UCN-2383 (3 11-80) OAK RIDGE NATIONAL LABORATORY Operated by UNION CARBIDE NUCLEAR COMPANY Division of Union Carbide Corporation Post c? Box X CENTRAL FILES NUMBER Oak Ridge, Tennessee _ DATE: December 26, 1961 COPY NO. éii/ SUBJECT: MSRE -~ Analog Computer Simulation of the System With a Servo Controller TO: G’O Ao CI'iS-ty FROM: 0. W. Burke ABSTRACT One purpose of this study was to determine whether the fuel salt -~ temperature inside the reactor could be controlled with a closed- loop servo controller. An "on-off" type controller was demonstrated using four different control signals. The stability of the system / when using the controller was of primary interest. These studies indicated that the system was stable for large and relatively fast power demand changes when using the controller with any one of the four control signals. NOTICE This document contains information of a preliminary nature and was prepared primarily for internal use at the Oak Ridge - National Laboratory. It is subject to revision or correction . and therefore does not represent a final report. The information N is not to be abstracted, reprinted or otherwise given public dissemination without the approval of the ORNL patent branch, Legal and Information Control Department. CONTENTS I. Introductionecseccococecosceoceecoososocococasso IT. Description of the System Simulated secoceecoecse IIT. Description of Controllerecececcoccccccocccocsoss V. Description of the Control Signals Used cecoo A. Control Signal No. 1, €, ccccccecooocssos B. Control Signal No. 2, € C. Control Signal No. 3,62 coeecccecccsoss €, ® 0 06 60 © 060 0 0 06 © 06 0 O 0 o D. Control Signal No. L Vo Procedure and Res-tfl.ts’0.000000000000000000000 © © 0 0 ¢ 6 0 6 0 0 0 0 0 00 l. Basic Flow Diagram of MSRE System ococeoceee 2. Identification of Temperature Symbols.... 3. MSRE Design Point Data_as of 12-13-60.... L. Generator Circuit for &/ ...ccccccoccsccs 5. Generator Circuilt for'f; ccoeescccocococe 6. Generator Circuit fOr€, eeceeccecoccccs 7. Generator Circuit forEL_ cocoeccoscoccee 8. Control Signal €, , Nuclear Power and Mean PFuel Temperature in Reactor vs. TiME cococooeocecccocscesossscooscoococcoonocosocos 9. Control Signal é&,, Nuclear Power and Mean Fuel Temperature in Reactor vs. TIiME ceeceococcsocsessosscoscoscooocsocoooccss 10. Control Signal 6; , Nuclear Power and Mean Fuel Temperature in Reactor vs. Time © 0 0 © O © O @ ©6 & & 06 ¢ 0 6 © ¢ 0 6 06 & 06 0 00 0 O © 0 0 00 © 0 0O 0 11. Control Signal 6;, Nuclear Power andT VSo Timeooooooooooooooooooooooo OI" BibliOgraphy ©6 000006006 0©00O0O0O0O0CS6 066 060O0OCO0COOCO0O0OS O00O0COCO0 OO0 Distributign e 06 6 6 6 0 0O 8 0 0O © 6 06 ©0 @ © & 0 © 6 0 0 @ 0 06 06 060 06 0 6 ©0 0 0 ©0 © ¢ 0 o O\ I —~J 9-10 11-12 13 14 15 16 17 18 19 20 22-23 IT. III © Introduction: It is desirable to provide a controlier for con- trolling the fuel temperature inside the reactor. There are many control conceptg that would do the job. The decision was made to try a simple "on-off" controller. E. R. Mann of the Instrumentation and Controls Division proposed four control signals which have definite possibilities and suggested that they be demonstrated on the analog computer. This report covers the analog computer demonstrations. Description of the System Simulated: A schematic flow sheet of the MSRE system is shown in Figure 1., The temperature symbols are identi- fied in Figure 2. The design information used in these studies is listed in Figure 3. The analog computer diagram is filed in the Engineering and Mechanical Division print files on Drawings 40331 and L0332, The simulation of the thermal system and nuclear system as used in these studies has been discussed in previous preliminary reports.~ There were two changes, however, that were significant. The temperature coefficient of reactivity of the graphite was changed from: 2x10% 6k to -6x10° Sk K-OF K-°F and the total secondary salt looP transit time was changed from 13 seconds to 24.2 seconds. Description of Controller: The controller simulated was a simple "on-off" servo controller. The rod drive motor was a constant speed motor, driving the rods at a constant velocity sufficient to change the reactivity at a rate of: 0002 O K K-sec. For the sake of simplicity, the rod worth was considered to be linear throughout the range used in these studies. The "time constant” of the controller was assumed to be 50 milliseconds. This "time constant" is the time required for the rod speed to attain 63% of full speed subsequent to receiving a demand signal to move the rods. The "dead band" of the con- troller was I 20F, Description of the Control Signals Jsed: The four different control signals used with the above described controller were as follows: A. Control Signal No. 1,€&, The egquation expressing éi is as follows: IR e 4 ) where, G = control signal gain factor or amplification factor. m, n, and a are coastants that may be varied at will. @ = neutron flux To = Fuel salt temperature at the reactor outlet. T T;] = TFuel salt temperature at the inlet to the reactor. r t g(t) = )\.J[acb - (To:l - ‘I’J - g (t)] dt r r 0 - L. This can be considered as a'"rese% mechanism." t:_yfifxffflwfivfi Tsp - The desired mean fuel temperature in the reactor. The controlled variable in E} is the mean fuel temperature in the reactor, Té] + TQJ » This variable appears only in the r T 2 second term of the contrcl signal. If this term alone is used as the control signal, the system 1s unstable. The first terflliILGV can be considered as a high frequency band pass stabilizing mechanism. It merely compares the rate of pro- duction of nuclear power to the rate of addition of heat to the fuel salt as it passes through the reactor. Note that for steady state operation: ddgg(t)}O =A.2[a 9 _(TOL- Tj]r>- g(t)] o g (t)=2a ¢ - <§é]r - Ti}é) This insures that the first term:flnf) will be zero for steady state operation whether the term: b (- o) is zero or not. For this reason, the constant, "a'", does not have to be reset for various power levels. thf) exceeds the dead band _)_J__J positively, rods will be inserted and iféi exceeds the dead band negatively, rods will be withdrawn. The analog computer diagram used to obtain 6} is shown in Figure L. The temperature sensing elements are thermocouples attached tc the walls of the pipes containing the fluids whose temperatures are to be measured. There is a time lag between the time at which a change in temperature of the fluild occurs and the time at which this change is reflected in the thermocouple output signal. This time lag varies with different thermocouple designs, pipe wall thicknesses, etc. The time constant for this lag in the salt temperature thermocouples was designated as'f£ and was considered to be 5 seconds. - =% # ¥ o G2 Ko i The time constant of the g(t) circuit wag%éhosen agt 10 times that of the thermocouple. This lorgtime constant was necessary in order to get "reset action" and still not interfere with the stabilizing effect during transients. The other three control signals are quite similar to €, and only their differences fromfi will be pointed out in the following descriptions of these signals. Control Signal Nooza,el, o The equation expressing€ is as follows: %67;: m a ¢ - fa(Tc;la‘ T;Ja>~ g(t) p+ n (TOJT+ TJJ)--TSP where, f, = air flow rate across the radiator TO = outlet air temperature from radiator Ja Ti = 1inlet air temperature to radiator J a The time constant used for the alr temperature sensing elements was 2.5 seconds and that used in the g(t) circuit was 25 seconds (T3 = 2.5and A}, = 0.04). Note that the controlled variable is the same as forf& . The stabilizing portion of the control signal is now formed by comparing the rate of production of power in the reactor to the rate of re- moval of power from the secondary salt by the alr flowing across the radiator. Note that a multiplier is required in this circuit. -5 - The analog computer diagram used to f@rmulateé; is shown in Figure 5. C. Control Signal No. 3363 o The equation expressing € %63 nia ¢ - (] JS>- 'g(fl + n (Tc]r+ Tflr>’2Tsp secondary salt temperature at the radiator inlet = I H I secondary salt temperature at the radiator outlet —_ S The controlled variable is the same as that 1n€ andC . The stabilizing circuit is formed by comparing the rate of power production in the reactor to the rate of power loss of the secondary salt as it flows through the radiator. No multiplier is required since the flow rate in the secondary salt system is constant. The "time constant" potentiometer settings are the same as those used in €, . The analog computer diagram used to obtain €, is shown in Flgure 6. D. Control Signal No. 4,€, . The equation describing € L€, { b (] - t)} (] ) This control signal is the same as €3 except that a different con- trolled variable is used. The outlet fuel temperature from the reactor is the controlled variable. The analog computer diagram used to deriveé; is shown in Figure 7. Procedure and Results: The system without a controller was shown to be unstable subsequent to any appreciable perturbation. The system was also shown to be unstable when using the controller with only the second term in the above control signals. The stability of the system with the gbove controllers was checked sub- sequent to large changes in the power demand or load. The changes in the load for the four runs, each using one of the four above described control signals to the controller, were not precisely equal in magnitude and rate of change. The change in load was accomplished by manually turning a potentiometer. Also, no attempt was made to get optimum settings for M and N in each case. Therefore, the results cannot be compared quantita- tively. In later runs linear ramp load changes will be used, and optimum -6 - values of M and N used, so that wortrollers can be compared. Record- ings of the controlled variliable and the neutron flux were made subssgquent to a load change, while uging each of the four control signals to the controller. The conditiong for these runs were ag follows: A U81ng;€' as the control signal, M, as shown on the computer diagram, wag set at 877 (qutg arbitrarily) and N was set at 0.5, The load, or the heat removal rate by the air across the radiator, was se+ at approximately 2 megawatt and the system permitted to stabilize. The load was increased from %'mw to 10 mw in 15 seconds, approximately at a constant rate. The curves obtained are shown in Figure 8. On all the curves only a relatively short time is shown. It can be seen that the curves are converging, which indicates stability. B. U31ng;€' as the control signal, M, as shown on the computer dlagram,was set at 0.877 and N set at 0.5. The load was changed from approximately 1.6 mw to 10 mw.in 17 seconds. The resguiting curves are shown in Figure 9. C. [knr@;f' as the coatrosl signal, M, as shown on tha computer dlagramfl was set at 0.25 and N was set at 0.5. The load was changed from approximately 1.6 mw to 10 mw in 13 seconds. The resulting curves are shown in Figure 10. De Using € 4 @8 the control signal, M, as shown on the computer diagram, was set at 0.50 and N was set at 1.00. The ioad was changed from approximately 1.6 mw to 10 mw in 11 seconds. The resulting curves are shown in Figure 11. The conclusion reached wag that the system would be stable using the con- troller with any of the four control signals. It should be pointed out that th= congtants M and N on the actual in- stallation could be changed ov=r a congiderable range. No attempt was made to get the optimum settings on the computer, due to time limitations. ORHL-LR-D—wg. 64899 UNCLASSIFIED PUMP PUMP s e | g | 200 GAM. Tes s, | " - = .T’:‘P‘/j Tes ‘ ¥ & v ‘ A T | ‘T;]R .T;z ‘ & -Tg TS3 - Tee _ t | AtrR — 'T,'Ja .,:j £ T ™ ] a —* ———— — , | L REACTOR | 'T;j; s s - | , RADIATOR F1G. 1 BASIC Flow DIAGRAM OF MSRE SYSTEIM Figure 2 TDENTIFICATION OF TEMPERATURE SYMBOULS Te - Circulating fuz2l mean temperature in the reactor corsa. Tro - Circulating fusl temperaturs at the outlet of the reactor corsz. Tf3 - Circulating fus=l tzmperature at the inlet to the primary heat exchanger. Lel - Circulating fuel mean tempsrature in the primary heat exchanger. Tf5 - Circulating fuel Temp ture at the outiet of ths primary h=at exchanger. Trg - Circulating fusl temperature at the inlet to the reactor cors, Tg - Mean temperaturs of the graphits in the rsactor z0rz. Emp - Mean temperature of the metal in the primary heat exchang=r wa.l. Ty - Mean *temperature of the secondary salt in the primary heat excrangs=r. Teo - Secondary salt temperaturs at the outlet of the primary heat exchangexz, Ts3 - Secondary salt temperaturs at ths inlet to the radiator. Taly - Mean temperaturs of the s=zomdary salt in ths radiator. Lss5 - Secondary salt tempsraturs at the radiator outlet. Ts6 - Secondary salt temperaturs ab tos inlet to the primary beat sxzarger Lo - Mean *temp=raturs of the metal in the radlator. Thot - Mean circulating fuel temperaturs in the "hot leg' of the primary system. Tcold Mean circulating fuel temperaturs in toe "oold leg" of the rrimary systeto Tha, - Mear air temperatire in the radlator. Figure 2 (contd.) Fuel temperature at reactor core inlet. Fuel temperature at reactor core outlet, Secondary salt temperature at the radiator inlet. Secondary salt temperature at the radiator outlet. Cooling air temperature at radiator inlet. Cooling ailr temperature at radiator outlet. = 10 - Figure 3 ’ ) - \ MSRE DESIGN POINT DATA AS OF 12—13160 Reactor inlet temperature: 1175 O Reactor outlet temperature: 1225 °F Mean graphite temperature: (with no fuel absorption) 1230 °F Residence time in reactor: | 7.63 sec. Film drop from graphite to fuel: Linear with power Heat capacity of graphite: 0.425 %EE_ # OF Prompt ]?’and neutron heating in graphite: 6% of 10 MW Residence time in piping from reactor outlet to H. E. inlet 3.09 sec. Residence time in H. E. 2,24 sec. Heat capacity of metal in H. E. | 200 BTU/°F Avg. film drop between primary coolant and metal at D. P. 55.2 OF Avg. drop in metal at D. P. | 56.7 OF Avg. film drop between metal and secondary coolant at D. P. 26,1 OF Film drop between primary coolant and metal as function of flow: See graph, displace curve if necessary so that at 6.2 fps velocity /\T = 55.2 °F. L . Mean secondary coolant temperature at D. P. 1062 F Residence time in piping between H. E. outlet and reactor 9.04 sec. inlet (including coolant annulus) | Total circulation time 22,0 sec. Temperature coefficient of reactivity of graphite: -6 x 10-5CSK/K=OF Temperature coefficient of reactivity of fuel: -3.3 x 10720 k/k-CF Melting point of primary coolant: 8up °F Melting point of secondary coolant: 860 °F - 1] - Figure 3 (contd.) Check points: N - Thermal resistances: ft. hr. OF BTU . . : _l o in primary coolant film: 3.28 x 10 | -l in metal: 3.32 x 10 : . =l in secondary coolant film: 1.56 x 10 Simulator data for secondary 1loop Air temperature rise in radiator 200 °F Air suction temperature 100 °F Air flow 166,000 cfm (7.11 x 10° #/nr) Heat capacity of radiator L2 BTU/OF . BTU Heat capacity of secondary salt 0.57 - # OF A~ Density of secondary salt 120 #/ft3 Residence times of secondary salt: in primary heat exchanger 1.75 ség;'{ in piping to radiator 5.20 sec. in radiator 7.14 sec. in piping from radiator 10.11 sec. Total 2L .20 sec. Residence time of air in radiator 0.0l sec. Temperature differences in radiator: in salt film 13.4 CF . in tube wall 78 .4 OF in air film (0.7 O AN - 12 - ORNL-LR~Dwg. 64900 +7;JF\’ | - H¢t) /‘ 5 3 NN ‘ CP w -&- (e =721 —#4)] ‘ + €, . = o.l(f,g—{) =&, = M{,a.cp =(Tde- T’T-JR)*?('&)} * N{(.T;JR.'-E]R) -c TSP} FIG 4. GENERATOR CIRCUIT FOR €, - 13 - | ORNL<=LR=DWg .. 64901 Unclassified - %(t)/l N —fa b= £ (T] )~ o) | . SENSe L £, . TIME . ‘ 'T‘,_j , LAG | ( ) S FIG.5 GENERATOR CIRCUIT FORE,. - 14 - . +T;JR ( > Unclessified ORNL-LR-Dwg. 64902 1) I T A LA "{Qtp ~(n]5-T°]5)~?(t)} l /gls G + A, o 4 © ® | N SENsoR +—r;jr? | TimMmfE LAG Y 7y | | | | “{('73.7«"* TL]R)' Z’TS"} —lo0oV %fi X %7 o A, = 0-}’ ('Cll"s3 Le =mfad-(T- -r;]s)__?cfl} + N{(Te] T ) =2 Ter G €3 FIG.6 GENERATOR CIRCUIT FOR €3. - 15 - ORNL-LR-Dwg . 64903 Unclassified - | L Ts Trine LA fad ~(1,~ 7)) - 1#)f Ae -D ) + ¢ a —O— | SENSOR /"T' “TTIME LAS /) _, 0 o + -T”JIP Z . \\, -+ 64 \. | \\ L G ~/ooVv Ao E 0. (6"}) Loe, = m{acp -'(72]3.“73]5)‘?(‘&)} + N (T = Tsr) FIG.7 GENERATOR CIRCUIT FOR €,. - 16 = (°F) 121 in Reactor 1200 1190 Mean Fuel Temp. Nuclear Power (mw) 0 Elapsed Time from Start of Transient (sec.) - 17 - ORNL~LR-Dwg. 6490k "w v %, %fi:’, 3 ¥ M b 1220 (°F) 1210 in Reactor 1200 1190 Mean Fuel Temp. 10 Nuclear Power (mw) O Elapsed Time from start of Transient (sec.) - 18 - ORNL~LR-Dwg. 64905 Unclassified (°F) in Reactor Mean Fuel Temp. Yuclear Power (mw) 1210 1200 1190 Elapsed Time from Start of Transient (sec.) - 19 - ORNL~-LR-Dwg. 64906 ORNL~LR-Dwg. 614907 e /,/ 50 D 1 1O o can 3 —— e e fea — e egeeies i ; . e g e v} o g ek i = e 1 Jamcd TS T “ O o .D.w,w 20 - Flapsed Time from Start of Transient (sec.) ) VO BIBLIOGRAPHY O. W. Burke, MSRE - Preliminary Analog Computer Study— Flow Accident in Primary System, ORNL CF 60-6-110 (June 27, 1960) O. W. Burke, MSRE - Analog Computer Simulation of a Loss of IFlow Accident in the Secondary System and a oimulation of a Controller Used to Hold the Reactor Power Constant at Low Power Levels, ORNL CF 60-11-20 (Nov. L, 1960) O. W Burke, MSRE - An Analog Computer Simulation of the System for Various Conditions - Progress Report No. 1, ORNL CF 61-3-42 (March 8, 1961) - 21 - f‘\ o e = O\ = O\ W D 12. e =W - \J1 16. 17. 18. 10. 20. 21. 20, o3, ol , 25, 26. 27. o8. 29, 30. 31. 32. 33. 3, 35. 36. 37. 38. 39. LO. b1, Lo, L3, Ly, L5, L6. MSRP Director's Office G L. ® ® e * . ® ° QurrUsSmEeEgdgHgQ=sgHOHQOQUEPRPHOEHOQR W =wW= HgegdsQ2nd ey OndidEROdE P OEH D >EH= D> M. G . B. . Bender . Bettis . Bettis . Billington . Blankenship . Boch GEGQE = nNnH Adamson Alexander Beall Bohlmann . BOlT Borkowski . Brandon . Bruce . Burke . Cole Conlin Cook Cristy Crowley Culler DeVan Doss Douglas . Dunwoody . Epler . Ergen . Ferguson . Fraas . Frye . Gabbard . Gallaher . Greenstreet Grimes Grindell . Guymon Harley Harrill Haubenreich Hise . Hoffman . HOlZ Howell . Jarvis Jordan DISTRIBUTION 9204 -1 2005 9204 -1 020k -1 9201-3 1000 9204 -1 3025 1500 9204 -1 9204 -1 9204 -1 3500 9201-3 1500 1000 4500 9201 -3 2000 1000 9204 -1 1500 9201-3 9201-3 2005 1000 3500 4500 4500 o704 -1 2000 9201-3 0204-1 9204 -1 11500 9201-3 ‘(500 9204 -1 3500 7500 9204 -1 9204 -1 9204-1 1000 1000 11500 b7, 18, 49, 50. 51, 52, 53. 5k 55. 56. o7 _ 58. 59. 60 61. 62. 63. 6L, 65. 66. 67 . 68. 69. 70, T1. T2, 3. Th. T5. T6. TT . T8. T9. 80. 81. 82. 83. 8L . 85. 86. 87, 88. 89. 0. g1. 92, Slfliiifii@1&12’E:IIZIC1C4U)G3$U*U . Kasten . Kedl . Keilholtz Kirslis Krewson Lane Leonard . Lindauer . Lundin . Lyon . MacPherson % QEHO4Y N9 . C. Maienschein R. Mann B. McDonald . F. McDuffie K. McGlothlan J. Miller C. Miller L. Moore C. Moyers W. Nestor E. Northup R. Osborn . F. Parsly . Patriarca R. Payne . M. Perry B. Pike . I.. Redford Richardson C. Robertson K. Roche W. Savage Scott . J. Skinner M. Slaughter N. Smith G. Smith Spiewak . Squires . A. Swartout Taboada R. Tallackson BE. Thoma B. Trauger C. Ulrich 920k -1 9204 -1 3550 11500 9204-1 4500 9204 -1 9204 -1 9201-3 9204 -1 o70L-1 3010 3500 o204 -1 4500 9204 -1 o70L -1 9204 -1 920Lk-1 9204k -1 920k -1 1000 970L-1 9204 -1 2005 9204 -1 9204 -1 9201-3 7500 9204 -1 9204 -1 2000-A 9201-3 9204 -1 4500 2005 9204 -1 9201-3 920k -1 9204 -1 4500 9204 -1 9204 -1 4500 9201-3 9204 -1 93. ok. 95. _ %. 97. 98. 99. 100-101. 102. -103. 104, 105=10T7. - 108. N B. S. Weaver B. H. Webster A. M. Weinberg J. H. Westsik L. V. Wilson C. E. Winters C. H. Wodtke Reactor Div. Library (2) Central Research Library (2) Document Reference Library (1) Laboratory Records (3) Laboratory Records ORNL-RC 4500 9204 -1 41500 0204 -1 9201-3 4500 9204 -1 9204 -1 4500 Or71l-1 4500 4500 s 3