OAK RIDGE NATIONAL L A B O R A ~ Y d’t’5T-; o p e r a t e d by
U N I O N CARBIDE CORPORATION
f o r the
U.S. ATOMIC ENERGY COMMISSION
ORNL- TM- 14-43 COPY NO.
April -5, 1966
SIMJIITORS FO3 TRAINING MOLTETJ-SALT REACTOR EXPERIMENT OPEMTORS
S . J . Ball
Two o n - s i t e r e a c t o r k i n e t i c s simulators were developed f o r t r a i n i n g ogerators of t h e Molten-Salt Reactor Experiment (MSm) i n nuclear s t a r t u p and power-level operating procedures. Both simulators were s e t up on general purpose, portable Electronic Associates, Inc., TR-10 analog comp u t e r s and were connected t o t h e r e a c t o r c o n t r o l and instrumentation system. The t r a i n i n g prograrLw a s successfully completed. Also, t h e r e a c t o r c o n t r o l and instrumentation system, t h e operating procedures, and t h e rod and radiator-door d r i v e s were checked o u t . Some minor modifications were made t o t h e system as a r e s u l t of the experience with t h e s e simulators.
LyucItEAR SCIENCF ASS‘IIAZTS
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* CONTENTS page Abstract 1.
................................................. Startup (Zero m e r ) Simulator ............................... Power Level Simulator ........................................ Time Required f o r Setup of Simulators ........................ Conclusions .................................................. Appendix ..................................................... 6.1 Details of Startup Simulation ........................... 6.2 Details of m e r Level Simulation ....................... 6.2.1 Neutron Kinetics Equations ....................... 6.2.2 Core Thermal Dynamic muations ................... 6.2.3 Radiator Effectiveness ........................... Introduction
8 13 13 15
15 19 19
21 22 23
Two reactor k i n e - - x simulators were developel f o r t r a i n i n g operators of t h e Molten-Salt Reactor Experiment (MSRE) i n nuclear s t a r t u p and powerl e v e l operation procedures. Both simulators were i n s t a l l e d a t the reactor s i t e , and were connected t o the reactor instrumentation and controls system. The operators were trained i n startup, or zero power, operation w i t h t h e simulator i n February 1965 and i n parer-level operation i n 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 t h e computers) was required. Although most of the simulation techniques were straightforward, a few special techniques were devised. This report describes t h e two simulators. STARTUP (ZERO POWER) SIMULATOR
The s t a r t u p simulator, s e t up on one 9 - 1 0 analog computer (Fig. l), computed the reactor neutron l e v e l from 10- w t o 1.5 Mw as a function of control-rod-induced r e a c t i v i t y perturbations. The e f f e c t of nuclear power on s y s t e m temperatures was not included.
ORNL DWG. 66-4834
RE ACTOR INSTRUMENTATION
N E U T R O N LEVEL!
FISSION CHAMBER POSITION
R R - 8 100 R R- 8200 CONSOLE METER: CHANNEL 1 CONSOLE M E T E R : CHANNEL 2 SPECIAL: ON CONSOLE
LINEAR FLUX RANGE
Fig. 1. Diagram of Startup Simulator.
6 Tbe inputs t o the sirhulator were signals indicating t h e a c t u a l positions of the control rods, and t h e outputs (indicated on t h e reactor instrumentation) were log count r a t e , period, l o g power, and l i n e a r power. The l i n e a r flux-range input signal was taken f r o m the s e l e c t o r switch on the reactor console. The fission-chamber position readout was provided by a meter mounted on the console. The f i s ion chamber is t h e detector f o r the wide-range counting channel system.' The chamber position i s servo-controlled to give a constant output s i m a l , and the charriber posit i o n i s r e l a t e d t o the log of the nuclear power. The period interlocks and t h e flux control system were a l s o used.
The operators practiced the approach-to-critical experiment (in which p l o t s of inverse count rate vs rod position are used t o extrapolate t o the c r i t i c a l rod position) and rod-bump experiments f o r calculating d i f f e r e n t i a l rod-reactivity worth from measurements of s t a b l e reactor period. The simulator was a l s o used t o check out t h e flux servo controller. Rod position simals were obtained f r o m the three potentiometers normally used by the MSRE computer. The "S" curve r e l a t i n g rod worth and position was approximated f o r t h e regulating rod by a diode f'unction gene r a t o r (Mg. 2). The rod worth vs position relationship f o r t h e other two rods w a s l i n e a r .
k . E . B a l l e t al., MSRF: Design and Operations Report, pdrt V, Reactor Safety Analysis Report, ORNL-TM-732 (August 1964), pp. 96-98. 1
ORNL IWG. 66-4835
DISTANCE WITHDRAWN (IN.)
Simulator Approximation of Regulating Rod Worth vs B s i t i o n .
7 The analog c i r c u i t used t o compute r e a c t i v i t y from t h e three rod posit i o n s included the e f f e c t s of the position of one rod on the t o t a l worth of t h e others ("able 1).
Bible 1. Full-Scale â‚Źbd Worths
Pos it ion
Shims out Shims i n
Regulating rod out Regulating rod i n
Full Scale Rod Worth (Q W K )
2.6 1.3 5.8 4.5
Reactivity vs Position "S" curve I'
The neutron l e v e l computation was made by converting the k i n e t i c s equations t o logarithmic form? since the neutron l e v e l varied over eight decades. 'lho effective delayed-neutron precursor groups were used. The usual method of including the source term i n these equations was found t o be unsatisfactory, and a special c i r c u i t was used (see Sect. 6.1). The conversion of log power t o l i n e a r power wag approximated by using a squaring device t h a t gave adequate accuracy over each l i n e a r (1.5 decade) range (Fig. 3 ) . A voltage signal from the reactor instrumentation l i n e a r 2A.E. Rogers and T.W. Connolly, Analog Computation i n Ehgineering Design, pp. 334-7, I k G r a w - H i l l , New York, 1960.
POWER SIGNAL FROM LOGARITHMIC CALCULATION
Approximate bg-to-Linear Conversion.
8 range selector c i r c u i t was subtracted from the l o g power signal, and t h i s difference was then converted t o the l i n e a r signal. The equations and analog computer c i r c u i t used f o r t h e s t a r t u p simul a t o r are given i n Sect. 6.1
POWER U:vEL SIMULATOR
The power l e v e l simulator, set up on two TR-10 analog computers (Fig. 4), simulated the k i n e t i c behavior of t h e MSRE f o r power levels
RADIATOR DOOR POSITIONS RADIATOR AIR AP REACTOR CONTROL MODE
“ L A ? - T -
NEUTRON LEVEL: LINEAR POWER LOG POWER LOG COUNT RATE PERIOD FISSION CHAMBER POSITION REACTOR INLET TEMPERATURE
REACTOR OUTLET TEMPERATURE RADIATOR SALT OUTLET TEMP.
RR-8100 RR-8200 CONSOLE METER: CHANNEL t CONSOLE METER: CHANNEL 2 SPEC’AL :ON
T R -202 -A 5
T I -202-A2
RADIATOR SALT A T
Td 1 2 01-A
RADIATOR HEAT POWER FLOW (CONST) X AT
X p R-201-A
Diagram of Parer Level Simulator.
between 0.5 and 12 Mw. The inputs were signals indicating the a c t u a l positions of t h e rods and the radiator doors and t h e a c t u a l pressure drop of t h e cooling a i r across the radiator. The outputs were neutron l e v e l s and temperatures. The usual nuclear information and key system temperat u r e outputs were indicated on the reactor instrumentation. The reactor power-level servo controller and radiator load control systems were a l s o used. m e r e a c t i v i t y inputs from control-rod position signals were computed as i n the s t a r t u p simulation. The neutron l e v e l computation (using two delayed-neutron precursor groups ) solved t h e linear, rather than logaranges rithmic, k i n e t i c s equations. Only the 0 t o 1.5 and the 0 t o 1 5 on t h e reactor l i n e a r power channels were operational. Conversion from l i n e a r t o l o g power was approximated using a square-root device (Fig. 5 ) .
Q.40 t I O V :
= SJUULATOR APPROXJMATION
COMPUTED LINEAR POWER -0
Fig. 5 .
Approximate Linear -to -Log Conversion.
10 Other r e a c t i v i t y inputs t o the power l e v e l simulator were f r o m computed xenon poisoning, noise, and f u e l and graphite temperature changes. The xenon-poisoning computation (Fig. 6 ) was included as an option. In consideration of t h e long time-constants of xenon buildup and decay, the equations were time scaled t o run a t t e n times real time. ORNL DWG. 66-4839
- b X e (FUEL)
DECAY 1 >*=2.9XlOJSEC-'
STRIPPING (DOMINANT) DECAY BURNUP
DECAY Ax = 2.1 X lo-' SEC-' BURNUP
Steady- State Xe Poisoning When P = 10 Mw: 6 K Fuel = -0.7% 6 K Graphite = - 0.79 5'0 Fig. 6. 'Ihe r e a c t i v i t y of usual simulators t h e noisy output of resistance feedback
Diagram of Xenon Poisoning Computation. noise input w a s included t o o f f s e t complaints t y p i c a l about how "smooth" t h e flux output i s compared w i t h a c t u a l reactors. An operational amplifier w i t h high (40 megohms) w a s used a s the noise source.
A simplified simulation of t h e thermal k i n e t i c s of the MSRE w a s used which was based on previous studies of reactor dynamics.3 The core was represented by two f u e l "lumps," or nodes, and the graphite by one. Six more lumps were used t o represent t h e r e s t of t h e system. The thermal c h a r a c t e r i s t i c s a r e summarized i n Table 2.
The heat removal rate f r o m the r a d i a t o r i s controlled by varying t h e a i r flow through t h e radiator; hence, the radiator s a l t o u t l e t temperature i s affected by s a l t i n l e t temperature, a i r i n l e t temperature, and a i r f l o w r a t e changes. A simple but f a i r l y accurate way of simulating the heat removal i s t o make use of t h e relationship of radiator cooling "effectiveness" a s a function of a i r flow r a t e . Cooling effectiveness i s defined as t h e r a t i o of the a c t u a l temperature decrease of t h e hot f l u i d t o t h e temperat u r e decrease i n an i d e a l ( i . e . , i n f i n i t e heat-transfer surface) heat exchanger:
3S.J. B a l l and T.W. Kerlin, S t a b i l i t y Analysis of the Molten-Salt Reactor Experiment, ORNL-TM-1070 (Dec. 1965).
MSm Thermal Characteristics Used i n the Power k v e l Simulator
Core t r a n s i t time, sec
lumps ) Graphite time-constant, sec
a Heat exchanger t o core t r a n s i t time, sec
Core t o heat exchanger t r a n s i t time, sec
Radiator t r a n s i t time, sec
a Radiator t o heat exchanger t r a n s i t time, sec
a Heat exchanger t o radiator t r a n s i t time, sec
Heat exchanger "effectiveness" factors a t steady stateb: rn I
T = 0.7029
Holdup time i n heat exchanger i s included i n t h e other t r a n s i t times.
P, primary; S, secondary; i, i n l e t ; and
Tsalt i n
The s a l t o u t l e t temperature i s computed from
Tsalt i n
Ec(Tsslt i n
- Tair i n 1 '
The calculated cooling effectiveness as a f'unction of a i r flow r a t e and the l i n e a r approximation used i n the simulator are shown i n Fig. 7.
ORNL DWG. 66-4840
COOL ING EFFECT IVENESS = TSALTIN- SALT OUT
TSALT IN - TAIRIN
0 0 U
COOLING AIR FLOW RATE Fig. 7.
MSRE Radiation Cooling Effectiveness vs A i r Flow Rate.
The a i r flow rate W
through t h e r a d i a t o r w a s computed from
K = constant adjusted t o give 10 Elw cooling a t f u l l a i r flow, APa
= measured a i r pressure-drop s i g n a l across t h e radiator, = measured r a d i a t o r door positions (inches raised).
Conversion of t h e analog computer voltages representing temperatures t o signals compatible w i t h t h e Fbxboro ECI instruments was done w i t h straightforward resistance divider networks. The equations and analog computer c i r c u i t used f o r t h e power l e v e l simulator are given i n Sect. 6.2.
TIME R E Q U m D FOR SETUP OF SIMULATORS
IIhe engineering and c r a f t time required t o develop, i n s t a l l , and check out t h e simulators and t o t r a i n t h e operators i n t h e i r use w a s as follows ( a l l values i n man-weeks):
Fower Level Simulator
Set up and check out
Lecturing on use
5. CONCLUSIONS The two on-site t r a i n i n g simulators were developed and operated satisf a c t o r i l y as p a r t of t h e MSRE operator t r a i n i n g program. Besides t h e obvious function of t r a i n i n g the operators, t h e 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 w e r e made t o the system as a r e s u l t of t h i s experience w i t h t h e simulators.
All manipulations required t o operate t h e simulated reactor were done from the reactor console, and t h e readout devices were p a r t of the standard reactor instrumentation.
6 . APPENDIX
6.1 Details of Startup Simulation The neutron k i n e t i c s equations are , b
i* [ k ( l - 4 ) -
= neutron population,
= t i m e , sec,
1* = prompt neutron lifetime, sec, k
& pi 'i
= reactor multiplication, = t o t a l delayed neutron fraction,
= e f f e c t i v e delayed neutron fraction for i t h precursor group with fuel s a l t circulating,
= decay constant f o r i t h precursor group,
it' precursor population,
= rate of neutron production by source.
R e w r i t e Eqs. (1)and ( 2 ) , assuming kpT M
-- "Pi - hiCi dt 1*
Divide EQs. ( 3 ) and (4) by n:
--1* - nBi I* -
i=1 1 dCi-
Define new variables: dn
M = - -
w = -S n
kSubstitute i n t o a s . ( 3 ' ) and (4'):
6 (5) dVi
Pi - - - p dt
%e usual method of computing the source term i s as follows: noting t h a t Wn = S and
or The analog computer can usually solve a f i r s t - o r d e r d i f f e r e n t i a l equation such as EQ. (7) f o r W; however i n t h i s case, W becomes so small when n >> S t h a t the voltage representing W i s within t h e noise l e v e l of t h e amplifier, s o f u r t h e r computation w i t h it i s meaningless. To avoid t h i s problem, t h e relationship between W and log n was approximated as shown i n Fig. 8.
:: k 5
V k al
I; I? I,
' H E
19 6.2 6.2.1
Details of Power Level Simulation
Neutron Kinetics Equations
Equations (1)and ( 2 ) of Sect. 6.1,with two delayed-neutron precursor groups, were used. An analog c i r c u i t (Fig. 1 0 ) developed many years ago5 w a s used t o solve these equations. This c i r c u i t i s superior 30 most of those published i n t h e l i t e r a t u r e , mainly because of t h e way i n which the amplitude scaling i s accomplished. A key point i n the scheme f o r simulating the equations i s the use of a small feedback capacitor f o r t h e integration of the neutron l e v e l equation, r a t h e r than solving d i r e c t l y f o r dn/dt and t h n integrating with a conventional large-feedback-capacitance integrator In Fig. 10, amplif i e r 1 (which solves f o r n ) has a feedback capacitor of 10 I* wf. The amplifier gain i s 1/10 1* Rin(sec-l), where Rin i s i n megohms. With the assumption t h a t a l l input r e s i s t o r s a r e 0.1 megohm, Eq. 1 can be rearranged t o show t h e desired form of the inputs t o amplifier 1, as follows:
- knp, - n
The quantity kn i s generated from n and 6k as shown i n Fig. 10. Typically k w i l l vary between 1.005 and 0.98 f o r control studies. Owing t o the inherent inaccuracy of the multiplier, it i s advantageous t o l e t the f u l l scale output of t h e (6k x n ) multiplier be only a few percent of kn. In the simulator, t h e voltage representing zero 6k w a s o f f s e t , i . e . , -1.5% < 6k I; +0.5$, because of the apparent deadband i n the quarter-square multiplier when one input oprates around zero v o l t s . The quantity kn& i s generated from 0.1 kn
pot 2 s e t t i n g
1 megohm input
t o amplifier 1 the gain reductions
thus allowing a reasonably large gain s e t t i n g on pot 2.
The 1* AiCiterms a r e obtained by first taking the Iaplace transform of EQ. 2;
which rearranged i s
5By E.R. Wnn (deceased), Instrumentation and Controls Division.
.ORNL DWG. 66-4843
I I L
-10x2 OTHER D E L A Y GROUPS 4 AS REQUIRED
NOTE! RUPL/F/€R GAIN OF ? IMPLIES ?-MEGOHM INPUT RESISTOR; W I N OF ?O= O.?M
Fig. 10. Analog Circuit Designed by E.R. Mann for Neutron Kinetics Equations.
where S i s t h e Laplacian argument. Solving f o r the output of integrator 4 [e(4)]: de (4 )
= 9 4 )
Multiplication of e
0.1 hi kn
by 100 pi gives -10
which i s seen from Eq. ( 9 ) t o equal -10 l*A.C. as required f o r generating dn/dt i n Eq. (8). Again, because the ampltfier gains were reduced, the gains on t h e pi pots could be increased.
Tis c i r c u i t
c l e a r l y shows t h a t f o r small values of l* (e.g., 10 4 1 0 ’ s e c ) t h e feedback capacitor f o r amplifier 1 w i l l be very small and thus w i l l have a negligible e f f e c t on t h e response of n f o r t h e slow variations normally encountered i n control studies. Under these condit i o n s t h e negligible e f f e c t of t h i s capacitor implies that t h e neutron k i n e t i c s are independent of 1*, and f o r m precursor groups, the neutron k i n e t i c s can be described by m d i f f e r e n t i a l equations, r a t h e r than (m + 1) equations. This simplification i s useful when the k i n e t i c s equations are solved on a d i g i t a l computer, because the maximum computation time inverval is usually governed by the l*/& time constant and must be made q u i t e small t o give stable (and accurate) answers. 6.2.2
Core Thermal Dynamic Equations
The f u e l f l o w i n the core is approximated by two f i r s t - o r d e r lags i n series, and heat t r a n s f e r takes place between the f i r s t f u e l lump and the graphite. The nuclear importancesof t h e two fuel lumps are equal. Fortyseven percent of t h e nuclear heat is generated i n each f u e l lump. ’Ihe remaining 6$ i s generated i n the graphite. The heat balance equations used f o r t h e core are as follows:
F i r s t f u e l lump dFc
0.246 Tci + 0.0329 n;
Second f u e l lump
- co- - - 0.263 at
Graphite dTG - - -
- 0.005 FG+ 0.005 Fc
Temperatures are i n OF, time i s i n seconds, and neutron l e v e l n i s i n megawatts. As discussed previously, the lags due t o holdup and heat t r a n s f e r i n the loop external t o t h e core were represented by six f i r s t - o r d e r lags. Each l a g i s described by t h e equation
a x -- 1- (xin at T
- Z) ,
where T i s the time constant of the lag.
Radiator Effectiveness The p l o t of radiator cooling effectiveness vs a i r flow w a s calculated
Tsalt i n Tsalt i n
- Tsalt out --
Tair i n
N1 exP‘ [-(1
= mass flow rate, lb/sec, = specific heat, Btu/lb-OF,
U = overall heat t r a n s f e r coefficient, Btu/sec-ft
A = heat t r a n s f e r area, ft2.
Since a i r flow i s perpendicular t o t h e tubes, the heat t r a n s f e r coefficient on t h e a i r side was assumed t o vary as t h e 0.6 power of flow r a t e . 6.2.4
Even when time scaled by a f a c t o r of 10, the xenon t r a n s i e n t s a r e very very slow, and care had t o be taken t o avoid large e r r o r s due t o integrator d r i f t . Manual d r i f t - c o n t r o l pots were added t o both integrators i n the circuit. Fuel xenon was assumed t o build up a t a r a t e equal t o iodine production, since the xenon stripping time-constant i s small compared w i t h those for decay, burnup, and diffusion t o the graphite.
Since simulation pressed t h e limitations of t h e accuracy of the computer, some of the coefficients had t o be f i e l d s e t t o give proper steadys t a t e output values. Although there would have been a number of advantages i n speeding up the computation even more, it was not done because we d i d n ' t want t o have t h e xenon dynamics confused with t h e reactor thermal dynamics. Fig. 11 i s the analog computer c i r c u i t used f o r the power l e v e l simulator.
Fig. 11. Analog Computer Circuit for t h e F d e r Level Simulator.
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H.F. McEuffie C.K. McGlothlan H.R. Byne A.M. Perry H.B. Piper B.E. Wince M. Richardson H.C. Roller H.C. Savage D. Scott H.E. Seagren M . J . Skinner A.N. Smith P.G. Smith R.C. Steffy R.E. Thoma G.M. Tolson W.C. Ulrich B.H. Webster A.M. Weinberg MSRP Director's Office, Rm. 219, 9204-1 Central Research Library Document Reference Section Laboratory Records Department Laboratory Records, ORNL R.C. ORNL Patent Office Division of Technical Information Extension Research and Development Division, OR0 D.F. Cope, OR0 R.G. Garrison, AEC, Washington H.M. Roth, OR0 W.L. Smalley, OR0 M . J . Whitman, AEC, Washington
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