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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Published on Oct 14, 2012