

TITITT

 

 

 

 

 

T

TITTITTIT]

TIIIITIL

 

73 80
LIt T]

 

T

TTTTTIIT]

TTIITITITITIIIIIITII]

 

73

 

 

TTTITTIII

 

TIITTTTIT

 

TITIITIII

 

TITITTIITL

 

HREERAER

 

 

T T T IIIIIL]

 

 

 

ITTTL

 

 

Fie To. Iudor tor One Case

‘91:
ey

.y

DK/DT,/DEG F

‘PROGRAM MURGATKoYD=-11

MSRE NORMALUTFLOW NO SOAK=-UP ™ 3727782

INBOT EDTT ———

19

Ta
Fiec. 2. Sampee Ourtpur

HEAY TRANSFER RATE (GRAPHIYE 7O FUEL)Y 0,020 MW/DEG F

FRACYION OF POWER GENERATED TW FUEL " 770,940

RESTDENCE TIMES

 

CORE 7,318 SEC

_Loop 17,3384 SEC

flgglwqggpchv. GRAPHITE FUEL
MWE*SEC/DEG F 3.53UE 0 is470E 00

T 6,000E=-0%  2.,800E=U5%

 

wrerean

DELAYED NEUTRON DATA

 

 

 

 

DELAY LAMBDA, GSTATIC EFFECTIVE GAMMA(T)Y, INITIAL ***GAMMA#BETA/LIFETIME
GROUP SECe*-] BETA RETA SEC**= | Cel) C # GAMMA/LAMBDA
| 0,0124 2,T12E=N4d 5,294E-05 2,170E=-0T 1,750& 01
2 0,0305 1,402g=03 4,258E-04 |,468¢ 00 4,813 0
g T T T 25 AR ST S UE ST T B3¢ 0T T A5 TE TT
4 0,3013 2,528E="3 | ,513E-03 5,216 00 1,731 0!
g I, 1400 7,400e~14  6,513c-04 2,246€ 00 T,970& 00
6 3.0100 2,700F=14 2,577E~D4 8,88B8E~01 2,953E=01
TOTAL 6,405E-43 3,381E-03

 

NEUTRON LIFETIME

2.900g=04 SEC

 

FUEL TEMPERATURE # 0,5U*INLET + 0,5U*QUTLET

 

DATA FOR PRESSURE CALCULATION

 

 

 

 

rE st R PR E D QUTLETY PIPE DATA 63'4000‘u¢lni FFFRNFRIREY TODUMP ROWL DATA TR L X KRR CORE SALT DATA Teasntee
'AREA, LENGTH, FLOW SPEED, FRICTION TERM,* * GAS VOLUME, PRESSURE, CP/CV * * VOLUME, DENSITY, =(1/V)(DV/DT),
‘SN FT FT FT/SEC PST/UFT/SECY**2% # CuBlC FT PS1 B * ¥ CUFT LB/CU FT PER DEG F
0.139 16,0 19,3 0,0203 . . 2.5 5,0 1,67 * * 19,6 154,5 | y26E=D4

 

PR R PP IR TR AN AT F R FRNFIITHEINIFAFETRRAT ARG TR

 

SN EZXERERERNEEE A A NN KN X R X N K N N N NN

TR TatNIRadpsRgaaaneassnpnnsanpnas
CASE l

20

Tie. I b,

"PROMPT CRITICAL STEP AT |4 MW

INTTIAL VALUES

T
FUEL TEMP

 GRAPHITE TEMP
STEP DELTA K

‘RAMP RATE
TIME STEP

- 14000 07 WATTS

. 1e00,000  LEGREES F

T1230.000 DEGREES F
0,338 PERCENT

" «0s  PERCENT PER SECOND
.. 5.000E=03 SECONUS

PRINT EVERY 20 STEPS

)

‘)
21

Fie T b, (Cont.)
MURGATROYD 1 CASE |

. TEMP,DEG F RISE.PSI  INPUT,PCT  FUEL  GRAPHITE PER SECOND

TIM ETWM"Mm"pUWEW ;TR IEL T EMP G
SEC_ WATTS  DEGF

0.100 2.170E 07 1200,369  1280,010  7,677€-01 0,381  0,0010 0,0000  5,468E 00

0.200  3,388E 07 1201,479 120,041  9,006E=01  0,338]  0,004]  0,0002 S:687E 00

 

 

0.500  4,873F U7 1203,346  124u,093  1,040E 00 0,338)  0,0094 0,0006  2,8(|E 00

0,400 6,006F 07 1205,988 1230,170 1,159 00 (0,338 0,0168 0,0010 24233k 00

|«769E 00

 

 

o

2500 7,331E 07 1209,396  1230,270 1,285 00 ,338]  0.0263  0,0016

VALUES AT PRESSURE MAXIMUM

 

 

 

TIME,SEC PRESSURE RISF,PSI - “

0.560 I,2503 00 ) ] B
5 EEs T ToesIAETU— _

0,570 | 2503 00 -

 

 

 

 

0,600  8,5626 07 1213,519 1230,395 | ,246E 00 0,338 0,0024 1,350 00

 

0,700

0.800

9.601E

i « 038F

07

08

1218,245 230,541

1223%,410 l230,706

o) 84E

| +058E

00

00

0,3381

0ed381I

0,U511

0,0655

. 00,0032

0.0042

9.576E~0 |

5,926E=~0]

0.900 I, 081E 08 {228,809 1230,883 8,922E=0| U.3381 0,0807 0,0053 2¢677E=0|

 

VALUES AT POWER MAX[MUM
TIMEL,SEC POWER, WATTS
0,990 | o 093RE 0B

 

DELN P) /DT

 

TATETITESTS

0,995 |, 0938E DA

 

=T 3Z30E-TUS

1.000 I1,0936E 08

 

 

 

 

I, 000 . 0G4E 178 1234 ,234 V201,069 7, 172E=0T1 0,33817 0,09%59 00,0064 e 682E»03

 

 

1. 100 I.UBIE 08 235,503 1237,257 5,594E~T1 0.,33817 0,1106 0,0075 =2,090e~01

 

 

7200 [ U508 U8 1249,483 231,345 4,335€~01 " 0,3387 0.7246 10,0087 =3,492E-0]

 

 

1,300 IQUIOE U8 l24@70?3W””WT?3T752@”WWW3fJZUE%UTWWWW”U}33BTMMNWUTI375 0.0098 «4,300E=01

0.0108

 

 

1.400 9.653F U7 1253,301 231,807 2,797E=01 " 0,3387 7 0,1392 ~ =4,634E-0)

 

 

1,500 9,214 07 12570110 TT1@3T,981 2,384E-01  0,338) ~4,637E=01

GITeT

gL s HIaTTy

 

 

 

1,600  BR,B(UBF 07 ey ,544 1232,149 2.l 05E=DI 0.1695 0.Ul29 - =4,440E-D 1|

‘T;7fifimnflmé;435?"fiVMMWT?637639W””"T?3?:3T3”mwwT{§U3Eéfif"”"M”U;3380 - 0.1782 0.UI39 wd,|45E=0|

0.1860

 

I.800  8,1C8E 07 1266,420 1232,472 1.744e-01 (,3381 0.0148  «3,812E~0|

17900 7,81BE 07 268,932  1232,627 1 6076~00 T 0.3381° T 0.1930° G 0iSE T n3.487Eep]
MURGATROYL

TIME,
SEC

2,000

.?9!90

5,930k

5,659

11 Cast

CPQUER,

WATTS
7.962¢
7.336F
7.135¢
6,305k

$£,794

A BABE

6,516F
6.396F

6,287

AL IRTE

- 6,UY5E

b, ulINE

5,793k
5,730k U

5.673F -

5,619k
5.569¢

.52k

5,479

5,43HF

5,359F

5., 364F

5,.83nF

7

g7
L7

7

7

el T,

NEL F

171,20
be/3,255
lel~, 116
17n,Rub
V27,34
1279.734
201,107
123,125

lend, 21

bend, 196

lZdb,Utl

1285, 86

g oA

1o/ ,163

12¢d7,74b

12834,271

1285 ,749

12389 ,174
1287 ,991

| €89 ,A%)

RN Y

129,408

1291, hYS

1275 , 4% )

i2vyl.0n/74

RAPH]TE
Yore, lik

282,779
582,928
1285,574
ldd&,zlc
1 23839, 3n1)

233,900

i 2383 ,A80

le33,77>

F288,911

P 284 ,1145

284,170
234,310

1234 ,440

'l254.57u

| 234 ,A9Y
12484 ,82)
734,359
F2dn s
1 2385,29/
285,332
.IRJb.456
123,58 )
23,7038
739,826

12385 ,94y

§

22

F‘(,. Ob ((on"‘.)

PRESOSURFE
RIsE,FS]

led433Fm |
| e $56E=101
| 256211
| iek=1
e U923 =101

9.6Jb6k= 12

B, 737602

7.924r=192
7. 164-m1)2
6,456E=1)2
S.7798=--02
Dol Bbr=l)2
4,616-=42

4,087k~)2

| Job92F'02

Jo14iE~02
2.718e-12
2.327&-&2
| e 9648E=(12
| o627p=02
. 316F=07
l«028E=02
7.,608k=03
5.1383F=33

2.8953%=1)0

NFLTA K
IN?“T'PCT

de S 3B
Le 38|
edo81
Ledd81
SRRy
e d3b |
UeddB I
LeddH |
Uedd81
ile 338 |
Ue 338
L3381
Ued38I
Ue 3381
e 338
deddb |
e d381
UedSK|
e $3b |
Ue S8
Ve 3db |
Je 3381
beddb|
e 38|

teddb|

PCT UK
F et

U994
TN
Qo213
feclDl
Daci94
0e.c2dd
" (.x268
0.23800
N.2330
0.2356
D.2881
0,403
0.,2423
N.c44)
0.2457
0.2472
0.2485
0,497

0.£5(47

ReEMOveD kY

kAP 4L TE
Doul67
Nedl 6
0e1%4
IPRIEER
Deiigle
Dell210
Heelb
D.0227
Q.u23d
D,UR4d
Debehl
VD.U259

DeULHO

D.U274

0.02482
DsURY0
N,eues?
0.US305
N2
Ne!820
ot 327
0,335
0.,0342
0,0L350

Deiid97

tl/sP)CDF/DT),
PER SELOND

4, 184F=01
2.9 1k=n|
~Zeb66BE=-0 |
~2.452E () |
~2¢260E=01
~2.N8BE=0 |
-l e934k~0|
=1e79%E-01
~le670E=D|

=1 +552E-01

=l 4451Ee0 ]

=1 4356E-01
= 14268E-01
=11 88E-DI
el 14E=D
= lend42E=0 )
=9,82eE-02
~9,236E=02
-8,699E=02
=8, 18YE-12
e7e722k=(2
«7.284E=072
=64881F-02
«b6.50/E~02

’60'5'E’02

N* -

0
MURGATRQOYD 11 CASE

MRS —PONERS
_SEC

_WATYS L

23

F1g T h. (cout)

DEGF

_ TeMPLDEG F

 

 

 

 

RISE,PSI

INPUT.PCT  FUEL  GRAPHITE

 

 

 

 

 

_ PER SECOND

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.500 5,298k 07  1291,225  1246,070  7,413e~04 0,338  0,2554 0,U364  -5,827Ee02
4.600 _5.268E 07  1291,353 236,191  =1,213E°08 0,381  0.2558 0,037)  ~5.,528E~02
4.700 5,2406 07 1291,459  1246,311 = »3,018E-03  0,3381  0.,2561  0.0379 -5,239E~02
4.800 5.2136 07  1291,545 1236,43]  =4,676E-03 0,3381  0.2563 0,0386  -4,9726-02
4,900 5.188E 07 1291,613  1236,55)  =6,2196=03 0,338 _ 0,565  0.,0393 __ -4,726En02
5,000  5,164E 07 1291,663  1246,670 w7,641En03 0,338  0,2567  0,0400 -4,496E-02
5,100  5,142E 07 1291,697  1236,789  »8,956E=03 0,3381  0,2568  0,0407 -4,283E~02
5,200 5,120 07 1291,717  1236,907  «1,017E=02 0,3381  0,2568  0,0414 ~4,083E=02
5,300 5.100E 07 1291,723  1237,025 |, |28E=02 0,3381  0,2568  0,0422 ., -3.894E-02
5,400 5.080E 07 1291,717  1237,143  «|,23|En02 0,3381  0,2568  0,0429 -3,722E-02
5,500 5,062E 07 129,699 1237,260 w|,325E*02 0,338 0.,2568 (0,0436 ~3559Ew02
5,600  5.044E 07  1291,670  1237,376  «|,413E=02 0,338  0,2567  0,0443 -3,408E=02
5,700 5,028E 07 1291,631  1237,493 | ,494E=02 0,3381  0,2566  0,0450 -3,269E-02
5.800  5.012E 07  1291,584  1237,609 w|,567E=02 U,3381  0,2564  0,0457 -3, 135E-02
5,900 4,996E 07 1291,528  1237,724  =1,634E-02 (0,338  0.2563  0,0463 -3,013E-02
6,000  4.982E 07  1291,464  1237,839  «l,697€=02 0.3381 0,2561  0,0470  =2,898E=02
6,100  4,967E 07  1291,393  1237,954 =] ,7556=02 0,3381  0,2559  0,0477 =2,794E-02
6,200 4,954E 07 1291,315  1238,069  =|,806E-02 0,338]  0,2557 0,0484  -2,693Em02
6,300  4,541E 07 1291,232  1238,183  «|,854E02  (,3381  0,2554 0,049 ~2,601E=02
8,400 4.928F 07 1291,143  1238,297  -1.898%-02  0,338)  0.2552 . 0.0498  -2,5136-02
6.500 4,916E 07  1291,048 1238,410 «|.939E=02 0,338 0,2549  0,0505 ~24437E-02
6.600  4,904E 07  1290,949 1238,524  w|,975E#02 0,338  0.2547 .05 -2,359E~02
6.700  4.B93E 07  1290,846  1238,637  =2,009E=02 0,338  0.2544 0,058 -2,292E-02
6.800 4,882F 07  1290,739 1238,749  «2,039E~02 0.338] 0,254 0.052§m”;w_“:?y22?fir02
6,900 4,871E 07 1290,628  1238,86]  w2,067E-02 0,3381 0.2538  0,0532  =2,169E-02

 

 

 
MURGATROYD 1] CASE

TiME,
SEC

7.000

7.100

PUWER

?

VATTS

UL

7.200

7.30¢

7.320

7,325
7.330

7,400
_7.500

7.6000

7.700

7.800

7.900

A.400

8.500

B.600

g.700

B.B00

R,730

v.000

4,Hh53F

9.100

4.8o10¢

4,841F

4,831F

07

07

a7

_t‘ 7 e

n
FUEL TEMP,

DEG F

12943,514

CVALUES AT PRESSURE MIN[MUM
TIME,SEC PRESSURE RISH,PS)

4,600¢

4.813F

4,795
4,786F
.ffi???fw_
4770k
4761
_4.753F
. 4.745E

4.738E

4,730k

4,8U4E

7o

87

a7

L7

V7

7

07

07
o7
07

87

W

1289,771

1284,507

e v o

1288,9648

1297,396
290,276

12914153

1299,028
1289,900

1289 ,640

1289,3738
1289,298
1289, 101
1283.824

;gaa,bas B

GRAPHITE
TEMP,DEG F

238,973

o 12dv.085

F2d9.096

025915??M “

1239,749

l249')35

12d0,294

 

4,722

4,707k

4. 700F

4.686F

4,715k

o

L

07
07
u7

w7

- 1287,976

1287,803

1287 ,68Y9

j284 o403
284,26

1288,119

1241 ,258

289,807

1239,418
239,699

1239,858
1289,968

240,077

1240,402
240,510
l240,618
tean,725
1240,838
1240,9489
Izal,046

1241,i152

ol

Fig. 2b Ccond)

. PRESSURE

RISE,PSI

~2,093E-02
=2, | I5E~02
-2,136E-02

=2,195E~02

=2, 159Be-02

»2,172E=02
7?!!89570?”,”w
-2,201E-02
m2,2|3E-02
-2,22%e-02
»2,233E-02

=2.24)E02

=2,250E=02
12(25§Ef02
~2,26|E=02

2, 266E=02

-2,273&?02»

-2.276E=02

~2.279€-02
r2,28|E~02

=2,270€-02

 DELTA K
INFUTLPCT

_0,3381
. 0'368'.,,
0.3d81

~0.3381

‘Less8)
D.3481
b.3d81
_U.3381
00381
ul.3381
U.3d81

Ue3981

Ued381

Vedd81

Ge338I

6.388)
Q'3§8!p;““
o Leddsl
~2,278E-02  0.8881
V3881

Ue338

FUEL
0.2534

044531
0.2528

0.2524

0,517
042514
0.2510

0,2506

0,2502

0.2499
0.2495
0,249

0.2487
0,2483

0.2479

0.2475

0.2471

00,2467

044459

0.2455

0.2463

PCT DK REMOVED BY.
GRAPHITE

0.U538
' 0.0545
0.U55%2

0.,0558

0.4521  0.0565
~0.0572
D.0578

0,058

0.U598
0.0605
o.u6t)

o.d0618

_ 0.0644
0.0650
0.0656

_0.0668

0.0659

0.u67§

D.05%2

0,624

0.0631

0,0637

CC1/P)(DP/LTY,
PER SECOND

-2.05/F=-02

=2, 010E=02

«14966E=02

=1+929E-02

=1.847E=-02

~1s78lE=CE

~1+758Ew(2

=1+726E-02

~1+703E=-02

=le1656E~GE
=leb37E=D2

=ls61BE=D2

=l+600E~0Z

= 14584E-02

=1+569E=02

_-};54ZE-02

-1 ¢528E =02

=1+BB2E=02

-1+813E-02

=1+554€E=02

r‘)

g
 

 

 

9.200
9.300

9.400

9.500

4,678E
4,671k
4,664F

4,657E

MURGATROYD 11 CASE

TIMEY
SEC .

07
v .

w

 

9,600

9,700

4.6250E

4,643E

07...

07

07

 

_4.637E

4,630k

07 _

97

MATYS

DEGF
1287,545
feB7,4001
287,257
1e87,112
. 1e86,967

_l28b,822

|1286,677

GRAPHITE

 TEMP,DEG F

1241,364

1241,470

1241,575

1241,889

 

|286,532

242,098

 

4,623k

07

1286,387

242,20

_1241,680

241,785

1241,994

22

PRESSURE

RISE,PSI

-2,283Er02

- =2,283E%02
»2,282E-02
m2,282E~02
=2,280€-02
~2,278E-02
r2,277€=02

n2,276E-02

2,274E=02

Fig. 2b (cent)

DELTA K
INPUT:PCT

0,338
0,398
be3381

043381

- b,3481

Ues38]

U,3381

PCT DK REMOVED BY {1 /BY(DF/DYY,

FUEL
0.245)

0,2447

GRAPHITE

0,2443

D,24389

0,2481

.0,2435

043381 D,e427

0, U682

0,0688
040695
0.,070)
0,0707

0,0713

 PER SECOND
=14522E-02
~12519En02
~ =1+¢502E~02
=|+494E~02

TN~ i} SRR e e

-|s475E=02

 

0,0720

0'0469E002

 

0.0726

-'04655802

 

 

Je33d81

0.0732

“w|4s459E=02

 

4,616E

07

|286,242

1242,305

-2,272€-02

06,3381

0,0738

-|¢4535'02

 

10.200

4,61 0E

07

1286,097

242,408

n2.27UE~02

0e3d81

0,0744

-|q448E902

 

 

 

10,300

4,603k

07

128%,952

|242,511

03381

 

10,400
10,500
10,600

4,596E
4,590E

4,583E

07
07

07

128%,807
1285 ,662

1269 ,517

|242,614
1242,716

.242'913

 

10,700
l0.800
10,900

4,577
4,570F

4,564E

07
07

07

j28%,372
| 285,228

128%,083

1242,921

243,022

1243, 124

 

 

 

11.000

4,557E

07

|284,93?7wm

 

1249.225

w2,265E%02
-2,2638-02
»2,260€-02
n2,257E=02
=2.254€-02
=2,25¢Em02

=2,249E702

0338

0,075

-|2441E=02

 

_b.338)

0,0757

10,0763

-.' Q440E"02

| 437E=02

 

U.3381 045

 

 

U338}

U, 3381

Ua3981

0.,0775

0,076%

=14432EX02

- ' 9427E’02

 

0,078

~|4425E=02

 

0.3381  0,¢

0.0787

0,0793

=14425E-02

"Q42'E?Ugw

 

 

 

 

 
FIG. Il

26

UNCLASSIFIED
ORNL-LR-DWG 67933

GAS SPACE

  
  
 

- PUMP BOWL

 

|*=— OUTLET PIPE

<+ CORE

 

 

N

SIMPLIFIED MODEL FOR PRESSURE CALCULATIONS

r/)

 

 
 

€y

(v

1“20

® ® ®

O O O\ W

10.
11.
12.
13.
1k,
15,
16.
17.
18.
190
20,
21,
22,
23,
2L,
25.
26.

28.
29.
30.
31.
32,
33
3.
32

37
38.
39.
40.
L1,
L2,
43.
Ll .
L5.
L6,
4T,
48.
49.
50.

27

Internal Distribution

MSRP Director's Office, 51,

Rm. 219, Bldg. 9204-1 52 o
G. M. Adamson 53.
L. G. Alexander 54,
V. E. Anderson, K=-25 55.
S. E. Beall 56.
M. Bender 5'7-,
L. L. Bennett 53,
C. E. Bettis 59.
E. S. Bettis 60.
D. S. Billington 61 .
M. Blander 62.
F. F. Blankenship 63.
A. L. Boch 64
E. G. Bohlmann 65.
S. E. Bolt 66 .
C. J. Borkowski 67 .
C. A. Brandon 68.
F. R. Bruce 69.
O. W, Burke T0.
S. Cantor TL.
R. S. Carlsmith 2.
W. L. Carter T3
R. D. Cheverton Th.
H. C. Claiborne T5e
T. E. Cole T6.
J. A, Conlin TT e
W. H. Cook 8.
L. T. Corbin 9.
G. A. Cristy 80.
F. L. Culler 81.
J. G. Delene. 82.
J. H. DeVan 83.
R. G. Donnelly 84 .
D. A. Douglas 85.
N. E. Dunwoody 86.
J. R. Engel 87.
E. P. Epler 88-92.
W. K. Ergen 93.
D. E. Ferguson oL.
T. B. Fowler 95.
A. P, Fraas 96,
J. Hs Frye 97 .
C. H. Gabbard 8.
R. B. Gallaher 99.
E. H. Gift 100.
D. R. Gilfillan 101.
B. L. Greenstreet 102.
W. R. Grimes 103.
A. G, Grindell 104,

R. H.
P. H.
C. S.
P. N.
E. C.
H. W.
P, P.
A. S.
L. N.
Je. Pe
W. H.
P. R.
R. Jo.
M. T.
M. J.
T. W,
Se Oe
J. W,
Je A.
W. Jo
M. P.
R. B.
M. 1.
R. N.
H. G.
F. C.
W. D.
E. R.
B. F.
W. B.
H. F.
C. K.
A. J.
E. C.
R. L.
J. C.
E. A.
C. W,
T. E.
W. R.
L. F.

Guymon
Harley
Harrill
Haubenreich
Hise
Hoffman
Holz
Householder
Howell
Harvis
Jordan
Kasten
Kedl
Kelley
Kelly
Kerlin
Kirslis
Krewson
Lane
Leonard
Lietzke
Lindauer
Lundin
Lyon
MacPherson
Maienschein
Manly
Mann
Maskewitz, K-25
McDonald
McDuffie
McGlothlan
Miller
Miller
Moore
Moyers
Nephew
Nestor
Northup
Osborn
Parsly

P. Patriarca

H. R.
A. M.
W. B.
P. H.
C. A.

Payne
Perry
Pike
Pitkanen
Preskitt

M. Richardson

R. C.
T‘ KC

Robertson
Roche
105. M.
106. H.
107. A.
108. J.
109. D.
110. C.
111, J.
112, M.
113. G.
114, A,
115. O.
116. P.
117. I.
118. B.
119. J.
1200 A.
121. J.
122. R,
123. M.
124, D.

28

Distribution - Cont'd

W. Rosenthal 126.
W. Savage 127.
W. Savolainen 128,
E. Savolainen 129.
Scott 130.
H. Secoy 131.
H. Shaffer 132.
J. Skinner 133.
M. Slaughter 13k.
N. Smith 135.
L. Smith 136.
G. Smith 137-138.
Spiewak 139-140.
Squires 141 -143,
A, Swartout 144146,
Taboada 147,
R. Tallackson 148.
E. Thoma

Tobias

B. Trauger

125. Marina Tsagaris

149-150.
151.
152,
153.
154,

155=-169.
170.

External Distribution

W.
R.
D.
B.
B.
A.
J e
J.
G.
L.
CO

C.

</

Ulrich

Van Winkle <

R.
S.
H.
M.
H.
c.
E.
V.
H.

Vondy
Weaver
Webster
Weinberg
Westsik
White
Whitesides
Wilson
Wodtke

Reactor Div. Library
Central Res. Library
Document Ref. Section
Laboratory Records
ORNL~RC

D. F. Cope, Reactor Division, AEC, ORO
M. Roth, Division of Research and Development, AEC, ORO <

H.
F.
R.
Te W

P. Self , AEC, ORO
A. DuVal, AEC Washington
. McIntosh, AEC Washington

Je. L. Crowley

Division of Technlcal Information Extension, AEC, ORO
Mrs. Margaret Butler, Argonne Code Center,
Argonne National Laboratory, Argonne, Illinois

 
 

S
ey
¢

£

 
[skipped page]Addendum to ORNL-TM-203

 

An addition has been made to the IBM-T090 program MURGATROYD to produce
a. rough graph of the reactor power versus time. A logical tape 6 is required
for storage of the power versus time results in addition to the standard input
and output tapes. The plotting frequency (analogous to the printout frequency)
is specified in columns 16-21 of the card containing the stop time and the num-
ber of ramp rate changes (see p 18, ORNL-TM-203). A sample of the graphical
output is attached for the case given as an example on pages 19-25. 1If the
plotting frequency specified in the input is zero or blank, no plot is produced;

however, a logical tape 6 must be specified even if no plot is desired.

Corrigendum

 

On page 15, in the last sentence, for "12AG" read "12A6".

 
4

PAGE

TIME
PROMPT CRITICAL STEP AT

"MURGATROYD POWER VS.

CASE

10 MW

 

 

(PMAX #1G.00DOE O7 WATTS)

0.4

Ol

0.6

 

 

oo G2
e X e e e o e

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0.

 

 

 

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0.5004--==—==—=t-

-

 

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+ +

 

 

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v

 

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2e SDG""“*‘:"_--—--'—-AP e =

 

 

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e S e e e

 

 

 

 

 

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N
™

 

3.500+--———————#--m——————p o —— e

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Foo=X==———%

 

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+

 

 

 

 

e e = e — e ———— ¢

 

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r

 

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5.000+--———=-——+==

 
 

1‘20

® * ®

O 0O~ O\ FW

10.
11.
12.

1k,
15.
16.
17.
18.
19.
20.
21.
22,
230
21“'0
25.
26.
27 .
28.
29.
30.
31.
320
33
31"'0

36.
3T
38.
39.
Lo,
Li.
L2,
L3.
L.
45.
L6,
LT,
L4L8.
L9,
50.

MSRP Director's Office,

G.
L.
V.
S.
M.
LQ
Ce.
E.
D.
M.
F.
A.
E,
S
C.
C.
Feo
0.
S.
R.
W.
R.
H.
T
Jde
W
L.
G.
F.
J.
Je
R.
D.
N.
Je
EO
W.
D.
T.
A,
Jde
C.
R.
E.
D.
B.
W,
A.

Rm.
MO
G
E.
E.

Interna}-Distribution

QM,MQ.%MJ
Adamson

Al exander
Anderson, K=25
Beall

Bender

L,
E.
Se
So

Bennett
Bettis
Bettis
Billington

Blander

F.
L.
G.
E.
Jo
A.
R.
W.

Blankenship
Boch
Bohlmann
Bolt
Borkowski
Brandon
Bruce

Burke

Cantor

S.
L.
D.
C.
E.

.A‘
H.
T.
A.
L.
G.
H.
G.
A.
E.
R.
P.
K.
E.
B.
PO
H.
He
B.
H.
R.
L.
R.
G

Carlsmith
Carter
Cheverton
Claiborne
Cole
Conlin
Cook
Corbin
Cristy
Culler
Delene.
DeVan
Donnelly
Douglas
Dunwoody
Engel
Epler
Ergen
Ferguson
Fowler
Fraas
Frye
Gabbard
Gallaher
Gift
Gilfillan
Greenstreet
Grimes
Grindell

51»
52 e
23
5}4'0
22
56.

3.
29.
60,
61.
62,
630
6l o
65.
66.
67 »
680
69.
T0O.
Tl.
72.
T3
Th.
e
760
[C
T8.

80,

R. H. Guymon

P. H. Harley

Ce S. Harrill

P. N. Haubenreich
E. C. Hise

He W. Hoffman

P. P. Holz

A. S. Householder
L. N. HOWell

J. Po Harvis

W. Ho Jordan

P. R. Kasten

R. J. Kedl

M. T. Kelley

M. J. Kelly

T. We Kerlin

Se Se Kirslis

Je. W. Krewson

Je A, Lane

We J. Leonard

M. P. Lietzke

R. B. Lindauer
M. I. Lundin

R. N. Lyon

H. G. MacPherson
F. C. Maienschein
W. D. Manly

E. R. Mann

B. F. Maskewitz, K-25
W. B. McDonald
He F. McDuffie
C. K. McGlothlan
A, J. Miller

E. C. Miller

R. L. Moore

J. C. Moyers

E. A. Nephew

C. Wo Nestor

T. E. Northup

W. R. Osborn

L. F. Parsly

P. Patriarca

H. R. Payne

A. M. Perry

W. B. Pike

P. H. Pitkanen
C. A. Preskitt
M. Richardson
R. C. Robertson
T. K. Roche
a

 
105. M.
106. H.
107. A.
108. J.
109. D.
110. C.
111. J.
112. M.
113. G.
114, A,
115, O.
116. P.
117. I.
118. B.
119. J.
120. A,
121. J.
122. R.
123. M.
124. D,

Distribution - Cont'd

W. Rosenthal 126. W. C. Ulrich

W. Savage 127. R. Van Winkle

W. Savolainen 128. D. R. Vondy

E. Savolainen 129. B. S. Weaver

Scott 130. B. H. Webster

H. Secoy 131. A. M. Weinberg

H. Shaffer 132. dJ. He Westsik

J. Skinner 133. J. C. White

M. Slaughter 134. G. E. Whitesides

N. Smith 135 L. V. Wilson

L. Smith 136, C. H. Wodtke

G. Smith 137-138. Reactor Div. Library
Spiewak 139-140. Central Res. Library
Squires 141 -143, Document Ref. Section
A. Swartout 144-146. Laboratory Records
Taboada 147. ORNL=RC

R. Tallackson 148. J. L. Crowley

E. Thoma

Tobias

B. Trauger

125. Marina Tsagaris

149-150.

| 151.
152,
153.
154,
155-169.
170.

External Distribution

D. F. Cope, Reactor Division, AEC, ORO
H. M. Roth, Division of Research and Development, AEC, ORO
F. P. Self, AEC, ORO
R. A. DuVal, AEC, Washington
T. W. MbIntosh AEC, Washington
Division of Technlcal Information Extension, AEC, ORO
Mrs. Margaret Butler, Argonne Code Center,
Argonne National Laboratory, Argonne, Illinois