ORNL-TM-1445.txt

 

O ¢
HC CoNEREL .
OAK RIDGE NATIONAL LABORA%'Q‘R’I“ e J

operated by

UNION CARBIDE CORPORATION
for the

U.S. ATOMIC ENERGY COMMISSION

  

ORNL- TM- 1445
COPY NO. - a4 ,

DATE - April 5, 1966

SIMULATORS FOR TRATINING MOLTEN-SALT REACTOR EXPERIMENT OPERATORS
S5.J. Ball
ABSTRACT

Two on-site reactor kinetics simulators were developed for training
operators of the Molten-Salt Reactor Experiment (MSRE) in nuclear startup
and power-level operating procedures. Both simulators were set up on
general purpose, portable Electronic Associates, Inc., TR-10 analog com-
x puters and were connected to the reactor control and instrumentation

system.

The training program was successfully completed. Also, the reactor
control and instrumentation system, the operating procedures, and the rod
and radiator-dcor drives were checked out. Some minor modifications were
made to the system as a result of the experience with these simulators.

 

RELEASED FOR ANNCUNCEMENT

IN NUCLEAR SCIENCE ABSTRACTS

 

 

NOTICE This document contains information of a preliminary nature
and was prepared primarily for internal use at the Oak Ridge National
Laboratery. It is subject to revision or correction and therefore does
not represent o final report.
 

 

 

 

 

LEGAL NOTICE

This report was prepared gs an account of Government _sponsoréd work. Neither fhe United States,

nor the Commission, nor any person acting on behalf of the Commission:

A. Mokes any warranty or representation, expressed or implied, with respect to the accuracy,
completeness, or usefulness of the information contained In this report, or that the use of -

-any informatien, epparatus, method, or process disclosed ln 'his report may not infrlngc
privately owned rights; ot -

B. Assumes any liabilities with respect fo the use of, or for dcmuges nsultmg from the use of
any infermation, apparatus, methed, or process disclosed in this report.

As used in the above, "“person acting on behalf of the Commission®’ includes any omployce or .
contractor of the Commission, or omploy-t of such contractor, to the extent that such -mployo.
or contractor of the Commission, or omployee of such contractor prepores, dussemmmes, of

pro\ndes access to, ony information pursuant to his employment ot contract with the Commission,
or his employment with such contractor.

 

 

 

 

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; ‘ \:‘

‘ 1

‘-

 

 

 

 

 

 

 

 
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=)

 

CONTENTS
Abstract Page
1. Imtroduction .......... 1
2. Startup (Zero Power) Simulator .... Ceetiiceicaateenareeae 5
3. Power Level Simulator ........ Cesetesttietreresrsrenane D
4. Time Required for Setup of Simulators 8
5. Conclusions tieeeereeeeeeasens tececcscscnasrassnnses 13
6. AppendiX ...eeiiiinnann ettt e s s 1B
6.1 Details of Startup Simulation .... prreeeeeeneneeeeees B
6.2 Details of Power Ievel Simmilation .'..-................._ 15
.6.2.1 Neutron Kinetics Equations .. e
. eereeererereieeiee.. 19

6.2.2 Core Thermal Dynamic Equations .........
6.2.3 Radiator Effectiveness ...... e
R~

6.2.4 Xenon Poisoning .....
* % 9 % 0 & 8 0 BP0 9 T e eSS e S SN 23

RELEASED FOR ANNCUNCEMENT

% ABSTRACTS

IN NUCLEAR SCIFV3

 

as an account o
acting on behalf of the Commission:

por any person
sentation, expressed or jmplied, with respect to the accu-
tained in this report, oF that the use

the informafion col
losed in this report may not infringe

of, of for damages resulting rlrom the

This report was prepared
Btates, nor the Commissaion,
; A. Makes any warranty or repre
racy, completeness, or usefulness of
of any information, apparatus, method, or process disc

privately owned rights; or o ]
B. Assumes any liabilities with respect to the use
method, or process disclosed in this report.
ton® includes any em-

tor, to the extent that
contractor prepares,
ent oF contract

- use of any tnformation, apparatus,
‘person acting on behalf of the Commiss

As used In the above,
Commission, oF employee of such contrac

" ployee or contractor of the

" such employee or contractor of the Commission, ©
" dispeminates, oF provides access to, any information pursuant 0 his employm
with the Commission, oT hia employment with such contractor. . )

r employee of such
O]
 

 

 

 
 

 

 

 

 
 

 

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1. INTRODUCTION

Two reactor kinetics simulators were developed for training operators
of the Molten-Salt Reactor Experiment (MSRE) in nuclear startup and power-
level operation procedures. Both simulators were installed at the reactor
site, and were connected to the reactor instrumentation and controls system.
The operators were trained in startup, or zero power, operation with the
simulator in February 1965 and in power-level operation in October 1965.

Both simulators were set up on general purpose, portable Electronic
Associates, Inc., TR-10 analog computers (borrowed from the Instrumentation
and Controls Division analog computer pool). No special hardware (other
than the computers) was required. Although most of the simulation tech-
niques were straightforward, a few special techniques were devised.

This report describes the two simulators.
2. STARTUP (ZERO POWER) SIMULATOR

The startup simulator, set up on one T§-10 enalog computer (Fig. 1),
computed the reactor neutron level from 107 w to 1.5 Mw as a function of
control -rod-induced reactivity perturbations. The effect of nuclear power
on system temperatures was not included.

ORNL DWG. 66-4834

 

 

INPUTS | OUTPUTS REACTOR INSTRUMENTATION
t—s S |+ NEUTRON LEVEL:
ROD . I | [UINEAR POWER - RR-8100
POSITIONS iM LOG POWER = - RR-8200
Ls—u {LOG COUNT RATE CONSOLE METER: CHANNEL 1
' PERIOD CONSOLE METER: CHANNEL 2
L ~ | FISSION CHAMBER SPECIAL: ON CONSOLE
A ~ POSITION AR -
T
LINEAR FLUX _0
" ‘RANGE R

 

 

 

Fig. 1. Diagram of Startup Simulator.
 

 

The inputs to the simulator were signals indicating the actual
positions of the control rods, and the outputs (indicated on the reactor
instrumentation) were log count rate, period, log power, and linear power. s

The linear flux-range input signal was taken from the selector switch
on the reactor console. The fission-chamber position readout was provided
by a meter mounted on the console. The fisiion chamber is the detector
for the wide-range counting channel system. The chamber position is
servo-controlled to give a constant output signal, and the chamber posi-
tion is related to the log of the nuclear power. The period interlocks
and the flux control system were also used.

The operators practiced the approach-to-critical experiment (in which
plots of inverse count rate vs rod position are used to extrapolate to the
critical rod position) and rod-bump experiments for calculating differential
rod-reactivity worth from measurements of stable reactor period. The
simulator was also used to check out the flux servo controller.

Rod position signals were obtained from the three potentiometers nor-
mally used by the MSRE computer. The "S" curve relating rod worth and
position was approximated for the regulating rod by a diode function gen-
erator (Fig. 2). The rod worth vs position relationship for the other
two rods was linear.

 

15.E. Beall et al., MSRE Design and Operations Report, Part V, Reactor
Safety Analysis Report, ORNL-TM-732 (August 1964), pp. 96-99.

 

ORNL DWG. 66-4835

 

1.0

0.8

0.6

0.4}

FRACTION OF TOTAL ROD WORTH

0.2

 

 

 

i 1 i L
o 10 20 30 40 50 €60

 

DISTANCE WITHDRAWN (IN.)

O .

Fig. 2. Simulator Approximation of Regulating Rod Worth vs Positionm.
 

 

 

s

ah

.’

L

7

The analog circuit used to compute reactivity from the tinree rod posi-
tions included the effects of the position of one rod on the total worth of
the others (Table 1). .

Teble 1. AFull-Scale Rod Worths

 

Full-Scale
| Rod Worth Reactivity
Rod Position (% 8K/K) vs Position
Regulating Rod Shims out 2.6 "S" curve
Shims in 1.3 "S" curve
Both Shims Regulating rod out 5.8 linear
Regulating rod in 4.5 linear

 

- The neutron level computation was made by converting the kinetics
equations to logarithmic :E‘orm,r2 since the neutron level varied over eight
decades. Two effective delayed-neutron precursor groups were used. The
usual method of including the source term in these equations was found to
be unsatisfactory, and a special circuit was used (see Sect. 6.1).

The conversion of log power to linear power was approximated by using
a squaring device that gave adequate accuracy over each linear (1.5 decade)
range (Fig. 3). A voltage signal from the reactor instrumentation linear-

 

2A.E. Rogers and T.W. Connolly, Analog Computation in Fngineering

Design, pp. 334-7, McGraw-Hill, New York, 1960.

ORNL IMG. 66-4836

 

RANGE CKT. BIAS

1.5 _
924
| sLoc1oN =N Linear
=3V. AT FULL
- VOL%ECADI SCALE x

125

 
    
     

X =APPROXIMATION CIRCUIT OUTPUT
1.0

DESIRED OUTPUT

INDICATED LINEAR POWER
O
-}
11 .4

0.5

0.25

 

 

% X i 1 1 1 ] I f 1 i 1
0 0.25 0.5 0.75 1.0 t.25 1.5

POWER SIGNAL FROM LOGARITHMIC CALCULATION

 

Fig. 3. Approximate log-to-Linear Conversion.
 

 

 

range selector circuit was subtracted from the log power signal, and this
difference was then converted to the linear signal.

The equations and analog computer circuit used for the startup simu-
lator are given in Sect. 6.1 '

3. POWER LEVEL SIMULATOR

The power level simulator, set up on two TR-10 analog computers
(Fig. 4), simulated the kinetic behavior of the MSRE for power levels

ORNL DWG. 66-4837

 

 

INPUTS QUTPUTS REACTOR INSTRUMENTATION
L A
ROD 1 e NEUTRON LEVEL.: RR-8100
POSITI LINEAR POWER =
OSITIONS| >, ] g5 LOG POWER RR-8200
LOG COUNT RATE CONSOLE METER: CHANNEL 1
3 — | PERIOD CONSOLE METER: CHANNEL 2
M FISSION CHAMBER POSITION  SPECIAL : ON CONSOLE
RADIATOR [ 1 —» }—= REACTOR INLET TEMPERATURE.
DOOR U TR~202-A5
POSITIONS | 2 — L —+»REACTOR OUTLET TEMPERATURE
A —"RADIATOR SALT OUTLET TEMP. TI-202-A2
RADIATOR
AIR T RADIATOR SALT AT Tal-201-A
AP
—»- RADIATOR HEAT POWER ,
o FLOW (CONST) X AT XpR-201-A
REACTOR R
CONTROL
MODE

 

 

 

Fig. 4. Diagram of Power Ievel Simulator.

between 0.5 and 12 Mv. The inputs were signals indicating the actual
positions of the rods and the radiator doors and the actual pressure drop
of the cooling air across the radiator. The outputs were neutron levels
and temperatures. The usual nuclear information and key system tempera-
ture outputs were indicated on the reactor instrumentation. The reactor
power-level servo controller and radiator load control systems were also
used.

The reactivity inputs from control-rod position signals were computed

as in the startup simulation. The neutron level computation (using two
delayed-neutron precursor groups) solved the linear, rather than loga-
rithmic, kinetics equations. Only the O to 1.5 and the O to 15 Mv ranges
on the reactor linear power channels were operational. Conversion from
linear to log power was approximated using a square-root device (Fig 5).

C .
 

oW

]

100(Mw)10.0 |-

INDICATED POWER SIGNAL (V)

ORNL DWG. 66-4838

 

 

 

 

 

10(Mw) 9.0

     

X

8.5 |
DESIRED OUTPUT

1 (Mw)8.0
7.5

0.1 ('M w)7.0

0 2 4 6 - 8 10
| | COMPUTED LINEAR POWER (Mw)

 

 

- Fig. 5. Approxirfiaté.,Linear-to -Iog_ Conversion.
10

Other reactivity inputs to the power level simulator were from com-
puted Xenon poisoning, noise, and fuel and graphite temperature changes.
The xenon-poisoning computation (Fig. 6) was included as an option. In
consideration of the long time-constants of xenon buildup and decay, the
equations were time scaled to run at ten times real time.

ORNL DWG. 66-4839

DIFFUSION

—»] 10DINE T Xe (FUEL) X e (GRAPHITE)
DECAY * STRIPPING (DOMINANT) +

 

 

 

 

 

 

 

 

 

 

 

 

Nr=2.9%X107 sec—! DECAY
I BURNUP DECAY Ay = 2.1 X 107% seC™!
A (TOTAL) 5> X g BURNUP Ap = 1.66x107¢ P sec-!

Steady- State Xe Poisoning When P =10 Mw:

5 K Fuel = -0.7%
6 K Graphite= -0.79 %

Fig. 6. Diagram of Xenon Poisoning Computation.

The reactivity noise input was included to offset complaints typical
of usual simulators about how "smooth" the flux output is compared with
the noisy output of actual reactors. An operational amplifier with high
resistance feedback (40 megohms) was used as the noise source.

A simplified simulation of the thermal kinetics of the MSRE was used
which was based on previous studies of reactor dynamics.

The core was represented by two fuel "lumps," or nodes, and the
graphite by one. Six more lumps were used to represent the rest of the
system. The thermal characteristics are summarized in Table 2,

The heat removal rate from the radiator is controlled by varying the
air flow through the radiator; hence, the radiator salt outlet temperature
is affected by salt inlet temperature, air inlet temperature, and air flow
rate changes. A simple but fairly accurate way of simulating the heat
removal is to make use of the relationship of radiator cooling "effectiveness"
as a function of air flow rate. Cooling effectiveness is defined as the
ratio of the actual temperature decrease of the hot fluid to the tempera-
ture decrease in an ideal (i.e., infinite heat-transfer surface) heat
exchanger:

 

3S.J . Ball and T.W. Kerlin, Stability Analysis of the Molten-Salt
Reactor Experiment, ORNL-TM-1070 (Dec. 1965).

 

ta

 
 

11

Fl]

Table 2. MSRE Thermal Characteristics Used in the Power level Simulator

 

Core transit time, sec 7.6 (two
lumps )
Graphite time-constant, sec : 200.0
Heat exchanger to core transit time, sec” 10.0
Core to heat exchanger transit time, sec 6.67
Radiator transit time, sec 6.67
Radiator to heat exchanger transit time, sec™ 10.0 (two
o lumps )
Heat exchanger to radiator transit time, sec 5.0

Heat exchanger "effectiveness" factors at steady stateb:

T T
B £= = 0.7029 £ = 0.2971
v pi si
TSO TSO
T—_.- = O.h-)-l-TS T-.- = (0.5522
pi si

 

aHoldup time in heat exchanger is included in the other transit times.

bP, primary; S, secondary; i, inlet; and o, outlet.
e L bl =1 b S8 5 L. ot 3 el 0 3008~ et e i 21 54 1 et .

 

g = Tsa1t in ~ Tsalt out
c . =T . L :
salt in air in

The salt outlet temperature is computed from

) .

Tsalt out — Tsait in - Fe(Tsalt in - Yair in

The calculated cooling effectiveness as a function of é.ir flow rate and
the linear approximation used in the simulator are shown in Fig. 7.

ORNL DWG. 66-4840

 

 

   
  

 

 

 

0.1
S COOLING EFFECT IVENESS
- = TSALTIN- T sALT our
o Ec T T 7/
" SALTIN- I AIRIN ~
2
L
> |
-
O CALCULATED
S n
L
L
W o.05
O
< APPROX IMATION
J
O
O
O
x
O
=
<
o
<
@ 0 J | ) 1 I 1
0 50 100

COOLING AIR FLOW RATE (%)

Fig. 7. MSRE Radiation Cooling Effectiveness vs Air Flow Rate.

.
 

-

"

13

The air flow rate Wé through the radiator was computed from

W= KVTE (X + X)),
where

K = constant adjusted to give 10 Mw cooling at full air flow,

AP
a

5%

Conversion of the analog computer voltages representing temperatures
to signals compatible with the Foxboro ECI instruments was done with
straightforward resistance divider networks.

measured air pressure-drop signal across the radiator,

measured radiator door positions (inches raised).

|

The equations and analog computer circuit used for the power level
simulator are given in Sect. 6.2.

4. TIME REQUIRED FOR SETUP OF SIMULATORS

The engineering and craft time required to develop, install, and
check out the simulators and to train the operators in their use was as
follows (all values in man-weeks):

 

Startup Power level
Simulator Simulator
Engineering labor
Development 1.6 1.4
Set up and check out ‘ 0.7 1.2
Iecturing on use | 0.3 1.0
Craft Iabor
Installation I 0.3 0.4

Total 2.9 k.0
5. CONCLUSIONS

The two on-site training simuilators were developed and operated satis-
factorily as part of the MSRE operator training program. Besides the
obvious function of training the operators, the simulators served as a
 

14

means Of checking out the reactor instrumentation and control system, the
operating procedures, and the rod and radiator-door drives. Some minor

modifications were made to the system as a result of this experience with
the simulators.

All manipulations required to operate the simulated reactor were done
from the reactor console, and the readout devices were part of the standard
reactor instrumentation.

tp
o

 

2

 

15

6. APPENDIX

6.1 Details of Startup Simulation

The neutron kinetics equations are

 

6
g-% = %*[k(l-aT)-:L] +z \Cy * S (1)
i=l
dcy knp,
T - TF MO (@)
where

n = neutron population,

t = time, sec,

1¥ = prompt neutron lifetime, sec,

k = reactor multiplication,

Bp = total delayed neutron fraction,

Bi = effective delayed neutron fraction for ith precursor group
with fuel salt circulating,

Ai = decay constant for 1th precursor group,

Ci = ith precursor population,

S = rate of neutron production by source.

fiewrite Eqs.-(l) and (2), assuming kBqp~ Pr and E;giww E?%-:

ok - . 6 .
g_fal. = _____.l*BTn +z MG, + S (3)
, i=1

dCi _‘- nBi
=% - ™ MY ()

Divide E@s. (3) and (4) by n:
16

 

 

: 6
ldn _ 8k - By MG s .
=% s =y 22 (3')
nd 1% n n
i=l
l_dci _ ?1.- xici (u')
n at 1* n
Define new variables:

dn

dt . .
M = -~ = Teciprocal period,

Ci
Vi T oao
w o= S,

n

_Substitute into Egs. (3') and (4'):

8 6
_ &k P
M_F_F+Zvi)\i+w, (5)
i=1
avy By
= - F oMY oM (6)

The usual method of computing the source term is as follows: noting
that Wn = S and

 

d'(wn)= é§. = 0
dt dt ?
therefore
n dw
T T T O
dw W dn
O — = -—— — -
¥ It o at M. (1)

The analog computer can usually solve a first-order differential
equation such as Bg. (7) for W; however in this case, W becomes so small
when n >> S that the voltage representing W is within the noise level of
the amplifier, so further computation with it is meaningless. To avoid
this problem, the relationship between W and log n was approximated as
shown in Fig. 8.

€3

 
 

 

 

&

 

17

ORNL DWG. 66-4841

 

ACTUAL

| /A PPROXIMATE

 

= OGN

 

Fig. 8. Approximation of Iogarithmic Source Term W.

- The six delayed-neutron precursor groups were approximated by two
groups, as follows: ' :
Bl = ) By = 0:002693,
1=, |

- B, g = 0.00092k,

1

:

i=1l

>
I
}:Dl
i
o
O\
w
0
o
Q
1
| e

1-3
Ei |
li-
1

‘KL_6' = 0.04Lk2 gec .

The prompt neutron lifetime 1* was 0.00024% sec, and was 0.0064 (ref 4).
’ Pr

The analog COmputer circuit for the startup simulator is shown in
Fig. 9.

 

: hR.B. Lindeuer, Revisions to MSRE Design Data Sheets, Issue No. 9,

ORNL-CF-64-6-43 (June 2k, 106%).

 

 
 

18

 

 

 

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MoTreS
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oMl#fi

SWE S/

=005 MV,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o
G/
RE G ReGULATING KOD
zoD
8K -0V
" mosirron oV
ip
(5%

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. ORNL IMG. 66-4842
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b
1
i
|

Fig. 9. Analog Computer Circuit for the Startup Simulator.

     

 

 
 

 

,)!

19
6.2 Details of Power Ievel Simulation

6.2.1 Neutron Kinetics Equations

 

Equations (1) and (2) of Sect. 6.1, with two delayed-neutron precursor
groups, were used. An analog circuit (Fig. 10) developed many years ago
was used to solve these equations. This circuit is superior to most of
those published in the literature, mainly because of the way in which the
amplitude scaling is accomplished. '

A key point in the scheme for simulating the equations is the use of
a small feedback capacitor for the integration of the neutron level equa-
tion, rather than solving directly for dn/dt and thgn integrating with a
conventional large-feedback-capacitance integrator. In Fig. 10, ampli-
fier 1 (which solves for n) has a feedback capacitor of 10 1% uf. The
amplifier gain is 1/10 1% Rin(sec'l), where Rip is in megohms. With the
assumption that all input resistors are 0.1 megohm, Eq. 1 can be rearranged
to show the desired form of the inputs to amplifier 1, as follows:

g%-%;-(kn - knBp - n + 1% C, + l*h202). (8)

The quantity kn is generated from n and 8k as shown in Fig. 10. Typically
k will vary between 1.005 and 0.98 for control studies. Owing to the
inherent inaccuracy of the multiplier, it is advantageous to let the full-
scale output of the (8k x n) multiplier be only a few percent of kn. In
the simulator, the voltage representing zero 8k was offset, i.e.,

-1.5% < 8k = +O.5%,'because of the apparent deadband in the quarter-square
multiplier when one input oprates around zero volts. The qQuantity knBp

is generated from

0.1 kn x 100 BT X 0.1

pot 2 setting =1 megohm input
- to amplifier 1

the gain reductions _thus_allowing a reasonably large gain setting on pot 2.

The 1% kiC; terms are cbtained by first taking the Iaplace transform
of Eq. 2: o |
kn B,
88 F ot MG

which rearranged is

 

5

By E.R. Mann (deceased), Instrumentation and Controls Division.
 

20

ORNL DWG. 66-4843

 

  
 
   

 

 

 

 
 
 
 

+Nn
O-++ 100V
FULL SCALE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10kn By fz\wofif _—
\&/
D™
10081 11 5,
-10MmCiL* 5 4 1 (:) L
A2
10032 1 A2
. 1
® §| —O——
~10X,C,2*
OTHER
DELAY GROUPS o—-———nud
AS REQUIRED
NOTE:

AMPLIFIER GAIN OF 1 IMPLIES 1-MEGONM INPUT RESISTOR; GAIN OF 10=0.1M

Fig. 10. Analog Circuit Designed by E.R. Mann for Neutron Kinetics
Equations. |
 

21

fooa -
1#,C, = knBi( 'é"?&'wq)’ | (9)

where S is the lLaplacian argument.

Solving for the output of integrator L4 [e(u)]:

de
(&) _ = e '

dt
Ri e
e(h) = =0.1 kn -é-—_;-r) ] (10)
y..‘"; 1

Ay )
Maltiplication of ey by 100 B, gives -10 knBi.‘ §—¢IT) ,
5
\

which is seen from Eq.(9) to equal -10 1*'kiCi as required for generating
dn/dt in Eq. (8). Again, because the amplifier gains were reduced, the
gains on the B. pots could be increased.

T%ls circuit clearly shows that for small values of 1% (e.g., 10
—» 107° sec) the feedback capacitor for amplifier 1 will be very small
and thus will have a negligible effect on the response of n for the slow
variations normally encountered in control studies. Under these condi-
tions the negligible effect of this capacitor implies that the neutron
kinetics are independent of 1%, and for m precursor groups, the neutron
kinetics can be described by m differential equations, rather than (m + 1)
equations. This simplification is useful when the kinetics equations are
solved on a digital computer, because the maximum computation time inverval
is usually governed by the 1*/Bp time constant and must be made quite small
to give stable (and accurate) answers.

6.2.2 Core Thermal Dynamic Equations

‘The fuel flow in the core is approximated by two first-order lags in

- series, and heat transfer takes place between the first fuel lump and the
r_graphlte. The nuclear importancesof the two fuel lumps are equal. Forty-

seven percent of the nuclear heat is generated in each fuel lump. The

~ remaining | % is generated in the graphlte. .The heat balance equations
~used for the core are &s follows | |

a. First fuel lump

—_— = - 0.263 Tc + 0.017 TG + 0.246 T,; *0.0329 n;
 

22

b. BSecond fuel lump

aT
co _ T .
55 - 0.263 T, + 0.263 T, + 0.0329 n;

 

= . 0.005 Té + 0.005 E; + 0.00084 n.

Temperatures are in °F, time is in seconds, and neutron level n is in
megawatts.

As discussed previously, the lags due to holdup and heat transfer
in the loop externmal to the core were represented by six first-order lags.
Each lag is described by the equation
X .

1 o
atv T K - %)

where T is the time constant of the lag.

6.2.3 Radiator Effectiveness

 

The plot of radiator cooling effectiveness vs air flow was calculated

 

 

 

by
B Tsa1t in = Tsalt out 1 -exp [-Q - Nl)Né]
= - - - ™ ’
¢ Tsa1t in ~ air in L-N exp [-(1 - NNl
where
N = (ch )sal‘b
! [ch]air
% e wcp salt
i W = mass flow rate, 1b/sec,
gf Cp = sgpecific heat, Btu/lb—oF,
U = overall heat transfer coefficient, Btu/sec-fta-oF, :
A = heat transfer ares, fte,

 
=

23

Since air flow is perpendicular to the tubes, the heat transfer coefficient
on the air side was assumed to vary as the 0.6 power of flow rate.

6.2.4 Xenon Poisoning

Even when time scaled by a factor of 10, the xenon transients are very
very slow, and care had to be teken to avoid large errors due to integrator

drift. Menual drift-control pots were added to both integrators in the
circuit. . -

- Fuel xenon was assumed to build up at a rate equal to iodine production,
since the xenon stripping time-constant is small compared with those for
decay, burnup, and diffusion to the graphite.

a(% 8k) '
L fuel¥e o (5,07 0 - 0.000295 (%K)

a(% ok)

fuel Xe] ?

graphite Xe _ '
=T 0.00025 (% Bk)fuel e

- 0.000198 (%sk)graphi‘te Xe

- 0.0000157 (% 6k)graphite P

Since simulation pressed the limitations of the accuracy of the com-
puter, some of the coefficients had to be field set to give proper steady-
state output values. Although there would have been a number of advantages
in speeding up the computation even more, it was not done because we

didn't want to have the xenon dynamics confused with the reactor thermal
dynamics. :

Fig. 11 is the anaiog Computer circuit used for the power level
simulator. '

 
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.G. Affel
.J. Ball

.E. Beall
.S. Bettis

. Blumberg
Bohlmann
Borkowski
Cristy
Crowley
Culler
Dandl
Engel
Epler
Ferguson
Gabbard
Gallaher
Grindell
Guymon
Harley
Harrill
Haubenreich
Holt
Holz
Hudson
Kasten

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Kerlin
Kirslis
Krakoviak
Tandin
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25

ORNL-TM-1L445

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L,
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L6,
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u8.
4o,
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52.

112 -ll 3 .
11k,

115.
Jll6g.'
- 117,

PRReDRMUPREoRORYEEEOR

McDuffie
McGlothlan
Payne
Perry
Piper
Prince

. Richardson

»

=W R

-

@
®
5
<

. Ulrich

Webster

. Weinberg
MSRP Director's Office, Rm. 219, 9204-1
Central Research Library
Document Reference Section
Iaboratory Records Department
Iaboratory Records, ORNL R.C.
ORNL Patent Office
Division of Technical Information Extension
Research and Development Division, ORO
D.F. Cope, ORO

=hoERodZup
2
B

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EXTERNAL DISTRIBUTION

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