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. O ; ‘ \:‘ ‘ 1 ‘- ‘B =) 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] ot ol" <) 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 o2 3, Zw (1) \J <2246 +i0 MoTreS AR o Raar Time eV:EC{ /N oMl#fi SWE S/ =005 MV, o G/ RE G ReGULATING KOD zoD 8K -0V " mosirron oV ip (5% . ORNL IMG. 66-4842 i 1 MEGS o " +ve N ' + Veange- 83t . | 12 ! _Mb-z_-D'-q.T 12 O-+ AV, K-’ " 1(r w 1 # A - __....:\N\' M,\N\___._ ‘ 924 s | " ,..-',.3 - 23\"‘; Loa T cm i 5 + ox o =l N "2 ) w’P -3 L AAAAA—DO +10V ", 119 1 3 3 ™ : ] ' : <) / Ler | o-2v .630 - ‘ FuL. w 10 G ANAAA 7 '“‘ SCALW sounc&'\/ 2ok - . | O ‘ 1 i - M - +Y . X L =M [ ’ r" | -y S +™ L X +M ' - | F—— 8 4342 ! “toa, 1 SO0K TP4 +M -™ 13 ‘ 15 NN e 70 L0 77 ‘ I VOLT = | DECADG AmpL,. 59 0 ‘ toa, Cw 10V sSI=TP2 ; (Lm0 =) 210" 7.m 10 fwarTe | i ' ‘ t 1Y i 1 Mz ! 17 " -2V | -Y 4 & +Low, T -x] . +X ; 'OJPT W - s ” . + ; 7—'—-—-souzce‘ COMPLIOSATION o : £ 7 | -0 - N TO CHAMBER 2 POSITION VM 0 A4 47 - Hea;:-f . L » Jau consoLe- & - > = LoADIVG, U“TJ T 7 A fl"’" £ D736 Fror 27 LD.) TR FE (Oéw &K [our Y - 4 77 EK RoLSs T UVEENE N \ 'o ) -LO0G CEM . - o o —— e N . OV &K 20.279 2% | zt->i105 CRITICAL I Py i no 5 ‘ orR G.eV ow I8 ' S okeEn. KD g i : +- . 18 i \/ P SHIM - e ebeem i e s e s o e o ] " - ; VA - * SCALING - 3.33K (sxd> ™ 1% /VvoLT * . ;x - | i Kl -1~ % 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. ' MAMUAL AT Lim Y9 4 wok® __“Ol -{1_-:'1‘1 . . mims seT -'h’ s P66 t+ameeny (] =ie 37 o nIAt +Ta [ "‘/nfi ~oK 1% j’_:_'"‘_in (*) ¥Trattg o ! b«" Xa {6) wjove 5% (e -‘Fg -n + ‘,‘."_',51, )R“ ik -y, ) ‘J'T’fi' / s + 0 12, 24 1OK 043 +ASK & 22 im , 10K FS 1 2™ K0 g ISz cgm" 2‘1’. 2 - 10V : ORML DHG. 66-4844 oo Lo o2t wrew Xa oot o T FLhmn . ™ Gk mmm Il ' Xe () r_'”_»'v._ Gams n 1t o ALr. = T0% S @ 10nw{ts) % N T Grapum ; LI O10)] ,,,T- =Gy (3310w .07 %, 5@ 1D mas t8) | (- ' . ' 015 ,,:‘: om ‘ L +Y 40 "™ +T, db ‘ P Bio : ' . "2t ¢ DRIET ConTR. " K I i 16% SO L e % 268 CorE im [z 6.67 e Te | NeTE: 2anci EAT TR 10 Campursrty Are Usep, TIwnrscanron Fexpbrcr CAPACITORS ARE 10 uldd . Tim& Seace = Rend Temp SemuE “ Iy o9 ak NOISE : ‘Tr,fi' 29 HEwT & XcHAM G R, To, qavr SxXj0p, . . Tee 046 =Cq :‘|Io$ 1 Tso - ——z, 582 x4} Tsi * ;wn‘:- ; } ) 22 Sm . Rav. AT AT -(T;-‘l.) s 5sgcl T4 p1 {3rRAT woog rELAY) ‘ " o hSEP WHEN REMSTOR N O=I5 Mw Rausl ‘ - . i -y w O=1.5 on - ena, 10, O°1% mw v wry [l Lol i PeSiTIoN ‘ = vm o + Taaur i ‘ -; Nr P amions) pRLL 333 Fom t2n's - o SOK vpz ™ toe Taa 10 15 8 e Aoy Ampe. 53 ! Raw ma - 10 . ._-