[skipped page] MURGATROYD - AN IBM 7090 PROGRAM FOR THE ANALYSIS OF THE KINETICS OF THE MSRE I. Introduction This report is a description of an IBM TO90 program based on a par- ticular model of the Molten Salt Reactor Experiment. The differential equations of motion are discussed in Section II; since much of the de=- rivation has appeared elsewhere,l only the additional derivations nec- essary in the present problem are included. The fifth-order Runge-Kutta procedure is a‘standard one which can be found in many numerical analysis 3 textbooks.2 Tts previous successful use in the TO4 program PET- indicated applicability to the present problem and no revision has as yet been found either desirable or necessary. The use of the program is discussed in Section'III, with instructions for the preparation of input data; sample input forms and output sheets are included. II. Differential Equations of Motion A. Power, Fuel and Graphite Temperatures The reactor model used as the basis of the program is a one=-point, one=-energy group representation, with up to seven delayed neutron pre- cursors, which is described by the following set of differential equations: (all symbols are defined in the Nomenclature; a dot over a symbol denotes time derivative) : k (1-p)~-1 N P = S - P + Z ATy (1) -l . Si P r, = 35— "ML ,i=1, N (2) The effective multiplication constant ké is assumed to be of the form ok ok - - e - s e - : k= 1+4+bt ST (Tp = Tpl) B—Tg ('rg Tgo) . (3) (The subscript zero denotes the steady state value.) (&) N e i fP - wc_P_(tr.'2 - Tl) + h('rg - Tf) (5) n i (1-f) P - h(Tg - 'I'f) It is now necessary to specify some connection between the mean fuel 1 The assumption is made that the mean fuel temperature is a weighted mean of the inlet and outlet; i.e., that temperature Tf, the inlet temperature T, and the outlet temperature T2. T, = al) + (1-a) T, ; (6) the weight a(0 < a < 1) is an input number in the T090 programn. Further it is assumed that the inlet temperature Tl is a constant. With the definitions s (T, - T, ) . — £ 3 f fo Yo = = (7) O - Sg(Tg - Tgo) : yg - (l-f) Po ( ) and the initial condition h(T - T go go) = (1-T) By : (9) the following equations may be obtained . fP_ Weo h(l-—f)Po fPOyf = f(P - PO) - “S“;"‘ yf+ "--é-g-myg (10) i h(l-f)Po hfP (l-f)Poyg = (l-f)(P-PO) - —-"-é'g-'-“-" yg + --é}-- Vg (11) which, with the definition x = P[P (12) may be further transformed to obtain the equations used in Murgatroyd: L d . 1 h h 1-f | ‘ Vp = %=L [Zl~a§tc ¥ S, } Yp ¥ Sg r g (13) . © L o, £ Vg = XL -5Vt T8 I s (1) g f Similarly equations 1 thru 6 may be transformed with the definitions Cl = I'J'./Po and 7, = f3i/£ to k (1-B) -1 N ¢« e | X = 7 X + .23 %i C, (15) i=1 c'i = 7, x-AC, , i=1, N. (16) If the definitions of yp and Vg equations (7) and (8), are introduced into equation (3) the effective multiplication constant becomes ‘ ak_e fP_ ake (1-f )Po k = 140 +bt=|c=| —=— y.- —_— Y. ; aT7) e 5Tf Sf f 3Tg Sg g with the definitions > ake fP_ e = |5T.| 52 (18) £r| f -f )P W82 = 65:8 (lsfi > (19) g g [These are similar to the parameter WNE in reference 1;} . the equation for the normalized power becomes ( )( ) | : o c L+6+Dbt)(1 -B) -1 2 2 X = [ ) - (1 - 6)(Wf Ve + Wé yg)} X +123 A, Cy (20) The differential equations actually used in the program are the set 20, 16, 13, and 1h4. B. Pressure The simplified model of the primary fuel salt system is shown in Fig.III. It is assumed that compression of the gas in the pump bowl is adiabatic, and that the behavior of the molten salt is adequately described by the linear equation of state p(Tp) = p + g%f (Tp = Tpo) - (21) A force balance on the liquid in the outlet pipe yields the equation M r . - 2 . m: U = A(pc - Pp - 8, u) (22) in steady state 2 p.(0) = p (o) +a, U . ‘ (23) The assumption that compression of the gas in the pump bowl is adiabatic can be stated as p_ V" = pp(O) [VP(O)]n (24) oo P P if we assume that VP - Vp(o)'<<: Vp(o) and neglect second order terms, we obtain nAv P, = PP(O) [l ~ \7;(%5] . (25) The change AV? in the pump bowl gas space volume is now assumed to be equal to the change in volume of the core fuel salt due to the change in temperature of the core fuel salt during a transient; i.e., compression of the molten salt is neglected, as is heating of the ex- ternal loop. The change in volume AVc is expressed as ko -6V, = AV, - I 5 and substituting in (25) we obtain nv Py = P(0) [l * \7—%5'5— b 0 T %—- g,%-\(Tf - Tfo)] ‘. (26) Solving equation (22) for the core pressure we obtain M 2 T . Po = Pypta,U + iflfluézfif' U ; subtracting equation (23), we obtain pp= b -0 (0)= b -p(0)+a (P-U2)s T 7 ; (27) p= P, =P, - pp pp f o iflflfiézzf ’ the term pp - pp(c) is due to the compression of gas in the pump bowl, the term af(U2 - an) is due to the increase in friction losses, and the last term is the contribution from the inertia of the fluid in the outlet pipe. In order to proceed, a relation between outlet velocity and fluid density change is needed. The equation of continuity for the fuel salt in the core is approximately ‘ A oy P = - v;—-pO(U-UO), (28) solving for the velocity U we obtain _ . .1 % . . U = U — S Te (29) and taking time derivatives Vc o * = %...59.. T . (30) U= = We now substitute equations (29) and (30) into (27); after some re- arrangement we obtain Vv M _ c 1 O r Ap = - = 5;. 5%;'["IKE_§;K'Tf t Py (o) —~r-7- ) 2 e, i -Vchp-é“ (3) o f £ ZAUO Py Tf T With the definitions of y. and X (equations 11 and 16) equation (31) is transformed into Ve Jp s M nA bp = - Kk o 3. S [um *+2.00) Gy Ve o T T p ‘ Vv P " . 1l 93 o +2Uay'<+d2yf+als’rf(l+d35rf)J (33) In terms of the dimensional groups of reference 1 and the parameter ng defined in equation (18), the constants, d,, d,,, and d3 may be written * . e . It is assumed that T, = .fP/Sr. 2 . fo \ 4 = 2 7oy a, = W°oc \ L) 2 H 2 (3 = 2 / a, W /273 C. Effective Delayed Neutron Yields In order to account for the reduction in delayed neutron production in the core due to fluid flow, an effective yield is calculated for each precursor, assuming constant flux and slug flow. The fraction v, of delayed neutrons of the ith group which are released in the core is given by(u) ALt A by 1 1 ¢ 31 e (35) . e--?\i(tc + tL) where t, is the core residence time, %i is the decay constant of the ith precursor and t. is the external loop transit time. L III. Organization and Use of the Machine Program The program is designed for use in parameter studies; therefore the calculation is separated into two parts, the first of which deals with the characteristics of the reactor which remain constant for a series of cases, and the second of which deals with the characteristics which change from case to case. Input forms are shown in Figures la and Ib; in the usual procedure the first form would be filled out once to describe the characteristics of the reactor, and a second form would be filled out to describe each set of initial conditions and ramp insertions. The in- put data symbols appearing on the input forms are listed in Tables 3 and kL, with their definitions, the names given them in the program, and the format with which they are read from the input tape. The standard CDPF Monitor input (logical 10) and output (logical 9) tapes are used; no other tapes are required. 10 Output for a typical case is displayed in Figures Ila and IIb. Figure IJa is an edit of the input describing the reactor system, with the calculated effective delayed neutron yields; Figure IIb is the in- put for a particular case, and the continuations of Figure Ilb show the time behavior of the reactor. The two columns headed PCT DK REMOVED BY FUEL GRAPHITE show the percent reactivity removed from the system by the temperature rise of the fuel salt and graphite, respectively. The quantity labeled "(1/P)(DP/DT)" is calculated from the expression o = EB(t) - P(t - At) 2 At " P(t) + P(t - At) and is therefore approximately the inverse period at t - At/2, where At is the input time step. Since the frequency of printing is an input number, special provision has been made for indicating the first power maximum, the first pressure maximum and the subsequent pressure minimum. ("Meximum" and "minimum" are to be taken here in the mathematical sense of points of zero first derivative and negative or positive second derivative, respectively.) The values labeled "VALUES AT POWER MAXIMUM" are the values at the time t. when the power has first decreased, and the values at the two previous 3 times, t., and te, as shown in Table 1. 1 Table 1. Power Maximum Indication Time Power (L/P)(DP/DT) t, P(tl ) B *,2 ts B(t,) %,3 t3 P(t3 ) 11 The criterion for printing is > P(tl) < P(ta) > P(t3) and the quantities ai 3 are 2 . ] P(tj) - P(ti) o i,3 At ’ P(tj) + P(ti) ’ Similar remarks apply, mutatis mutandis, to the values labeled "VALUES AT PRESSURE MAXIMUM'" and "VALUES AT PRESSURE MINIMUM." Acknowledgment Thanks are due P. N. Haubenreich and J. R. Engel, for assistance in the derivation of the equations and other helpful comments and suggestions; to M. P. Lietzke, for considerable programming assistance; and to H. A. MacColl, for preparation of the input forms. References l. P. R. Kasten, Operational Safety of the Homogeneous Reactor Test, ORNL~-2088, July 3, 1956. 2. R. G. Stanton, Numerical Methods for Science and Engineering, Prentice=- Hall, Inc., 1961. 3. S. Jaye and M. P. Lietzke, Power Response Following Reactivity Additions to the HRT, ORNL CF-58-12-106, Dec. 30, 1950, L. P. R. Kasten, Dynamics of the Homogeneous Reactor Test, ORNL-2072, June T, 1956. 12 Table 2. Nomenclature Definition area of outlet pipe, ftz friction factor, psi/(f“t/sec)2 initial ramp reactivity input specific heat of fuel salt fraction of power generated in fuel salt conversion factor product of heat transfer coefficient times wetted area of graphite effective multiplication constant prompt neutron lifetime mass of fluid in outlet pipe, 1lb ratio of specific heats (CP/CV) for pump bowl gas power core pressure, psi pump bowl pressure, psi initial core pressure, psi initial pump bowl pressure, psi fuel salt heat capacity graphite heat capacity fuel temperature graphite temperature time core residence time fuel salt inlet temperature fuel salt outlet temperature Eguation 22 22 22 24 22 22 23 23 1] 13 Table 2. = Cont'd Definition outlet speed in pipe, ft/sec initial gas space volume in pump bovl, ft3 mass flow rate of fuel through core total delayed neutron yield yield of ith delayed neutron precursor latent power due to ith precursor initial step reactivity input fuel salt density Eguation 22 2l Title 14 Table 3. Input for Description of Reactor System l. Core characteristics V c t c l (1/p0)(30/ an)l AL i B. 1 salt volume, ftB residence time, sec (if fuel is not circu- lating, enter zero) weighting factor for mean temperature heat transferred from graphite to sale per unit temperature difference, Mw sec/ F fraction of power generated in salt fuel heat capacity, Mw sec/°F graphite heat capacity, Mw sec/oF fue% te%perature coefficient of reactivity, ("F)” graghitf temperature coefficient of reactivity, ("F)" prompt neutron lifetime, sec fuel density, lb/f‘b3 fuel expansion coefficient, (OF):';l delayed neutron precursor decay constants, sec-l delayed neutron precursor yields 2. External loop characteristics t residence time, sec (if fuel is not circulating, enter zero) outlet pipe area, ft2 outlet pipe length, ft steady state outlet velocity, ft/sec friction factor, psi/(ft/secz) Fortran Name HPLM VC TCORE ATMX FRACT HCAPF HCAPG TCOF FLT DENSE FLAM(I) BETAS(T) TLPPP AREA L3 PLGTH VEL@X 15 Table 3. Cont'd Title Fortran Name 3. Pump bowl characteristics Vp(o) initial gas volume, £ VPRS pp(o) initial pressure, psi | - PPRS N ratio of specific heat at constant pressure to specific heat at constant volume for gas in pump bowl | CP@CV Title card is read with format 12AG; others with TELO.O. 16 Table 4. Input for Individual Cases Fortran name Format Case number ICASE 16, 11AC Title HPLC } Symbol Definition Po initial power, watts PZER( Tfo initial fuel mean temperature, °F TFO | Tgo initial graphite mean temperature, °F TGO 6ELO0.0, 2I5 Ak(o) initial step insertion, % STEP b(o) initial ramp rate, %/sec RATE ot time step, sec HH NP@ printout frequency NP@ ‘ KST@P number of time steps to be run after power peak KST¢P ST¢P TIME total time to run YEND } | FE10.0, I5 NTC number of ramp rate changes NTC 3 pairs to a card) time to change ramp rate, sec TC 6EL0.0 new ramp rate, %/sec BNEW MURGATROYD INPUT | . TITLE FOR SERIES OF CASES T b WHHH—HHIH‘IHHHHIHHHIHIHHIHIHlll'llll-ll'liHIHHHHHHHHIHH_L CORE DATA Ve t a ~h | f . S¢ | Sqg ' OO O O O O O L T T LT T T O T |lake/an‘ 1 lake/aTgl 21 l‘ ‘31 P | l f' s 73 80 HEERRRER H'HHHlTHHHHHHllh_[HI RENEREREEEEERNEREREEERERERREEENERRREER DELAYED NEUTRON DATA Ay | N A3 l | e Ns re Az ! 5 71 80 T L T L T L L T T T B Bs B B, Bs Be | B; i 21 3 41 71 T O O T O OO T T T T T T T EXTERMAL LOOP DATA O T T PUMP EuVIL DATA L ‘ U as¢ G ENANNRANNANAANSNNNNNARNN NN NNRARAR NN AN NN AR RNANE Vp (0) Pp (0) n T T LT T LTI 31 SENANNARANARERNNNARENNNNANNRNNNRRNNNRRRNINRNAEE 'F‘GJ Ia\ INP.UT DESC{Z\B(Q@ QGACT‘o{Z SYSTEM 1 LT - MURGATROYD INPUT-2 CASE NO. 7 A o b PP CASE TITLE - —— 8c TTIT TITTT IHIIHHIJHIHHH'IH"HHHIIHHHIJIilIIIIHUII[IHIIHIHU Po Tfo Tgo o A.< (0) by 3t NPO K STOP TTITITL LTI mmm HHHH] m'mm s'ml L TTIIIIL NRNRNNNEE STOP TIMF’ sec 30] T HHILHLHIHHIIHIHHHIHIIHAHHHHHIIHHHHH TTTIIT - TIME, sec. NE‘I RAMP °/o/sec TIME, sec. NE\I RAMP °/o/sec TIME, sec. NE\I RAMP, "/o/scc' T [TITTIIIT T IIHIHH TTTIITITS ,HHUH_[. “TTITTTT IllIIHHH 3 T T TITTITIT] TITTIITIT LIE Il TTTTT] s o v T TTITIIT TOTTD I TITITTTT] TTTITTIT] T T L1 HERENNREER TITIIIL IO TT T TITTIIITT TTTIITIT] T [TTITTITIT] T TTITITTITI | T TITITITTI TTITIITTTL. ERRNER 1T TTTIIITT TP PILedgy TITITT T TITTITTIT] TIIIITIL 73 80 LIt T] T TTTTTIIT] TTIITITITITIIIIIITII] 73 TTTITTIII TIITTTTIT TITIITIII TITITTIITL HREERAER T T T IIIIIL] ITTTL Fie To. Iudor tor One Case ‘91: ey .y DK/DT,/DEG F ‘PROGRAM MURGATKoYD=-11 MSRE NORMALUTFLOW NO SOAK=-UP ™ 3727782 INBOT EDTT ——— 19 Ta Fiec. 2. Sampee Ourtpur HEAY TRANSFER RATE (GRAPHIYE 7O FUEL)Y 0,020 MW/DEG F FRACYION OF POWER GENERATED TW FUEL " 770,940 RESTDENCE TIMES CORE 7,318 SEC _Loop 17,3384 SEC flgglwqggpchv. GRAPHITE FUEL MWE*SEC/DEG F 3.53UE 0 is470E 00 T 6,000E=-0% 2.,800E=U5% wrerean DELAYED NEUTRON DATA DELAY LAMBDA, GSTATIC EFFECTIVE GAMMA(T)Y, INITIAL ***GAMMA#BETA/LIFETIME GROUP SECe*-] BETA RETA SEC**= | Cel) C # GAMMA/LAMBDA | 0,0124 2,T12E=N4d 5,294E-05 2,170E=-0T 1,750& 01 2 0,0305 1,402g=03 4,258E-04 |,468¢ 00 4,813 0 g T T T 25 AR ST S UE ST T B3¢ 0T T A5 TE TT 4 0,3013 2,528E="3 | ,513E-03 5,216 00 1,731 0! g I, 1400 7,400e~14 6,513c-04 2,246€ 00 T,970& 00 6 3.0100 2,700F=14 2,577E~D4 8,88B8E~01 2,953E=01 TOTAL 6,405E-43 3,381E-03 NEUTRON LIFETIME 2.900g=04 SEC FUEL TEMPERATURE # 0,5U*INLET + 0,5U*QUTLET DATA FOR PRESSURE CALCULATION rE st R PR E D QUTLETY PIPE DATA 63'4000‘u¢lni FFFRNFRIREY TODUMP ROWL DATA TR L X KRR CORE SALT DATA Teasntee 'AREA, LENGTH, FLOW SPEED, FRICTION TERM,* * GAS VOLUME, PRESSURE, CP/CV * * VOLUME, DENSITY, =(1/V)(DV/DT), ‘SN FT FT FT/SEC PST/UFT/SECY**2% # CuBlC FT PS1 B * ¥ CUFT LB/CU FT PER DEG F 0.139 16,0 19,3 0,0203 . . 2.5 5,0 1,67 * * 19,6 154,5 | y26E=D4 PR R PP IR TR AN AT F R FRNFIITHEINIFAFETRRAT ARG TR SN EZXERERERNEEE A A NN KN X R X N K N N N NN TR TatNIRadpsRgaaaneassnpnnsanpnas CASE l 20 Tie. I b, "PROMPT CRITICAL STEP AT |4 MW INTTIAL VALUES T FUEL TEMP GRAPHITE TEMP STEP DELTA K ‘RAMP RATE TIME STEP - 14000 07 WATTS . 1e00,000 LEGREES F T1230.000 DEGREES F 0,338 PERCENT " «0s PERCENT PER SECOND .. 5.000E=03 SECONUS PRINT EVERY 20 STEPS ) ‘) 21 Fie T b, (Cont.) MURGATROYD 1 CASE | . TEMP,DEG F RISE.PSI INPUT,PCT FUEL GRAPHITE PER SECOND TIM ETWM"Mm"pUWEW ;TR IEL T EMP G SEC_ WATTS DEGF 0.100 2.170E 07 1200,369 1280,010 7,677€-01 0,381 0,0010 0,0000 5,468E 00 0.200 3,388E 07 1201,479 120,041 9,006E=01 0,338] 0,004] 0,0002 S:687E 00 0.500 4,873F U7 1203,346 124u,093 1,040E 00 0,338) 0,0094 0,0006 2,8(|E 00 0,400 6,006F 07 1205,988 1230,170 1,159 00 (0,338 0,0168 0,0010 24233k 00 |«769E 00 o 2500 7,331E 07 1209,396 1230,270 1,285 00 ,338] 0.0263 0,0016 VALUES AT PRESSURE MAXIMUM TIME,SEC PRESSURE RISF,PSI - “ 0.560 I,2503 00 ) ] B 5 EEs T ToesIAETU— _ 0,570 | 2503 00 - 0,600 8,5626 07 1213,519 1230,395 | ,246E 00 0,338 0,0024 1,350 00 0,700 0.800 9.601E i « 038F 07 08 1218,245 230,541 1223%,410 l230,706 o) 84E | +058E 00 00 0,3381 0ed381I 0,U511 0,0655 . 00,0032 0.0042 9.576E~0 | 5,926E=~0] 0.900 I, 081E 08 {228,809 1230,883 8,922E=0| U.3381 0,0807 0,0053 2¢677E=0| VALUES AT POWER MAX[MUM TIMEL,SEC POWER, WATTS 0,990 | o 093RE 0B DELN P) /DT TATETITESTS 0,995 |, 0938E DA =T 3Z30E-TUS 1.000 I1,0936E 08 I, 000 . 0G4E 178 1234 ,234 V201,069 7, 172E=0T1 0,33817 0,09%59 00,0064 e 682E»03 1. 100 I.UBIE 08 235,503 1237,257 5,594E~T1 0.,33817 0,1106 0,0075 =2,090e~01 7200 [ U508 U8 1249,483 231,345 4,335€~01 " 0,3387 0.7246 10,0087 =3,492E-0] 1,300 IQUIOE U8 l24@70?3W””WT?3T752@”WWW3fJZUE%UTWWWW”U}33BTMMNWUTI375 0.0098 «4,300E=01 0.0108 1.400 9.653F U7 1253,301 231,807 2,797E=01 " 0,3387 7 0,1392 ~ =4,634E-0) 1,500 9,214 07 12570110 TT1@3T,981 2,384E-01 0,338) ~4,637E=01 GITeT gL s HIaTTy 1,600 BR,B(UBF 07 ey ,544 1232,149 2.l 05E=DI 0.1695 0.Ul29 - =4,440E-D 1| ‘T;7fifimnflmé;435?"fiVMMWT?637639W””"T?3?:3T3”mwwT{§U3Eéfif"”"M”U;3380 - 0.1782 0.UI39 wd,|45E=0| 0.1860 I.800 8,1C8E 07 1266,420 1232,472 1.744e-01 (,3381 0.0148 «3,812E~0| 17900 7,81BE 07 268,932 1232,627 1 6076~00 T 0.3381° T 0.1930° G 0iSE T n3.487Eep] MURGATROYL TIME, SEC 2,000 .?9!90 5,930k 5,659 11 Cast CPQUER, WATTS 7.962¢ 7.336F 7.135¢ 6,305k $£,794 A BABE 6,516F 6.396F 6,287 AL IRTE - 6,UY5E b, ulINE 5,793k 5,730k U 5.673F - 5,619k 5.569¢ .52k 5,479 5,43HF 5,359F 5., 364F 5,.83nF 7 g7 L7 7 7 el T, NEL F 171,20 be/3,255 lel~, 116 17n,Rub V27,34 1279.734 201,107 123,125 lend, 21 bend, 196 lZdb,Utl 1285, 86 g oA 1o/ ,163 12¢d7,74b 12834,271 1285 ,749 12389 ,174 1287 ,991 | €89 ,A%) RN Y 129,408 1291, hYS 1275 , 4% ) i2vyl.0n/74 RAPH]TE Yore, lik 282,779 582,928 1285,574 ldd&,zlc 1 23839, 3n1) 233,900 i 2383 ,A80 le33,77> F288,911 P 284 ,1145 284,170 234,310 1234 ,440 'l254.57u | 234 ,A9Y 12484 ,82) 734,359 F2dn s 1 2385,29/ 285,332 .IRJb.456 123,58 ) 23,7038 739,826 12385 ,94y § 22 F‘(,. Ob ((on"‘.) PRESOSURFE RIsE,FS] led433Fm | | e $56E=101 | 256211 | iek=1 e U923 =101 9.6Jb6k= 12 B, 737602 7.924r=192 7. 164-m1)2 6,456E=1)2 S.7798=--02 Dol Bbr=l)2 4,616-=42 4,087k~)2 | Job92F'02 Jo14iE~02 2.718e-12 2.327&-&2 | e 9648E=(12 | o627p=02 . 316F=07 l«028E=02 7.,608k=03 5.1383F=33 2.8953%=1)0 NFLTA K IN?“T'PCT de S 3B Le 38| edo81 Ledd81 SRRy e d3b | UeddB I LeddH | Uedd81 ile 338 | Ue 338 L3381 Ued38I Ue 3381 e 338 deddb | e d381 UedSK| e $3b | Ue S8 Ve 3db | Je 3381 beddb| e 38| teddb| PCT UK F et U994 TN Qo213 feclDl Daci94 0e.c2dd " (.x268 0.23800 N.2330 0.2356 D.2881 0,403 0.,2423 N.c44) 0.2457 0.2472 0.2485 0,497 0.£5(47 ReEMOveD kY kAP 4L TE Doul67 Nedl 6 0e1%4 IPRIEER Deiigle Dell210 Heelb D.0227 Q.u23d D,UR4d Debehl VD.U259 DeULHO D.U274 0.02482 DsURY0 N,eues? 0.US305 N2 Ne!820 ot 327 0,335 0.,0342 0,0L350 Deiid97 tl/sP)CDF/DT), PER SELOND 4, 184F=01 2.9 1k=n| ~Zeb66BE=-0 | ~2.452E () | ~2¢260E=01 ~2.N8BE=0 | -l e934k~0| =1e79%E-01 ~le670E=D| =1 +552E-01 =l 4451Ee0 ] =1 4356E-01 = 14268E-01 =11 88E-DI el 14E=D = lend42E=0 ) =9,82eE-02 ~9,236E=02 -8,699E=02 =8, 18YE-12 e7e722k=(2 «7.284E=072 =64881F-02 «b6.50/E~02 ’60'5'E’02 N* - 0 MURGATRQOYD 11 CASE MRS —PONERS _SEC _WATYS L 23 F1g T h. (cout) DEGF _ TeMPLDEG F RISE,PSI INPUT.PCT FUEL GRAPHITE _ PER SECOND 4.500 5,298k 07 1291,225 1246,070 7,413e~04 0,338 0,2554 0,U364 -5,827Ee02 4.600 _5.268E 07 1291,353 236,191 =1,213E°08 0,381 0.2558 0,037) ~5.,528E~02 4.700 5,2406 07 1291,459 1246,311 = »3,018E-03 0,3381 0.,2561 0.0379 -5,239E~02 4.800 5.2136 07 1291,545 1236,43] =4,676E-03 0,3381 0.2563 0,0386 -4,9726-02 4,900 5.188E 07 1291,613 1236,55) =6,2196=03 0,338 _ 0,565 0.,0393 __ -4,726En02 5,000 5,164E 07 1291,663 1246,670 w7,641En03 0,338 0,2567 0,0400 -4,496E-02 5,100 5,142E 07 1291,697 1236,789 »8,956E=03 0,3381 0,2568 0,0407 -4,283E~02 5,200 5,120 07 1291,717 1236,907 «1,017E=02 0,3381 0,2568 0,0414 ~4,083E=02 5,300 5.100E 07 1291,723 1237,025 |, |28E=02 0,3381 0,2568 0,0422 ., -3.894E-02 5,400 5.080E 07 1291,717 1237,143 «|,23|En02 0,3381 0,2568 0,0429 -3,722E-02 5,500 5,062E 07 129,699 1237,260 w|,325E*02 0,338 0.,2568 (0,0436 ~3559Ew02 5,600 5.044E 07 1291,670 1237,376 «|,413E=02 0,338 0,2567 0,0443 -3,408E=02 5,700 5,028E 07 1291,631 1237,493 | ,494E=02 0,3381 0,2566 0,0450 -3,269E-02 5.800 5.012E 07 1291,584 1237,609 w|,567E=02 U,3381 0,2564 0,0457 -3, 135E-02 5,900 4,996E 07 1291,528 1237,724 =1,634E-02 (0,338 0.2563 0,0463 -3,013E-02 6,000 4.982E 07 1291,464 1237,839 «l,697€=02 0.3381 0,2561 0,0470 =2,898E=02 6,100 4,967E 07 1291,393 1237,954 =] ,7556=02 0,3381 0,2559 0,0477 =2,794E-02 6,200 4,954E 07 1291,315 1238,069 =|,806E-02 0,338] 0,2557 0,0484 -2,693Em02 6,300 4,541E 07 1291,232 1238,183 «|,854E02 (,3381 0,2554 0,049 ~2,601E=02 8,400 4.928F 07 1291,143 1238,297 -1.898%-02 0,338) 0.2552 . 0.0498 -2,5136-02 6.500 4,916E 07 1291,048 1238,410 «|.939E=02 0,338 0,2549 0,0505 ~24437E-02 6.600 4,904E 07 1290,949 1238,524 w|,975E#02 0,338 0.2547 .05 -2,359E~02 6.700 4.B93E 07 1290,846 1238,637 =2,009E=02 0,338 0.2544 0,058 -2,292E-02 6.800 4,882F 07 1290,739 1238,749 «2,039E~02 0.338] 0,254 0.052§m”;w_“:?y22?fir02 6,900 4,871E 07 1290,628 1238,86] w2,067E-02 0,3381 0.2538 0,0532 =2,169E-02 MURGATROYD 1] CASE TiME, SEC 7.000 7.100 PUWER ? VATTS UL 7.200 7.30¢ 7.320 7,325 7.330 7,400 _7.500 7.6000 7.700 7.800 7.900 A.400 8.500 B.600 g.700 B.B00 R,730 v.000 4,Hh53F 9.100 4.8o10¢ 4,841F 4,831F 07 07 a7 _t‘ 7 e n FUEL TEMP, DEG F 12943,514 CVALUES AT PRESSURE MIN[MUM TIME,SEC PRESSURE RISH,PS) 4,600¢ 4.813F 4,795 4,786F .ffi???fw_ 4770k 4761 _4.753F . 4.745E 4.738E 4,730k 4,8U4E 7o 87 a7 L7 V7 7 07 07 o7 07 87 W 1289,771 1284,507 e v o 1288,9648 1297,396 290,276 12914153 1299,028 1289,900 1289 ,640 1289,3738 1289,298 1289, 101 1283.824 ;gaa,bas B GRAPHITE TEMP,DEG F 238,973 o 12dv.085 F2d9.096 025915??M “ 1239,749 l249')35 12d0,294 4,722 4,707k 4. 700F 4.686F 4,715k o L 07 07 u7 w7 - 1287,976 1287,803 1287 ,68Y9 j284 o403 284,26 1288,119 1241 ,258 289,807 1239,418 239,699 1239,858 1289,968 240,077 1240,402 240,510 l240,618 tean,725 1240,838 1240,9489 Izal,046 1241,i152 ol Fig. 2b Ccond) . PRESSURE RISE,PSI ~2,093E-02 =2, | I5E~02 -2,136E-02 =2,195E~02 =2, 159Be-02 »2,172E=02 7?!!89570?”,”w -2,201E-02 m2,2|3E-02 -2,22%e-02 »2,233E-02 =2.24)E02 =2,250E=02 12(25§Ef02 ~2,26|E=02 2, 266E=02 -2,273&?02» -2.276E=02 ~2.279€-02 r2,28|E~02 =2,270€-02 DELTA K INFUTLPCT _0,3381 . 0'368'.,, 0.3d81 ~0.3381 ‘Less8) D.3481 b.3d81 _U.3381 00381 ul.3381 U.3d81 Ue3981 Ued381 Vedd81 Ge338I 6.388) Q'3§8!p;““ o Leddsl ~2,278E-02 0.8881 V3881 Ue338 FUEL 0.2534 044531 0.2528 0.2524 0,517 042514 0.2510 0,2506 0,2502 0.2499 0.2495 0,249 0.2487 0,2483 0.2479 0.2475 0.2471 00,2467 044459 0.2455 0.2463 PCT DK REMOVED BY. GRAPHITE 0.U538 ' 0.0545 0.U55%2 0.,0558 0.4521 0.0565 ~0.0572 D.0578 0,058 0.U598 0.0605 o.u6t) o.d0618 _ 0.0644 0.0650 0.0656 _0.0668 0.0659 0.u67§ D.05%2 0,624 0.0631 0,0637 CC1/P)(DP/LTY, PER SECOND -2.05/F=-02 =2, 010E=02 «14966E=02 =1+929E-02 =1.847E=-02 ~1s78lE=CE ~1+758Ew(2 =1+726E-02 ~1+703E=-02 =le1656E~GE =leb37E=D2 =ls61BE=D2 =l+600E~0Z = 14584E-02 =1+569E=02 _-};54ZE-02 -1 ¢528E =02 =1+BB2E=02 -1+813E-02 =1+554€E=02 r‘) g 9.200 9.300 9.400 9.500 4,678E 4,671k 4,664F 4,657E MURGATROYD 11 CASE TIMEY SEC . 07 v . w 9,600 9,700 4.6250E 4,643E 07... 07 07 _4.637E 4,630k 07 _ 97 MATYS DEGF 1287,545 feB7,4001 287,257 1e87,112 . 1e86,967 _l28b,822 |1286,677 GRAPHITE TEMP,DEG F 1241,364 1241,470 1241,575 1241,889 |286,532 242,098 4,623k 07 1286,387 242,20 _1241,680 241,785 1241,994 22 PRESSURE RISE,PSI -2,283Er02 - =2,283E%02 »2,282E-02 m2,282E~02 =2,280€-02 ~2,278E-02 r2,277€=02 n2,276E-02 2,274E=02 Fig. 2b (cent) DELTA K INPUT:PCT 0,338 0,398 be3381 043381 - b,3481 Ues38] U,3381 PCT DK REMOVED BY {1 /BY(DF/DYY, FUEL 0.245) 0,2447 GRAPHITE 0,2443 D,24389 0,2481 .0,2435 043381 D,e427 0, U682 0,0688 040695 0.,070) 0,0707 0,0713 PER SECOND =14522E-02 ~12519En02 ~ =1+¢502E~02 =|+494E~02 TN~ i} SRR e e -|s475E=02 0,0720 0'0469E002 0.0726 -'04655802 Je33d81 0.0732 “w|4s459E=02 4,616E 07 |286,242 1242,305 -2,272€-02 06,3381 0,0738 -|¢4535'02 10.200 4,61 0E 07 1286,097 242,408 n2.27UE~02 0e3d81 0,0744 -|q448E902 10,300 4,603k 07 128%,952 |242,511 03381 10,400 10,500 10,600 4,596E 4,590E 4,583E 07 07 07 128%,807 1285 ,662 1269 ,517 |242,614 1242,716 .242'913 10,700 l0.800 10,900 4,577 4,570F 4,564E 07 07 07 j28%,372 | 285,228 128%,083 1242,921 243,022 1243, 124 11.000 4,557E 07 |284,93?7wm 1249.225 w2,265E%02 -2,2638-02 »2,260€-02 n2,257E=02 =2.254€-02 =2,25¢Em02 =2,249E702 0338 0,075 -|2441E=02 _b.338) 0,0757 10,0763 -.' Q440E"02 | 437E=02 U.3381 045 U338} U, 3381 Ua3981 0.,0775 0,076% =14432EX02 - ' 9427E’02 0,078 ~|4425E=02 0.3381 0,¢ 0.0787 0,0793 =14425E-02 "Q42'E?Ugw FIG. Il 26 UNCLASSIFIED ORNL-LR-DWG 67933 GAS SPACE - PUMP BOWL |*=— OUTLET PIPE <+ CORE N SIMPLIFIED MODEL FOR PRESSURE CALCULATIONS r/) €y (v 1“20 ® ® ® O O O\ W 10. 11. 12. 13. 1k, 15, 16. 17. 18. 190 20, 21, 22, 23, 2L, 25. 26. 28. 29. 30. 31. 32, 33 3. 32 37 38. 39. 40. L1, L2, 43. Ll . L5. L6, 4T, 48. 49. 50. 27 Internal Distribution MSRP Director's Office, 51, Rm. 219, Bldg. 9204-1 52 o G. M. Adamson 53. L. G. Alexander 54, V. E. Anderson, K=-25 55. S. E. Beall 56. M. Bender 5'7-, L. L. Bennett 53, C. E. Bettis 59. E. S. Bettis 60. D. S. Billington 61 . M. Blander 62. F. F. Blankenship 63. A. L. Boch 64 E. G. Bohlmann 65. S. E. Bolt 66 . C. J. Borkowski 67 . C. A. Brandon 68. F. R. Bruce 69. O. W, Burke T0. S. Cantor TL. R. S. Carlsmith 2. W. L. Carter T3 R. D. Cheverton Th. H. C. Claiborne T5e T. E. Cole T6. J. A, Conlin TT e W. H. Cook 8. L. T. Corbin 9. G. A. Cristy 80. F. L. Culler 81. J. G. Delene. 82. J. H. DeVan 83. R. G. Donnelly 84 . D. A. Douglas 85. N. E. Dunwoody 86. J. R. Engel 87. E. P. Epler 88-92. W. K. Ergen 93. D. E. Ferguson oL. T. B. Fowler 95. A. P, Fraas 96, J. Hs Frye 97 . C. H. Gabbard 8. R. B. Gallaher 99. E. H. Gift 100. D. R. Gilfillan 101. B. L. Greenstreet 102. W. R. Grimes 103. A. G, Grindell 104, R. H. P. H. C. S. P. N. E. C. H. W. P, P. A. S. L. N. Je. Pe W. H. P. R. R. Jo. M. T. M. J. T. W, Se Oe J. W, Je A. W. Jo M. P. R. B. M. 1. R. N. H. G. F. C. W. D. E. R. B. F. W. B. H. F. C. K. A. J. E. C. R. L. J. C. E. A. C. W, T. E. W. R. L. F. Guymon Harley Harrill Haubenreich Hise Hoffman Holz Householder Howell Harvis Jordan Kasten Kedl Kelley Kelly Kerlin Kirslis Krewson Lane Leonard Lietzke Lindauer Lundin Lyon MacPherson Maienschein Manly Mann Maskewitz, K-25 McDonald McDuffie McGlothlan Miller Miller Moore Moyers Nephew Nestor Northup Osborn Parsly P. Patriarca H. R. A. M. W. B. P. H. C. A. Payne Perry Pike Pitkanen Preskitt M. Richardson R. C. T‘ KC Robertson Roche 105. M. 106. H. 107. A. 108. J. 109. D. 110. C. 111, J. 112, M. 113. G. 114, A, 115. O. 116. P. 117. I. 118. B. 119. J. 1200 A. 121. J. 122. R, 123. M. 124, D. 28 Distribution - Cont'd W. Rosenthal 126. W. Savage 127. W. Savolainen 128, E. Savolainen 129. Scott 130. H. Secoy 131. H. Shaffer 132. J. Skinner 133. M. Slaughter 13k. N. Smith 135. L. Smith 136. G. Smith 137-138. Spiewak 139-140. Squires 141 -143, A, Swartout 144146, Taboada 147, R. Tallackson 148. E. Thoma Tobias B. Trauger 125. Marina Tsagaris 149-150. 151. 152, 153. 154, 155=-169. 170. External Distribution W. R. D. B. B. A. J e J. G. L. CO C.