) )y 1wy w k. RECEV : R E’\, PT! r— - r OAK RIDGE NATIONAL LABORATORY operated by UNION CARBIDE CORPORATION = NUCLEAR DIVISION m for the U.S. ATOMIC ENERGY COMMISSION ORNL- TM-~ 2815 COMPUTER PROGRAMS FOR MSBR HEAT EXCHANGERS C. E. Bettis T. W. Pickel W. K. Crowley M. Siman-Tov H. A. Nelms W. C. Stoddart NOTICE This document contains information of a preliminary noture and was prepared primarily for internal use ot the Ook Ridge National Loboratory. It is subject to revision or correction and therefore does not represent a final report. DISTRIBUTION OF THIS DOCUMENT 1S UNLIMITED This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights, OAK RIDGE NATIONAL LABORATORY OPERATED BY UNION CARBIDE CORPORATION NUCLEAR DIVISION UNION CARBIDE POST OFFICE BOX X OAK RIDGE, TENNESSEE 37830 June 24, 1971 To: Recipients of Subject Report Report No. : ORNL-TM-2815 Classification: _ Unclassified Author(s):E; E. Bettis, W. K. Crowley, H. A. Nelms, T. W. Pickel Subject: Computer Programs For MSBR Heat Exchangers Request compliance with indicated action: Please affix the attached corrected pages 6, 7, 58, 62, 63, 86,87,88,89, 117, 124, 125 to pages with same numbers in your copy(ies) of the subject report. They are prepared on gummed stock for your convenience. Also prepared on gummed stock is a correction for the bottom two lines on page 9 of the report. Please cerrect your copies promptly to avoid further errors. The corrected design data for the primary heat exchanger agree with the data shown in Report No. ORNL-4541. Laboratory Records/Department Technical Information Division Table 2.1. Design Data for MSBR Primary Heat Exchanger Type Number required Rate of heat transfer per unit, MW Btu/hr Tube-side conditions Hot fluid Entrance temperature, °F Exit temperature, °F Entrance pressure, psi Pressure drop across exchanger, psi Mass flow rate, 1lb/hr Shell-side conditions Cold fluid Entrance temperature, °F Exit temperature, °F Exit pressure, psi Pressure drop across exchanger, psi Mass flow rate, 1b/hr Tube Material Number required Pitch, in. Outside diameter, in. Wall thickness, in, Length, ft Tube sheet Material Thickness, 1in. Sheet~-to-sheet distance, ft Total heat transfer area, ft2 Basis for area calculation Volume of fuel salt in tubes, ££3 Shell Material Thickness, in. Inside diameter, in. Central tube diameter, in. Baffle Type Number Spacing, in. Shell-and-tube one-pass vertical exchanger with disk and doughnut baffles Four 556.5 1.9 x 10° Fuel salt 1300 1050 180 130 23.4 x 100 Coolant salt 850 1150 34 115.7 17.8 x 10° Hastelloy N 5803 0.75 0.375 0.035 24.4 Hastelloy N 4,75 23,2 13,916 Outside of tubes 71.9 Hastelloy N 0.5 67.6 20.0 Disk and doughnut 21 11.23 Table 2.1 (continued) Disk outside diameter, in. 54,20 Doughnut inside diameter, in. 45.3 Overall heaf transfer coefficient, U, Btu/hr.ft*.°F 784.8 Tube Maximum primary (P) stresses Calculated, psi 683 Allowable, psi 4232 Maximum primary and secondary (P + Q) stresses Calculated, psi 12,484 Allowable, psi 12,696 Maximum peak (P + Q + F) stresses Calculated, psi 13,563 Allowable, psi 25,000 wave configuration., The tubes are held in place by wire lacing in this upper portion of the tube bundle. Since baffling is not employed in this region, the bent-tube portion of the bundle experiences essentially parallel flow and a relatively lower heat transfer performance. Below the bent-tube region of the bundle, evenly spaced doughnut- shaped baffles are used to hold the tubes in place and to produce cross flow. The baffles spacings and cross-flow velocities are designed to min- imize the possibility of flow-induced vibration. The tubes in this baf- fled region of the heat exchanger have a helical indentation knurled into their surface to enhance the film heat transfer coefficients and thereby reduce the fuel salt inventory in the exchanger. No enhancement of this nature was used in the upper bent-tube region because of present uncertainty about the reliability of tubes that are both bent and indented. Bottom of page 9: For completely turbulent flow with Reynolds numbers greater than 12,000, Q.14 h.d ub u—l") (EFl) (2.3) i3 k., i = 0*'8 1/3 0.0217(NRe) (NPr) 1047 FORMAT(31HGBERGLIN MODIFICATION FACTOR = ,F542) MSBR 500 1048 FORMAT(1HQ, 2X+1HIs7TX43HTCI,9X43HTCO,9X,3HCWT 99Xy 3HTFI,9X,3HTFG, MSBR 510 19Xy 3HF WT y 8X y4HTWDT/ /11Xy 1HF y11Xy1HF,11X,1HF 411X, MSBF 511 2 1HF 311X 91HFy 11 X3 1HF 311Xl HF // (1 X3 12,7TE1264)) MSBR 512 1049 FORMAT (1HCy 2X y1HI»9Xy2HV1y 9X,2HV2 ,9X,2HV3 ,9X,3HVW1 ,9X,3HVW2 , MSBF 520 1 8Xy4HPDSCy 8X y4HPLTC//32Xs 6HFT/SEC 33X THLB/SQFT//(1X,13,7F12.4)) MSBR 521 105C FORMAT(1HO, 2X s1HI s 5Xy5SHRENTO,7X+5HPRNTO s 7TX EHRENSOL ,€X ,6HRENSC2, MSBR 530 16X, 6HKENSC2 y7X933HHTO$ 8Xy 4HAHSO 39X 9 3HUCA y8X s 4HHEAT//TTX, MSBR 531 ¢ 13HBTU/HR/SQFT/F4313X,6HBTU/HR// (1X:13,9E12e4)) MSBR 532 1051 FORMAT{(27FCTUBE WALL AVERAGE TEMPe = +F10e2) MSBR 54C 1052 FORMAT (28FCSHELL SIDE AVERAGE TEMPe = 4 F1lGe2) ' MSBR 55C 1053 FORMAT(1HO,24+P STRESS AT TUBE 0D AND TUBE ID = , 2F10.241Xy MSBR S6C 1 9H(LB/SQIN)//18H(SHOULD NOT EXCEEDsF1l0e243H 1)) MSBR 561 1054 FORMAT(1HC,36FP+Q STRESS AT TUBE OD AND TUBE ID = , MSBR 570 1 2F10e2+s1X49H(LB/SQIN}//18H{ SHOULD NOT EXCEEDyFlC.2, MSBR 571 2 3H 1)) MSBR 572 1055 FORMAT(1HC,38FP+Q+F STRESS AT TUBE OD AND TUBE ID = , MSBR 580 i 2F10e42s1X,SH(LB/SQIN)//18H(SHOULD NOT EXCEEDsFl0e2, MSBR 581 2 34 1)) MSBR £82 MSBR €50 READ IN ANC PRINT OUT INPUT DATA MSBR €6C KEYT= 1 MSBR 610 VM1{1)=0e MSBR 620 VM2(1)=0. MSBR €30 VM3(1)=0. MSBR 640 VWO1(1l)=C, MSBR €50 VWO3(1)=0. : MSBR 660 RENSO1(1)=Ce MSBR 670 RENSGO2(1) =0, MSBR 680 RENSO3(1) =0, MSBR 690 HS01(1)=0. MSBR 700 HSO02(1)=0, MSBR 710 HS03(1)=0. MSBR 720 MSBR 810 8¢ 10 IF(KEY1leEQe C)BSOI=Cs5*(BSL+BSH) CURVES=C o C6S812%ARC* EXPRAD+ Oe4*(KAB—RAS)+625*%BSOI IT =0 KFINAL =0 I=1 HEFI HEFO TSUM=C, SSUM=C, THEATO = Q.0 TPDTO = 0.0 1. 1. i TPDSO = 040 TFO(I)}=FTC TCI(I)=CTC TIF=~5,0 TIC2—500 CDTF=0, FDTF=C. BSO = BSQO1 BRL1 = GBRL = Coe 77%BRL1%%(-,138) AWO1l = BSC*xLAWOL AWO3 = BSC*LAWO3 AWl = SQRT{AWO1*APO1l) AWZ = {(AWO1l+AW03)/2 AW3 = SQRT(AWC3*APD3) GSO1 = QC/AMW] GS02 = QC/AW2 GS03 = QC/AW3 BSO=CURVES EQVBSO= CURVES+ 13.,* (CIA+DIAT) KEY4=C KEY5=( ATC TCI(I) + (TIC/260) CFT = ATC +CDTF*HSFCT ATF = TFO(I)+TIF/2. FFT=ATF-FLT F*HSFCT FI=1 own TUBLN(I) =(FI-1,)%BSOI+CURVES BSC/ ({RAB=(KAB=RAT)/26)=(RAS+(RAE6~RAS)/2.)) MSB MSB MSB MSB MSE 1850 1860 1870 188C 1890 MSBR 7320 MSBk 740 MSB MSB MSB MS8B MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSE MSB MSB MSB MSB MSB MSB MSB MSB 1900 1910 1920 193C 1940 1950 1960 1970 l98C 199G 2000 2010 2020 2030 204C 2050 2060 2C70 2C80 2090 21G0 2110 2120 2130 2140 2150 2160 2180 2200 2210 Z9 CVIS=Ce2l21%EXP(4032e/(4€04+ATC)) MSB 222C CVISW=0e 2121%EXP(40324/(4604+CFT)) MSB 223C CDEN=141,27-0.02466*ATC MSB 2240 CCON=Co24C MSB 2250 CSPH=0¢36 MSB 2260 FVIS=0e2637T*EXP(T3€24/(460.+ATF)) MSB 2270 FVISW=0e 2E3T*EXP(T2624/(460,+FFT)) MSB 228C FDEN=234 ¢4 S7T~0,C2317*ATF MSB 229C FCON=0,70 MSB 230C FSPH=0e324 MSB 2310 VISK = (CVIS/CVISW)**(0,14 MSB 2320 FVISK=(FVIS/FVISW)**C,14 MSB 2330 DCVIS = DIA/CVIS | MSB 2340 CCDEN = 14/CCEN MSB 2350C QCCDEN = QC*CCDEN MSB 2360 CALCULATE REYNOLS AND PRANDTL NUMBER TUBE SIDE MSB 2550 RENTO(I)=CIAI*GTO/FVIS MSB 2380 PRNTO(I)=FVIS*FSPH/FCCN MSB 239C IF(KENTBe EQel e ANDeRENTC(I) ¢GTe1l00le eANDe IeNEol) MSB 2400 IHEF I=1 e+ { (RENTG(I)=1G00e)/90C0e )%%045 MSB 2401 POTO(I)={ «0C28+4 25%FENTO**(~4,32) ) *EQVBSO*GTQ**%2%HEF1/ MSB 2410 1l (DIAI*FDEN*4171824C0,) MSB 2411 CALCULATE HEAT TRANSFER COEFF TUBE SIDE MSB 2640 IF(RENTO(I)LT412CCC6 IGO0 TO 12 HTO(I ) =FCCON/CIA*eC217*{RENTO(I ) *%¢8)* (PRNTC(I)%%,3323)%FVISK*HEFI MSB 2430 GO TO 15 MSB 2440 12 IF(RENTO(I).LT421CCe) GO TO 14 MSB 245C i3 HTO(I) = FCON/DIA¥eCB9% (RENTO(I )**467895-14141272)* (PRNTO(]) 1%%¢ 3333 )% FVISK¥HEF I* (1e+e3233%(DIAI/TUBLN(I) ) %% ,6666) GO TO 15 MSB 2470 14 HTO(I) = FCCN/CIA%*(4 426+ (0o025%RENTO(I)*PRNTO(I)I*DIAT/TUBLN(TI) MSB 2480 1 )1/(le+C 0C12%RENTC(I)*PRNTO(I)*DIAI/TUBLN(I)}) MSB 2481 i5 IF(I+EQe1)GC TO 1€ MSB 2490 CALCULATE FLCw AREAS SHELL SIDE MSB 248C VWO1(I) = QCCLEN/AWOL MSB 2510 VWO3(I) = QCCDEN/AWC3 MSB 2520 VM1(I) = GSO1*CCDEN MSB 2530 VMe(I) = GSO2*CCDEN - MSB 2540 VM3(I) = GSGC3*CCDEN MSB 2550 €9 Computer Output for Reference MSBR Primary Heat Exchanger TOTAL HEAT TRANSFERED = 18G€217984e (BTU/HR) ( 9949 PERCENT) MASS FLOW RATE OF COOLANT = 1759C736. (LB/HR) MASS FLOW RATE OF FUEL = 2345432C. (LB/HR) SHELL-SIDE TOTAL PRESSURE CRCP = 115.75 (LB/SQIN) ( SGe¢7 PERCENT]} TUBE-SIDE TOTAL PRESSURE CROP = 129,32 (LB/SQIN) ( 9S.,5 PERCENT) NOMINAL SHELL RADIUS = 2e81€2 (FT) UNIFORM BAFFLE SPACING = (eS386 (FT) TUBE FLUID VOLUME CONTAINEC IN TUBES = 71.92 (CUBIC FEET) TOTAL HEAT TRANSFER AREA BASED ON TUBE OeDe = 13916632 (SQFT) TOTAL NUMBER OF TUBES = 58032, TOTAL TUBE LENGTH = 24,43 (FT) HEAT EXCHe APPROXe LENGTFH = 22422 (FEET) STRAIGHT SECTICN OF TUBE LENGTH = 2Ce26 (FT) RADIUS OF THERMAL EXPANSION CURVES = Oe86 (FEET) BERGLIN MODIFICATION FACTOR = Q679 TUBE WALL AVERAGE TEMP, = 1116454 SHELL SIDE AVERAGE TEMP. = 1012, 6¢€ 98 P STRESS AT TUBE OD AND TUBE ID = 683442 €46e47 (LB/SQINI SHOULD NOT EXCEED 4232422 ) P+Q STRESS AT TUBE OD ANC TUBE IC = 12484439 8890,S7 (LB/SQIN) SHOULD NOT EXCEED 126967C ) P+Q+F STRESS AT TUBE OD AND TUBE IC = 13562677 1098155 (LB/SQIN) SHOULD NOT EXCEED 2500C.CO0 ) I TCI TCC CWT TF1 TFO FWT TWDT F F F F F F F 1 D.1150E 04 0.,1i22E 04 (C,124CE C4 0Q.1276E 04 (.13COF 04 0.1256E 04 0Q.1549E 2 0el1i22E 04 061108E G4 0Qe61178E C4 Qe1265E 04 0e1276E 04 061223E 04 Co4528E 3 0e1108E G4 O0.1094E 04 O0.,1165E 04 O0ei254FE 04 0e012¢65E 04 0601210E 04 0.4516E 4 0.1094E (4 O0.1G81lE 04 (C.1152E 04 0.1242E 04 OQ.1254F 04 0.1198FE C4 0,4525E 5 0el08lE 04 0.,1067E C4 0ell3SE 04 0e1231E 04 0e1242E 04 C(Q.1185E 04 O044533E 6 0.1067E 04 04,1053E 04 0e112¢E 04 O0,1219E C4 061231F 04 Geo1172E C4 Ce4538E 7 0.1053E 04 0.1039E 04 0.1113E 04 (0.1208E 04 0.1219E 04 (0.1159E 04 0.4540E 8 0Uel039E 04 O061025E 04 (ellCGCE 04 O0e1196E 04 061208E 04 001146E 04 (0,4540E 9 D.1025E 04 0.1012E 04 C.l087E 04 O0.1185FE 04 0e119¢E 04 041133E 04 O0.4538E 10 0.1012E 04 0.9979E C3 O0.1074E 04 O0.1173E 04 O0.1185E 04 O0.1119E G4 (Qe.4532E 1l 0,9979E 03 0e9842E 03 (e01C61E 04 Cell62E C4 061173E 04 O061106E 04 O0.4F24E 12 0,9842E C2 0e9705E U3 0.1048E 04 O0.115CE 04 (Q.1162E 04 0,1093E 04 0.4513E 13 0.9705E 03 0.9569€ 03 C.1lC35E G4 O0.1139E 04 0.1150F 04 0.1080E G4 0e4499E 14 0¢9569E 03 0e9433E 03 0e1C22E 04 (Qe1l128E 04 0e1139E 04 O0.1067E 04 044482E 15 069433E 03 069297TE 03 CelOO9E C4 O0e01116E C4 0Qe61128E 04 061053E 04 Ce44€2E 16 0,9297E 03 0,9162E 03 0.9557E 03 0.1105E 04 O0.1116E 04 O0.1040E 04 0.444CE 17 0e9162E 03 069029E C3 CeSB27TE 03 0.10S4E 04 O0e1105E 04 O0.1027E 04 0Oe4414E 18 0.9C29E 03 068895E 03 Ce9€¢SGTE 03 0,1083E 04 061094E 04 0.1014E 04 C4%3285E 19 0C.8895E 03 C.8763E G3 (C.9568E C3 0.1072E 04 0.1C83E 04 O0.1000E 04 O0.4353E 20 0e8T7T63E 03 0e8632E 03 Ce943SE 03 0.1061E 04 0.1072E 04 0.9871E 03 0.4318E 2l 0e863ZE 03 O0e8503E (02 0e9311E (3 0,1050E 04 0.,1061E 04 O0.9739E 02 0.428CE G2 02 02 02 02 G2 02 02 02 Cc2 02 02 C2 02 c2 02 02 02 02 L8 o o b N OO D=0 WP o e N N P et b e s ROV~ WP W V1 Oe0 641833 6e1646 6el467 bel286€ €.1106 be0G926& 60748 560570 6+03G4 640219 660045 59872 59702 5¢953¢ 59365 59199 59035 58€73 58713 548555 V2 0.C 6e 9424 6e5 218 669Cl4 6.8810 6.8¢€08 6e 8406 6e 8206 6.8006 e 78C 8 beT7612 CeT41l6 6e 1223 6e 7031 6e 6 E41 €Ce 6E53 e 46T 666283 666101 6e 5521 6e 5144 V3 FT/SEC C.0 N 6.7022 €. 6825 Ce 6628 Ee€4322 606236 606042 €.584S 60,5658 6o 54€7 65278 6o 5C91 6064905 6.4T21 604539 604358 64180 6.40C4 603830 6o 3€59 VWl Oe.0 €e3719 63530 Ce3342 6e3155 642970 6e2785 642601 6.2418 6e2236 642055 6.1876 6e1699 6.1522 6.1348 661175 61004 6.0836 €. 0669 60504 60341 VW3 0.0 Te6251 T7.6025 745801 75577 7.5255 Te5133 74913 74694 Te44T7 Te4261 T.4046 Te3834 703623 72414 72208 73003 7.2801 72601 Te2404 7.2210 PDSO LB/SQFT 84Te4312 84744312 841.4097 8354158 8294214 82344299 81lTe4436€ Blle 4666 805.501C 79S¢ 5500 7936187 787.7100 7818259 7759714 770.1499 76443652 7584 6204 752.9199 714762676 T41.,6660 736.1208 PDTO 286961321 86l.8818 85349421 84640403 83861379 83042402 82263506 8l4e4T4E 80666165 7987803 7902712 78341628 1754529 7677529 7600996 75244968 74449495 7137.4624 730.GC410 T2206892 715.4114 88 (5N CWO®=~O VI WP - ™ = T s bt (o b Bt pd et COHO~NOCWMEIW n - RENTO 0.1138E 0.1091E 041061E 0.1031E 0.1001E 0.9721E De9434E 0.9151E 0.8874E 0.8601E 0.8333E 0.8071E 0.7814E D.7562E 0e.7316E 0.7075E 0.6840¢E 0.66l11E D+6389E 0.6172E Ue5961E PRNTC 0.8232E 0.8589E 0.8835E 0.9092E 049360E 0.9641E 0.9934E 0.1024E 0.1056E 0+.1090E 0.1125E Oe1l61E 0+1199E 041239E 0e1281lE 0.1325E 0.1370E 0.1417E O.1467E O«1518E D0.1572E o1 o1 01 01 01 o1 02 02 Q2 02 02 02 02 02 0e 0e 02 02 02 RENSC1 0.0 0.2887E Ce2822E 0.,2758E 6,2695E 0e2631E 0.2568E 0. 2506E 0. 2443E Ce2382E Ce232CE Ce226(E 0s2199E 0.2140E 0.2081E 0.2023E Ce1G96€E 0.191CE Cel854E Cel8CCE 0el174¢E 05 05 05 05 05 ¢S 05 05 05 05 05 05 05 05 05 05 05 05 05 RENSO2 0.0 0.3241E 0.3169t 0. 3097E 0.3026E 0+ 2955E O« 2884E 0.2813E 0.2743E Oe 26T74E Q0. 2605E 042537E O+ 2469E 0.2403E 0.2337€ 0.2272E 0.2207E 0. 2144E 0.,2082E 0. 2021E 0e1961E RENSO3 0.0 0.3138E D«3068E 0+2999E 0.2930E 0.2861E 0.,2792E 0.27 24E 0.2656E 0.2589E 0.2523E 0. 2456E 0.2391E 0.2326E 0.2263E 0.,2199E 0.2137E 06207¢€E 0,2016E 0¢1956E 0.1898E 05 05 oS 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 HTO 0.1732E 0.3422E 0.3318E 0.3232E 0.3147E 0.3063E 0e2979E 0.2896E 0.281l4E 0.2T32E 0.2651E 0.2571E 0.2492E 0.2413E 0.2335E 0.2258E 0.2183E 0.2108E 0. 2034E 0.1961E 0.1889E AHSO 0e5314E 0.2580E 0.2532¢ 0.2507E 0.2481lE 0e2456E 0. 2430E 0.2403E 02377E 0.2351E 0.2324E 0«2298E C.2271E 0.2245E 0e.2218E 0«2192E 0.2165E 0.2139E 0.2112E 0.2086E 0.2059E BTU/HR/SQFT/F 03 04 UGA 0.3653E 0.1044E 0.1026E 0«1014E 0.1001E 0.9881E 0.9751¢E 0.9619E O« 9485E 0.9349E 0.9211E 0.9071E 0.8929E 0.8786E 0.8640E 0.8493E 0.8345E 0.8194E 0.804 2E 0.7888E 0. 7733E HEAT BTU/HR Ge1793E C. 87COE Ce 8678E 0.8695E Ce8TI0E Ce8T1SE Co 8724E 0.8724E 0. 8719E 0. 87C8E C.B8692E 0.8672E 0. 8645E C.8612E Oe 8574E Ce 8521E C.8481E 0. 8426E Qe 8364E 0.82STE 0. 8224E 68 117 CALCULATE THE DIFFERENCE BETWEEN THE TOTAL TUBE SIDE DELTA- P (SDPT) AND THE ALLOWABLE TUBE SIDE DELTA-P (DELPTA) v YES NO CHECK TO SEE IF SDPT IS WITHIN 3% OF DELPTA >—— A 2 ADJUST THE NUMBER OF TUBES IN THE EXCHANGER (NUMT) 66 2 CALCULATE THE DIFFERENCE BETWEEN THE TOTAL SHELL SIDE DELTA- P (SDPS) AND THE ALLOWABLE SHELL SIDE DELTA-P (DELPSA) v NO CHECK TO SEE IF SDPS IS WITHIN 3% OF DELPSA )——“ ADJUST THE BAFFLE SPACING (BS(K)) #@ \\\\ ALL OF THE HEAT HAS BEEN TRANSFERRED--THE TOTAL PRESSURE DROPS ON BOTH TUBE AND SHELL SIDE ARE WITHIN LIMITS. WE HAVE AN ACCEPTABLE SOLUTION. WRITE OUT THE RESULTS. Fig. D.l. (continued) 16 161 162 17 18 19 MS=1 $X=0 S85=0 TC(l)=7C2 TH(1)=TH1 RWK=DTO*LCGF(LTO/DTI)/2,0 PCll)=PC2 CALL SVHIZyPCZ:TC2430UMHC(1)) BN=FLODATF (N) QAX=QT/ BN DECT=QX/ { WH*CPH) DECH=QX/WC I=1 K=1 SB = SBK*8SL LOPT=0 TCON=TH(I)}=CTPB/2.C IF(1eEQel) GO TO 161 VMUD=0,21 22*EXPF{40226/1TH#+460,.)) VMUB=0421 22*EXPF (40324 /( TCON+460. ) ) FACT=(VMUC/VMUB)**0,14 GO TO 162 FACT=1,0 CONTINUE DENH=1414 2B8E+(C-2,4¢6E-02*TCON VISH=0,2]1 22E+00*EXPF(4032.CE+CO/( TCON®4 60, CE+CO)) DHOT(K)=DENH VHOT(K )=V ISF CON1=(CPH*VISF/TCH)**Co6€YE+QQ GM=WH/ 58 RECB=DTO*CM/V 1ISH IF(RECB-800.0117,18,18 HJB=0, 571 /{RECB**C¢456) GOTO19 HJB=0e 346 /( RECB**(0, 282) HB=(HJB*CPH*GM/CON1 } *FACT GW=WH/ SW GS=SQRTF( CM*GNW) RECW=DTO*CS/V ISH IF(RECW-800,0)20,21,21 Sup SUP SUP SupP SUP SUP SUP SUP SUP SUPpP SUP Sup sue SupP SUP suep SUP 1020 103¢ 1€ 4C 1050 1069 1074 1CRo 109C 1100 111¢ 1120 1130 1140 1150 1160 1170 1180 sSup=*11°1 SUP%*1182 SUP#*1182 SUP*1184 SUpP=*1185 SUP*1186 SUP*1187 sue SUP SuUP SUP SUP SUP sup SUP SUP Sup SUP 1190 12CC 1210 1220 123C 124C 125C 1260 1270 1280 1290 SUP*1300 SuP SUP SUP SuUP 1310 1320 133¢ 1340 A 20 21 22 23 24 25 26 28 29 30 31 32 33 HIW=0,571 /{RECW*%) ,456) 6G0TO022 HIW=0e 346 /(RECW**0,382) HW= (HJW*CPH*GS/CONL ) *FACT HO=(HB*( 1 s0=2C¥PW) +HW*{ 2,0%PW) ) *BLFH HO = HO*GEBRL RO(K)=1s07/HC THUI+1)=TH({ I)=-DECT LOP5=0 HC{I+1)=HC{1)-CECH DELPP=(0.0 PC{I+1)=PC{ I)+CELPP LOP3=0 LOP4&=0 TC(I+1)=TC{ 1)-CECH CALL SVH{2,PC(I+1),YC{I+1),DUM,HCG} EH=ABSF(HC(I+1)-HLG) [IF(EH-0.0C1#+-C(1+41)1})31,31,26 TRIAL=TC( 1+1) HRIAL=HCG TCUI+L)I=TC{I+1)+(HC (141 )=HCGI®R(TC(I)-TC{I+1))/{HCLI)=~HCG) CALLSVH{2 PC{1I+1),TC(I¢1),DUM,HCG) EH=ABSF(HC(I+1)-HCG) IF{EH-0,0C1*HC(I+1))31,31,28 TNEXT=TC( I+1) +(HC(T+1)=HCG)*(TC(I+1)-TRIAL)/(HCG-HRIAL) TRIAL=TC( I+1) HRTIAL=HCG TC(I+1)=TNEXY LOP3=L0OP3+] IF(LOP3-1C)30,30,29 WRITEQUTPUTTAPESL,1015,LCP3 GOTO80 GOTO27 DENOM=(TH(TI+1 )=TC{I+1 )/ (TH(I)-TC(I}) TOEN=ABSF (DENCM-1,0} IF(TDEN-0,05) 32,33,33 DELTEM=0o SE4+QC*(TH(I+1)=TC{I+1)+TH(I)=TC(I)} GO TO 34 sup SuP Sup 1350 1360 137¢C SUP%x1380 SUP sue sup SUP sue SUP SUP sSup Sup SuUP SuUP SuUP Sup sup SUp SuUP SuUp SUP SuUpP Sup SupP SuUPpP SUP sup SuUP SupP Sup Sup sup SupP SUP Sup sup sur DELTLM=(TH{ 1+1)=TCUI¢L)=TH{I)I+TC(I))/LOGFUUTH{I+1)=TCCTI+1))/(TH(L)SUP 1-TC(I))) sye 1390 140C 1410 1420 1430 1440 1450 1460 1470 1480 149C 1500 1510 1520 1530 154¢ 155¢C 1560 157¢ 158¢C 159C 1600 1610 162C 1630 164C 1650 1660 1670 1680 169G 1700 1710 1720 173¢ 1731 Gel ORNL TM-2815 Contract No. W-7405-eng-26 General Engineering Division COMPUTER PROGRAMS FOR MSBR HEAT EXCHANGERS C. E. Bettis T. W. Pickel W. K. Crowley M. Siman-Tov H. A. Nelms W. C. Stoddart APRIL 1971 LEGAL NOTICE This report was prepared as an account of work sponsored by the United States Government, Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express of implied, or assumes any legal liability or responsibility for the accuracy, com- pleteness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights, OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee operated by UNION CARBIDE CORPORATION for the U.S. ATOMIC ENERGY COMMISSION DISTRIBUTION OF THIS DOCUMENT 18 UNLIMITED Dot AbStraCt 8 8 & S B SR E B ENSS S G s 8 Pt N R A AN N S et s e INTRODUCTION ....QQ.Il.l....tl.'..‘.'......!l..l.'.'.l’.l‘..... 1. 2. iii CONTENTS PRIMEX, THE PRIMARY HEAT EXCHANGER PROGRAM ..cetvtevcscasce 2.1 Description of Priméry Heat Exchanger .cceccecercecase 2.2 Design Calculations +eceseeesvsetresaccrssssncsonconsssans 2.3 Description of PRIMEX +.veevsrorosasoasoccns cesesacnae 2.4 Evaluation o0f PRIMEX cseceeeevoostososocosesnonnosscsas RETEX, THE STEAM REHEATER EXCHANGER PROGRAM ........ ceatsess 3.1 Description of Steam Reheater +¢eoeeervnersocesceniosans 3.2 Design Calculations .+eeveievvcrecnccncnn cesresserennanns 3.3 Description of RETEX +cevveereceorsnoosnssssososssssss 3-4 Evaluation Of R-ETEX ® & & B 4 & 4 5 ¥ ¢ 8 & & & ¥ S B AR NE NS SUPEX, THE STEAM GENERATOR SUPERHEATER PROGRAM ...ciivveeass 4.1 Description of Steam Generator «iesesisecscrasarsass ciraen 4.2 Design Calculations .......... Cree s aeeses e eirenaanne 4.3 Description of SUPEX .t..vtveriireiereecnnottsenesonnsnnns Lol FEvaluation Of SUPEX s eeveeesnseonnneeansoeaneoenansnns REFERENCES * 9 8 8 B 8 & 0PI 8 e e # 0 & & & 9 % s 0 2 s 0 0 4 © & 5 & 2 8 &8 & B 8 e 2 e s s * b o & Appendix A: PHYSICAL PROPERTY DATA ...ccecerererecccnannnnns .o Appendix Appendix B : THE PRImX PROGRAM @ 5 6 3 & ¢ ¢ 8 4 b 0 0 s a2 s ® & & & & & 0 & 8 8 8 s d & & 9 v 8 Appendix C: THE RETEX PROGRAM ...t rerenesttttnarasnassscsanns D : THE SU PEX PROGRAM 4 ® &8 8 0 8 4 % 8 0 s 8 02 0o 4 5 2 & 8 5 2 % 9 8 0 8 0 s A s 0 W e 16 17 19 20 23 23 24 26 27 29 37 39 41 45 49 90 Figure Number 2.1 2.2 3.1 4.1 B.1 C.1 D.1 LIST OF FIGURES Title Cross-Sectional Elevation of a Typical MSBR Primary Heat Exchanger Zones of Flow Between Two Baffles in the Shell Side of the MSBR Primary Heat Exchanger Typical MSBR Steam Reheater Exchanger Typical MSBR Steam Generator Superheater Exchanger Simplified Flow Diagram of the PRIMEX Computer Program Simplified Flow Diagram of the RETEX Computer Program Simplified Flow Diagram of the SUPEX Computer Program Page Number 12 21 27 50 91 115 Table Number 2.1 3-1 4-1 4.2 4.3 A.l A.2 A.3 B.1 B.2 C.1 C.2 D.1 D.2 vii LIST OF TABLES Title Design Data for MSBR Primary Heat Exchanger Design Data for MSBR Steam Reheater Exchanger Design Data for MSBR Steam Generator Superheater Exchanger Preliminary Stress Calculations for MSBR Steam Generator Percentage Deviations Resulting From Calculational Uncertainties Related to MSBR Steam Generator Exchanger Design Properties of MSBR Fuel Salt Design Properties of MSBR Coolant Salt Design Properties of Hastelloy N Computer Input Data for PRIMEX Program Output Data From PRIMEX Program Computer Input Data for RETEX Program Output Data From RETEX Program Computer Input Data for SUPEX Program Output Data From SUPEX Program Page Number 20 28 37 40 46 47 48 53 54 94 95 118 119 COMPUTER PROGRAMS FOR MSBR HEAT EXCHANGERS Abstract Three computer programs were developed to make design calculations for the heat exchangers for Molten-Salt Breeder Reactor concepts. They are the program for the primary heat exchangers, PRIMEX; the program for the reheaters, RETEX; and the program for the steam generator superheaters, SUPEX. Each type of exchanger analyzed is described, the basic equa- tions used in each analysis are given, and the logic used in each program is discussed briefly in this report. Flow dia- grams, lists of input required and output received, complete program listings, and the nomenclature for the programs as well as example computer input and output for the exchangers described are appended. 1. TINTRODUCTION The concept of a single-fluid Molten-Salt Breeder Reactor (MSBR) with a thermal capacity of 2250 MW and a net electrical output of 1000 MW has some very special heat exchange requirements. In the present concep- tual design for the MSBR plant, there are four heat exchangers in the primary system that transfer heat from the molten fluoride fuel-salt mix- ture to the molten sodium fluoroborate coolant salt. In the secondary system, there are eight reheaters and 16 steam generators that transfer heat from the coolant salt. The manner in which these exchangers were designed to meet the special heat exchange requirements and the computer programs that were developed to calculate the design numbers are described in this report. The development of MSBR concepts passed through a number of stages during which the plant layout was improved, core configurations were optimized, and physical property data were refined. The first formal study of a MSBR heat exchange system made by the authors was reported in 1967 (GE&C Division Design Analysis Section, "Design Study of a Heat- Exchange System For One MSBR Concept,'" USAEC Report ORNL TM-1545, Oak Ridge National Laboratory, September 1967). To analyze one exchanger at each stage of its subsequent development without programming a large por- tion of the necessary calculations would have meant almost continual rep- etition of these calculations over a period of many months. With com- puter programs available, the design for an exchanger could easily be updated for changed capacity, physical properties, temperatures, pres- sures, etc. Three such computer programs were developed. One computer program was written to make the design calculations for the primary heat exchanger, and it is the PRIMEX program. This program was modified at one stage of its development to perform the calculations for the steam reheater exchangers. This modified version is the RETEX program. A third computer program was wéitten to perform the design calculations for the steam generator superheater exchangers, and it is the SUPEX program. The design data for each of these three types of exchanger, the basic equations used in each design analysis, and each of the computer programs developed to perform the analysis are described in the following sections of this report. Flow charts for each program, lists of the input required and the output provided by each program, complete program list- ings, nomenclature lists for each program, and the computer input and output for each type of heat exchanger discussed are appended. 2. PRIMEX, THE PRIMARY HEAT EXCHANGER PROGRAM There are four primary heat exchangers, which transfer heat from the fuel salt to the coolant salt, in the conceptual design for a single- fluid MSBR. Each of these exchangers has a thermal capacity of 556 MW and each is of the same design. The fuel salt circuits for the primary heat exchangers are in parallel, each having its own fuel pump. The coolant salt from each exchanger is circulated through its own system of two reheater exchangers and four steam generators. At full design load, the fuel salt enters the top of the primary heat exchanger at a temperature of 1300°F and exits from the bottom at a temperature of 1050°F for return to the reactor. The coolant salt at a temperature of 850°F enters the top of the primary heat exchanger and is directed to the bottom of the exchanger through a central downcomer where it enters the shell side of the exchanger, flows upward in counterflow to the fuel salt, and leaves the top of the exchanger at a temperature of 1150°F. This coolant salt is circulated through the steam reheaters and steam generators where its heat is transferred to the exhaust steam and feedwater, respectively. The design conditions for the primary heat exchanger were partially dictated by the overall requirements of the MSBR system. The heat load, entrance and exit temperatures of the fuel and coolant salts, and the maximum or desired pressure drops across the shell and tube sides of the exchanger were specified by the operating conditions of the system. Design considerations for the overall system dictated the type of exchanger, arrangement of nozzles to facilitate piping, minimum tube diameter considered to be consistent with fabrication practices, and the limit on the overall length of the exchanger. Certain criteria such as the maximum allowable temperature drop across the tube walls and the need to build in enough tube flexibility to compensate for differential ther- mal expansion were established by the strength of the materials. Vibra- tion considerations placed limits on flow velocities and the spacing between baffles. In addition, it is highly desirable that the volume of fuel salt be kept at a minimum to lower the doubling time of the reactor. Within the framework of these requirements and guidelines, a computer program was developed to perform a parameter study and select the design for the primary heat exchanger that employs a minimum volume of fuel salt. The design data and equations discussed in the following subsections were used to develop the computer program for the primary heat exchanger (PRIMEX). 2.1 Description of Primary Heat Exchanger Each of the four primary heat exchangers is a vertical shell-and- tube type with a single counterflow pass on both the tube and shell sides. Each unit is about 6 ft in diameter and about 22 ft tall, not including the coolant salt U-bend piping ét the top. A cross-sectional elevation of a typical primary heat exchanger is illustrated in Fig. 2.1, and the pertinent design data are given in Table 2.1. The fuel (primary) salt enters the tube side of the primary heat exchanger at the top and flows out the bottom of the exchanger after a single pass through the 3/8-in.-0D tubes. The coolant (secondary) salt enters at the top of the exchanger, flows to the bottom of the exchanger through a central 20-in.~diameter downcomer where it enters the annular shell containing the tubes, flows upward around modified disk and dough- nut baffles, and exits through a 28-in.-diameter pipe concentric with the inlet pipe at the top. The tubes are arranged in concentric rings in the bundle with a con- stant radial pitch and a circumferential pitch that is as constant as can be obtained. The L-shaped tubes are welded into a horizontal tube sheet at the bottom and into a vertical tube sheet at the top. The toroidal-shaped top head and tube sheet assembly has a significant strength advantage, simplifies the arrangement for coolant-salt flow, and allows the seal weld for the top closure to be located outside the heat exchanger. To accommodate differential thermal expansion between the shell and tubes, about 4 ft of the upper portion of the tubing is bent into a sine ORNL-DWG 69-6004 SEAL WELD N A 3 SECONDARY PRIMARY __ SALT \ I SECONDARY SALT Lt T PRIMARY SALT Fig. 2.1. Cross-Sectional Elevation of a Typical MSBR Primary Heat Exchanger. Table 2.1. Design Data for MSBR Primary Heat Exchanger Type Number required Rate of heat transfer per unit, MW Btu/hr Tube-side conditions Hot fluid Entrance temperature, °F Exit temperature, °F Entrance pressure, psi Pressure drop across exchanger, psi Mass flow rate, lb/hr Shell-side conditions Cold fluid Entrance temperature, °F Exit temperature, °F Exit pressure, psi Pressure drop across exchanger, psi Mass flow rate, 1lb/hr Tube Material Number required Pitch, in. Outside diameter, in. Wall thickness, in. length, ft Tube sheet Material Thickness, in. Sheet-to-sheet distance, ft Total heat transfer area, ft< Basis for area calculation Volume of fuel salt in tubes, £t2 Shell Material Thickness, in. Inside diameter, in. Central tube diameter, in. Baffle Type Number Spacing, in. Shell-and-tube one-pass vertical exchanger with disk and dough- nut baffles Four Fuel salt 1300 1050 180 130 23.45 x 10° Coolant salt 850 1150 34 116.2 17.8 x 10° Hastelloy N 5896 0.75 0.375 0.035 22.57 Hastelloy N 4.75 21.31 13,037 Outside of tubes 67.38 Hastelloy N 0.5 68.07 20.0 Disk and doughnut 21 11.23 Table 2.1 (continued) Disk outside diameter, in. 54.56 Doughnut inside diameter, in. 45.54 Overall heat transfer coefficient, U, Btu/hr.ft=«°F 838.3 Tube Maximum primary (P) stresses Calculated, psi 674 Allowable, psi 3912 Maximum primary and secondary (P + Q) stresses Calculated, psi 11,639 Allowable, psi 11,737 Maximum peak (P + Q + F) stresses Calculated, psi 13,006 Allowable, psi 25,000 wave configuration. The tubes are held in place by wire lacing in this upper portion of the tube bundle. Since baffling is not employed in this region, the bent-tube portion of the bundle experiences essentially parallel flow and a relatively lower heat transfer performance. Below the bent-tube region of the bundle, evenly spaced doughnut- shaped baffles are used to hold the tubes in place and to produce cross flow. The baffle spacings and cross-flow velocities are designed to min- imize the possibility of flow-induced wvibration. The tubes in this baf- fled region of the heat exchanger have a helical indentation knurled into their surface to enhance the film heat transfer coefficients and thereby reduce the fuel salt inventory in the exchanger. No enhancement of this nature was used in the upper bent-tube region because of present uncertainty about the reliability of tubes that are both bent and indented. 2.2 Design Calculations Since experience with both the fuel and coolant salts is limited, there was and still is a certain degree of uncertainty associated with the transport properties of salt and its behavior as a heat transfer medium. The design properties of the fuel salt, coolant salt, and of Hastelloy N used in the concept of a single-fluid MSBR and incorporated in the primary heat exchanger computer program are given in Appendix A. As previously described, the tubes in the baffled portion of the primary heat exchanger are helically indented to improve heat transfer performance. Experiments performed by C. G. Lawson, R. J. Kedl, and R. E. McDonald® indicated that this indentation is expected to result in an improvement by a factor of 2 in the tube-side heat transfer coefficient. An enhancement factor of 1.3 for the heat transfer coefficient outside the tubes is suggested by Lawson™ although no experiments have been done to support this recommendation. The experimental work” that was per- formed was limited to Reynolds numbers greater than 10,000, and there is some uncertainty about the degree of improvement that can be expected for Reynolds numbers of less than 10,000. It was assumed that no improvement can be expected in a truly laminar flow (Reynolds numbers less than 1000), and the improvement expected for the intermediate range was extrapolated by using a method suggested by H. A. McLain.> The resulting enhancement factors (EF) are EFi = 2.0 and EF_ = 1.3 for Reynolds numbers > 10,000 and EF, = 1.0 and EFO = 1.0 for Reynolds numbers < 1000, where EFi = enhancement factor inside tube and EFO = enhancement factor outside tube (cross flow). For 1000 < Reynolds number < 10,000, Np, - 1000 1/z . = 1.0 + . EF1 1.0 5000 (2.1) and Np, - 1000 1/2 = 1.0 + 0. 2. EFO 1.0 + 0.3 9000 (2.2) where N, = the corresponding Reynolds number. Re The enhancement factors for heat transfer resulting from the helical indentation of the tubes in the baffled region were assumed to have a proportionate effect on pressure drop. The shell-side pressure drop was calculated by using the procedure reported by 0. P. Bergelin et al.,* and the tube-side pressure drop was calculated by using the conventional friction-factor method. An overall leakage factor of 0.5 was used for the pressure drop in the shell side of the heat exchanger, and a factor of 0.8 was used in the heat transfer calculations. These leakage factors were selected on the basis of recommendations reported by Bergelin et al.” The correct leakage factor, which is dependent upon various clearances between tubes and baffles and between baffles and the shell, will have to be calculated when the actual design for the primary heat exchanger has been completed. Since molten fluoride salts do not wet Hastelloy N, the containing material of the heat exchanger, it was suspected that the usual heat transfer correlations, which are normally based on experiments with water or petroleum products, might not be valid. However, recent experiments performed by B. Cox” indicated that basicaily the behavior of the fuel salt is similar to that of conventional fluids. The correlations devel- oped by Cox result in heat transfer coefficients somewhat lower than those obtained from the Sieder and Tate cofrelations for turbulent regions,7 Hansen's equation for transition regions,8 and the Sieder and Tate correlations for laminar regions.7 The correlations used in this study are those based on the data developed by Cox that were recommended by H. A. McLain.® These are given in Eqs. 2.3, 2.4, and 2.5. For completely turbulent flow with Reynolds numbers greater than 12,000, 0.14 (EF;) (2.3) h.d, i’i kg 1/3 Eh Hi _ 0.8 = 0.217(Ng,) (N Pr) 10 where hi = heat transfer coefficient inside tube, Btu/hr.ft2-°F, ;= inside diameter of tube, ft, k; = thermal conductivity of fluid inside tube, Btu/hr.ft-°F, NRe = Reynolds number, Npr = Prandtl number, B = viscosity at temperature of bulk fluid, 1b/hr.ft, By = viscosity of fluid at temperature of inside surface of tube, 1b/hr«ft, and EF. = enhancement factor for helically indented tubes given in Eq. 2.1. Based on the inside diameter of the tube, the Reynolds number Re By where Gi = mean mass velocity of fluid inside the tube, lb/hr-ftg. For completely laminar flow with Reynolds numbers less than 2100, di) NReNPr'E— 1 +0.0012 h.d. 0.023 = 14.36 + di EFi (2.4) Pr I_ NReN where £ = length of tube from the entrance to the local point, ft. For the intermediate region where 2100 < Reynolds number < 12000, 2/3 0. 14 b1y b (EFi)' (2.5) 1 1 k, i d, 1 £ = 0-089[(1\1&,_)2/3 - 125](Npr)3“/3 1+ % i The pressure drop inside the tubes was calculated by using the expression 2 G - ML Vg )y (2.6) AP. 1 di Zpigc i where friction factor, I." " length of tube, ft, . H inside diameter of tube, ft, 11 mean mass velocity of fluid inside tube, lb/hr-fte, G, = i p; = density of fluid inside tube, 1b/ft", 8. = dimensional conversion factor = 4.18 x 108 1bm-ft/lbf-hr2, and EFi = enhancement factor for helically indented tubes given in Eq. 2.1. The friction factor for turbulent flow (Ng, > 2100) is given by the expression =-0Q.32 (2.7) £ = 0.0014 + 0.125(Ng,) ’ and the friction factor for laminar flow (NRe < 2100) is given by the expression f=— . (2.8) The heat transfer coefficient across the tube wall is given by the expression d -d _ | k} o i hw - (d t) d ’ (2.9) © ln =2 d, i where k = thermal conductivity, Btu/hr.ft:°F, dO = outside diameter of tube, ft, t = wall thickness, ft, and d, = inside diameter of tube, ft. No experiments have been performed to date to develop correlations for the heat transfer behavior of a sodium fluoroborate coolant salt in the shell side of the heat exchanger. The correlation developed byIO. P. Bergelin et al.® was used for the baffled region of the MSBR primary heat O exchanger, and the correlation developed by D. A. Donohuel® was used for the unbaffled region. Although selected as being the most representative available for the % is strictly for cross flow and baffled region, Bergelin's correlation his data were based on work with half-moon shaped baffles with straight edges. Since disk and doughnut baffles are used in the MSBR primary heat exchanger, the adaptation of Bergelin's data involved certain interpreta- tions in determining the cross-sectional areas involved. The correlation 12 for cross flow was also modified by the introduction of a correction factor. This correction factor is dependent upon the degree of actual cross flow that exists as determined by the ratio between the baffle spacing and the annular thickness of the vessel. Data from Bergelin's original experiment4 were used to estimate the value of the correction factor, which is expressed as _00188 BCF = 0.77(3] (2.10) where BCF = correction factor for shell-side heat transfer coefficient as proposed by Bergelin,4 = baffle spacing (as illustrated in Fig. 2.2), ft, and Y = radial distance from center of window to center of opposing window (as illustrated in Fig. 2.2), ft. | l ¢ | T T S S S S S | S _— OUTER SHELL INNER SHELb— [ () - WINDOW ZONE (@ - BAFFLE ZONE (PURE CROSS FLOW) (3 - WINDOW ZONE Fig.k2.2. Zones of Flow Between Two Baffles in the Shell Side of the MSBR Primary Heat Exchanger. 13 In the method advanced by Bergelin,? the region between two baffles is considered as three parts: one pure cross-flow zone between two win- dow zones, as illustrated in Fig. 2.2. The mass velocity in each zone is based on the effective area of each zone. In a window zone, the effective area is given by the expression S, = (sWsB)1/2 (2.11) where SW = free cross-sectional area in baffle window, ftZ, and SB = free cross-sectional area for cross flow between tubes applied at lip of the baffle, ftZ. The effective area of the pure cross-flow zone is given by the expression S = 0-5(Sp + 5 ) (2.12) B2 where the indices 1 and 2 indicate the sides of the pure cross-flow zone. Based on this definition of the areas or zones used to calculate the mass velocity, the Reynolds number for each zone is determined from the expression N = ng (2.13) Re My ’ where d = outside diameter of the tube, ft, 0 G = mass velocity of the fluid outside the tubes, lb/hr-ftZ, and % The relationship between the Reynolds number for each flow zone and viscosity at temperature of bulk fluid, 1b/hr-ft. an appropriate heat transfer factor (J) is developed in Bergelin's meth- od.* The heat transfer factor for the window zone is determined from the expression hw C ub 2/3 . 0.14 I, =T = (EF_) (BCF) (LF) (2.14) P m b where | hW = heat transfer coefficient for window zone, Btu/hr-ftZ.°F, specific heat, Btu/1b.°F, mean mass velocity of fluid, 1b/hr-ft=, 14 k = thermal conductivity, Btu/hr-ft-°F, m = viscosity at temperature of bulk fluid, 1b/hr- ft, viscosity of fluid at temperature of wall surface, 1b/hr-ft, T I EFo = enhancement factor outside helically indented tube given by Eq. 2.2, BCF = correction factor for shell-side heat transfer coefficient given by Eq. 2.10, and LF = leakage factor for heat transfer taken as 0.8. The heat transfer factor for the cross-flow zone (JB) is determined from the expression 2/8 0.14 (EFO)(BCF)(LF) . (2.15) 3! S " Equations 2.16 and 2.17 were derived from the graph of J versus NRe given in Ref. 4 to determine the values of J. The values of J determined from Eqs. 2.16 and 2.17 were then used in Eqs. 2.14 and 2.15 to determine the heat transfer coefficients for the window zones and the cross-flow zone (hw and hB). For 800 < N_ < 10°, J = 0.346(NRe)°-382 (2.16) For 100 < N__ < 800, J 0.571(NRe)°'456 (2.17) The values of the heat transfer coefficients for the window zones (hW and hwg) and the value for the cross-flow zone (hB) were then combined in Eq. 2.18 to determine the total heat transfer coefficient for the region between two baffles. h, =h_a +h_ a +h t B B Wi W1 W23W2 ? (2.18) where a = the area of heat transfer surface in each zone, ft2/ft. The data reported by D. A. Donochuel® were used for heat transfer calculations involving parallel flow on the shell side of the MSBR pri- mary heat exchanger. The heat transfer coefficient outside the tubes is given by the expression k_ [ 4,6\°°[C n h = 0.128( )(12d )OO 2 e o eq do ub ko 0.33 0.14 (2.19) o |oF 15 where , = thermal conductivity of fluid outside tubes, Btu/hr-ft.°F, do = outside diameter of tube, ft, deq = equivalent diameter, ft, G = mass velocity of fluid outside tubes, 1b/hr. £t2, m = viscosity at temperature of bulk fluid, 1b/hr-ft, Cp = gpecific heat, Btu/lb.°F, and poo= viscosity of fluid at temperature of wall surface, 1lb/hr-ft. The overall heat transfer coefficient was then calculated by using the expression U == —T (2.20) + = + —-9) D‘Ir—l D"r-—l d Sdin 0 ivii where ho, hW’ and hi are the shell-side, wall, and tube-side heat trans- fer coefficients, respectively. The shell-side pressure drops in the baffled region of the MSBR primary heat exchanger were calculated by using the equations reported by 0. P. Bergelin et al.* The pressure drop across the cross-flow zone is given by the expression v 2 cross floy = 0670 552 (PLF) (EF) (2.21) where rp = number of cross-flow restrictions, o = density of fluid, 1b/ft2, Vm = cross-flow velocity of fluid (based on effective area Sm given by Eq. 2.12), ft/sec, g, = dimensional conversion factor = 32.2 lby,-ft/lbf-sec®, PLF = pressure drop leakage factor taken as 0.5, and EF = enhancement factor outside helically indented tubes taken as 1.3. The pressure drop across the window zone is given by the expression 2 DVZ 2gC (PLF) (EF) (2.22) = + 0. window (1 0 6rw) 16 where r, = number of restrictions in the window zone and Vz = mean flow velocity (based on the effective area Sz given by Eq. 2.11), ft/sec. The number of restrictions was interpreted as being the number of rows of tubes in the direction of cross flow. The full number was used for the cross-flow zone, while only half of the number of rows was used for each of the window zones. The shell-side pressure drop in the upper bent-tube region of the exchanger was taken as being approximately equal to the pressure drop across one baffled zone. 2.3 Description of PRIMEX The computer program for the MSBR primary heat exchanger, PRIMEX, is presented in Appendix B. 1In this program, each zone between two baf- fles was considered as one increment length. The calculations are begun on the hot side of the heat exchanger, and increments are added until a complete heat balance is achieved. The dependence of each of the physi- cal properties on temperature is given as an empirical equatibn, and these equations are incorporated in the main program. If any of these equations are changed, the appropriate data card must be replaced. The physical property data as well as the other input data required for the PRIMEX program are listed in Appendix B. A list of the output data received from the computer is also presented. A stress analysis subroutine, TUBSTR, is incorporated in the main program. This subroutine performs a preliminary stress analysis of the tubes with the assumption that the maximum tube stress will occur in the upper bent-tube region of the heat exchanger. Pressure stresses, stresses resulting from thermal expansion, and stresses resulting from the thermal gradient across the tube wall are considered. The primary and secondary stresses are computed, and these computed values are compared with the allowable values given in Section III, Nuclear Vessels, of the ASME Boiler and Pressure Vessel Code. A second subroutine, LAGR, is used for 17 interpolation of values from a given table. The complete listing for the main program together with its two subroutines is given in Appendix B. To illustrate the use of the PRIMEX program, the computer input data for the MSBR primary heat exchanger discussed in Subsection 2.1 and the output data printed by the computer are included in Appendix B. The time required for a typical IBM 360/91 computer run of this program is about 2 minutes. 2.4 Evaluation of PRIMEX It is believed that the use of the PRIMEX computer program will result in a primary heat exchanger whose volume of fuel salt will be kept to a minimum and whose design will be more reliable than can be achieved with normal hand calculations. Variations in physical properties and complicated geometries are handled easily, and an extensive parameter study can be made in a very short time. However, the output of a computer program cannot bé better than the input. The input data which have a significant effect on the design of the heat exchanger are the physical properties of the fuel and coolant salts, the heat transfer correlations used, the enhancement factors assumed for the helically indented tubes, and the leakage factors associ- ated with fabrication clearances. The average deviations in the physical properties of the fuel and coolant salts presently used in the program 1 The most notable uncertainties are those reported by J. R. McWherter.? in the physical property values presently are associated with the viscos- ity and thermal conductivity of the fuel salt. The average deviation for the fuel-salt heat transfer correlation is reported® as being about 5.7%. The deviation or error resulting from the use of Bergelin's cor- relation® is not certain, but shell-side heat transfer coefficients nor- mally have a deviation of about 25%. The leakage factor deviation for the pressure drop might be about 20%, and the leakage factor deviation for the shell-side heat transfer coefficient might be about 10%. The enhancement factor deviation might be about 15%. 18 The two extreme cases were checked. All of the pessimistic values were used in one case, and all of the optimistic values were used in the other case. The result was a maximum estimated deviation in the overall heat transfer area (or volume of fuel salt) of +38% (additional area required) for the pessimistic case and -28% (less area required) for the optimistic case. 19 3. RETEX, THE STEAM REHEATER EXCHANGER PROGRAM The coolant salt circulating system in the conceptual design of a single~-fluid MSBR consists of four independent loops, each containing salt circulating pumps, steam generators, steam reheaters, and the shell side of one of the four primary heat exchangers. There are two steam reheater exchangers, which transfer heat from the coolant salt to pre- heated exhaust steam from the high-pressure turbine, in each coolant salt loop; with a total of eight reheaters to meet the total steam reheating requirement of approximately 5.1 X 10% 1b/hr. Each reheater is of the same design, and each has a thermal capacity of about 36.6 MW. At full design load, the coolant salt from the primary heat exchanger enters the shell side of the reheater at a temperature of 1150°F and exits at a temperature of 850°F for return to the primary heat exchanger. The preheated exhaust steam from the high-pressure turbine enters the tube side of the reheater at a temperature of 650°F, flows through the tubes in counterflow to the coolant salt, and leaves the reheater at a temperature of 1000°F for delivery to the intermediate-pressure turbine. Basically, the steam reheater exchangers must meet the same system requirements prescribed for the primary heat exchangers that were dis- cussed in Section 2 of this report. However, since no fuel salt is involved, the desirability of keeping the fluid volume at a minimum is not a critical factor in the design of the reheater. 1In addition, the lower heat load and average temperatures permit more freedom in designing the geometry of the reheater to avoid problems associated with vibration or overstress. Since the design for the steam reheater exchanger is similar to that for the primary heat exchanger, an early version of the basic PRIMEX computer program was modified to fit the requirements of the steam reheater, thereby becoming the RETEX program. The design data and equa- tions used to develop the RETEX computer program are discussed in the following subsections. 20 3.1 Description of Steam Reheater Each of the eight steam reheater exchangers is a horizontal shell- and-tube unit with a single counterflow pass on both the shell and tube sides. 22 in. Each unit is about 30 ft long and has an outside diameter of A typical reheater is illustrated in Fig. 3.1. The preheated exhaust steam enters the tube side of the reheater at a pressure of about 580 psi, flows through the 0.75-in.-0D tubes, and exits at a pressure of 550 psi. There are 400 straight tubes arranged in a triangular-pitch array in each reheater. The surfaces of these tubes are not helically indented to enhance heat transfer, as are those in the primary heat exchanger. The coolant salt enters the shell side of the reheater at a pressure of about 228 psi, flows around disk and doughnut baffles in counterflow to the exhaust steam, and exits at a pressure of 168 psi. Other perti- nent design data for the steam reheater exchanger are given in Table 3.1. Table 3.1. Design Data for MSBR Steam Reheater Exchanger Type Straight shell-and-tube one-pass horizontal unit with disk and doughnut baffles Number required Eight Rate of heat transfer per unit, MW 36.6 Btu/hr 1.25 x 10° Shell~side conditions Hot fluid Entrance temperature, °F Coolant salt 1150 Exit temperature, °F 850 Entrance pressure, psi 228 Exit pressure, psi 168 Pressure drop across exchanger, psi 59.52 Mass flow rate, 1lb/hr 1.16 x 10° Tube-side conditions Cold fluid Exhaust steam Entrance temperature, °F 650 Exit temperature, °F 1000 Entrance pressure, psi 580 Exit pressure, psi 550 Pressure drop across exchanger, psi 29.85 Mass flow rate, 1lb/hr 6.41 x 10° 21 ORNL Dwg 65-1238I - STEAM OUTLET “STUBE SHEET SALT INLET ; I : I *. i i i ’ W; TIE ROD & SPACER | | ‘TT‘ A ;1 ; TUBULAR SHELL _ /"jfiflll[ L ——TUBES //// | ——DISC BAFFLE = DOUGHNUT BAFFLE | —SALT COUTLET INSULATION BAFFLE i ~—_DRAIN LINE ““““““ ~STEAM INLET Fig. 3.1. Typical MSBR Steam Reheater Exchanger. 22 Table 3.1 (continued) Tube Material Number required Pitch, in. Qutside diameter, in. Wall thickness, in. Length (tube sheet to tube sheet), ft Tube sheet material Total heat transfer area, £t2 Basis for area calculation Shell Material Thickness, in. Inside diameter, in. Baffle Type Number Spacing, in. Disk outside diameter, in. Doughnut inside diameter, in. Overall heat transfer coefficient, U, Btu/hr. ft° Tube Maximum primary (P,) stress Calculated, psi Allowable, psi Maximum primary and secondary (P, + Q) stress Calculated, psi Allowable, psi Shell Maximum primary (P,) stress Calculated, psi Allowable, psi Maximum primary and secondary (P, * Q) stress Calculated, psi Allowable, psi Hastelloy N 400 1.0 (triangular) 0.75 0.035 30.26 Hastelloy N 2376 Qutside of tubes Hastelloy N 0.5 21.2 Disk and doughnut 21 each 8.65 17.75 11.61 306 4582 13,000 14,090 39,000 5016 9500 14,550 28,500 23 3.2 Design Calculations When developing the computer program RETEX to analyze the steam reheater exchanger, the properties of the steam were assumed to be essen- tially constant along the length of the exchanger even though it was recognized that some gain in the reliability of the estimates could have been realized by incorporating the steam properties as a function of pressure and temperature. The usual Dittus-Boelter equations were used for the film heat transfer coefficient on the tube side of the exchanger. The other procedures and correlations used in the analysis of the reheater are basically the same as those used for the primary heat exchanger dis- cussed in Subsection 2.2 of this report. Manual computational methods were used to determine the stresses in the steam reheater exchanger. This preliminary stress analysis was based on the requirements of Section III, Nuclear Vessels, of the ASME Boiler and Pressure Vessel Code; and the calculated values are compared with the allowable wvalues in Table 3.1. However, a complete stress analysis as required by Section III of the ASME Boiler and Pressure Ves- sel Code has not been made. 3.3 Description of RETEX The RETEX program, a modified version of the PRIMEX program, was used to analyze the steam reheater exchanger. In the RETEX program, each zone between two baffles is considered as one increment length. The cal- culations are begun on the hot side of the exchanger, and increments are added until a complete heat balance is achieved. The physical property equations for the fuel salt in the PRIMEX program are replaced with the physical property data for the exhaust steam in the RETEX program, and these properties are considered as being essentially constant along the length of the exchanger. The physical properties of the coolant salt are evaluated at the average temperatfire of each increment. The dependence- of the physical properties on temperature is presently expressed in the 24 form of empirical equations incorporated in the main program. If any of these equations are changed, the appropriate data card must be replaced. The RETEX computer program differs from the PRIMEX computer program in that 1. the reheater tubes are not helically indented to enhance heat trans- fer, and no enhancement factors are used in the RETEX program; 2. the reheater tubes are arranged in a triangular-pitch array rather than in concentric circles, and certain geometric calculations are therefore made differently in the RETEX program; 3. none of the reheater tubes are bent in a sine-wave configuration to accommodate differential thermal expansion; and 4. no stress analysis subroutines are included in the RETEX program (stresses were calculated by hand). The computer program for the MSBR steam reheater exchanger, RETEX, is given in Appendix C. A simplified outline of the program in block- diagram form, a list of the input data required, a list of the output received from the computer, and a complete listing of the main program are presented. The RETEX program terms which differ from those of the PRIMEX program are defined. To illustrate the use of the RETEX program, the computer input data for the steam reheater exchanger discussed in Subsection 3.1 and the output printed by the computer are also included in Appendix C. The time required for a typical IBM 360/91 computer run of this program is about 1 minute. 3.4 Evaluation of RETEX Confidence in the design calculations for the steam reheater exchanger is greater than that in the calculations for the primary heat exchanger because the characteristics of steam are more familiar than those of the fuel salt and because no enhancement factors are involved. Vibration problems are not likely to be encountered in the steam reheater because velocities are less than 6.5 fps and the tubes are supported by baffles with a relatively close spacing. 25 The uncertainties associated with the coolant salt are involved in the RETEX program, and the deviations applied for the primary heat exchanger (discussed in Subsection 2.4) are also applicable to the steam reheater. Again, two extreme cases were considered. All the pessimistic values were used in one case, and all the optimistic values were used in the other. The result was a maximum estimated deviation in the overall heat transfer area of +23% (additional area required) for the pessimistic case and -13% (less area required) for the optimistic case. 26 4. SUPEX, THE STEAM GENERATOR SUPERHEATER PROGRAM There are four steam generator superheater exchangers, which transfer heat from the coolant salt to feedwater, in each of the four coolant salt circulating loops of the MSBR concept. The total steam generation require- ment, which includes that needed for the feedwater and preheating the exhaust steam, of about 10 X 10%® 1b/hr is provided by the 16 steam gener- ators, each having a thermal capacity of about 121 MW. These exchangers serve as both steam generators and superheaters. They are operated in parallel with respect to the coolant salt and steam flows, and they are identical in design and operation. At full design load, preheated feedwater enters the exchanger at a temperature of 700°F, and the supercritical steam exits at a temperature of 1000°F. The cool- ant salt enters the exchanger at a temperature of 1150°F and exits at a temperature of 850°F for return to the primary heat exchanger. The factors influencing the design of the steam generator exchanger are partially dependent upon the requirements for the overall MSBR system. The exit temperature and pressure of the steam were dictated by the steam power system selected. The inlet temperature of the steam was determined by considerations relative to the liquidus temperature of the salt and the rapid increase in heat capacity of the supercritical water at temper- atures above 700°F. The inlet and exit temperatures of the coolant salt, the pressure drop, and the total heat to be transferred were dictated by the requirements for the reactor and primary heat exchange systems. In addition to these system requirements, the design for the steam generator exchanger must satisfy stress, stability, and space requirements. Because of the marked changes in the physical properties of the feed- water as the temperature is raised above the critical temperature at supercritical pressures, the heat transfer and flow characteristics wvary considerably throughout the exchanger. The SUPEX computer program was developed to account for these changes by making the heat transfer and pressure drop calculations for incremental tube lengths. The design data and equations used to develop this computer program for analysis of the steam generator exchanger are discussed in the following subsections. 27 4.1 Description of Steam Generator Each of the 16 steam generator superheater exchangers is a U-tube, U-shell unit mounted horizontally with one leg above the other. Each has a single pass on the shell and tube sides with the flow in one side coun- ter to that in the other. The overall length of each exchanger is about 40 ft, and the overall height from the feedwater inlet plenum to the steam outlet plenum is about 12 ft. A typical steam generator is shown in Fig. 4.1. ORNL-DWG TO-1195¢ STeEAM OUTLET FEEDWATER INLET Fig. 4.1. Typical MSBR Steam Generator Superheater Exchanger. 28 The feedwater enters the tube side of the exchanger at a pressure of 3754 psi, flows through the 0.50-in.-0D tubes, and the supercritical steam exits at a pressure of 3600 psi. .The coolant salt enters the shell side of the exchanger at a pressure of 233 psi, circulates in counterflow to the supercritical fluid around segmental baffles, and exits at a pres- sure of 172 psi. Segmental baffles are used to improve the heat transfer coefficient for the salt film and to minimize salt stratification. A baffle on the shell side of each tube sheet provides a stagnant layer of salt to help reduce stresses resulting from temperature gradients across the tube sheets. Location of the steam generator exchanger in a horizontal position reduces the possibility of unstable flow conditions for the supercritical fluid in the tubes. The U-tubes are arranged in a triangular-pitch array and the ends of the tubes are turned 90° to equalize the lengths of the tubes in the exchanger. This equalization of tube lengths further reduces the possibility of unstable flow conditions. The pertinent design data for the steam generator exchanger are given in Table 4.1. Table 4.1. Design Data for MSBR Steam Generator Superheater Exchanger Type U-shell, U-tube one-pass hori- zontal unit with cross-flow baffles Number required 16 Rate of heat transfer per unit, MW 121 Btu/hr 4.13 x 10° Shell-side conditions Hot fluid Coolant salt Entrance temperature, °F 1150 Exit temperature, °F 850 Entrance pressure, psi 233.0 Exit pressure, psi 172.0 Pressure drop across exchanger, psi 61.0 Mass flow rate, 1b/hr 3.82 x 10° 29 Table 4.1 (continued) Tube-side conditions Cold fluid Entrance temperature, °F Exit temperature, °F Entrance pressure, psi Exit pressure, psi Pressure drop across exchanger, psi Mass flow rate, 1b/hr Mass velocity, 1b/hr-ft® Tube Material Number required Pitch, in. Outside diameter, in. Wall thickness, in. Length (tube sheet to tube sheet), ft Tube sheet Material Thickness, in. Total heat transfer area, ft2 Basis for area calculation Shell Material Wall thickness, in. Inside diameter, in. Baffle Type Spacing, ft Number of spaces Supercritical fluid 700 1000 3754 3600 154 6.33 x 10° 2.47 x 10° Hastelloy N 393 0.875 (triangular) 0.50 0.077 76.4 Hastelloy N 4-5 3929 Outside of tubes Hastelloy N 0.375 18.25 Cross flow 4002 19 4.2 Design Calculations The heat transfer coefficient for the supercritical fluid film on the inside of the tube walls is determined by using the correlation reported by H. S. Swenson et al.'® This correlation is given in Eq. 4.1. h.d, d,6\°"%2°MH. - H_ g ) T 1 1 g e 0.231 ) (4.1) 0.813 By b k. v, i i 30 where hi = heat transfer coefficient inside tube, Btu/hr-ftZ-:°F, di = inside diameter of tube, ft, k; = thermal conductivity of fluid inside tube, Btu/hr-£ftZ. °F per ft, G = mass velocity of fluid, 1b/hr-ftZ, By = viscosity of fluid at temperature of inside surface of tube, Ib/hr. ft, H, = enthalpy at temperature of inside surface of tube, Btu/lb, H_ = enthalpy at temperature of bulk fluid, Btu/lb, Ti = temperature of fluid at inside surface of tube, °F, Tb = temperature of bulk fluid, °F, v, = specific volume of bulk fluid, ft3/1b, and v, = specific volume of fluid inside tube, ft3/1b. The values of specific volume and enthalpy for the supercritical fluid under various conditions of pressure and temperature are taken from data 13 A table look-up subroutine reported by J. H. Kennan and F. G. Keyes. is included in the SUPEX computer program for determination of these values. The values of thermal conductivity and viscosity for the super- critical fluid are determined from data reported by E. S. Nowak and R. J. Grosh.’® These data were represented by Eqs. 4.2 and 4.3 in the SUPEX computer program. 2 _ v T + 460|253 1478 BT 0’02191(v - 0.012 492 T + 1446) (4.2) and k = (1.093 X 10 ©)(T + 460)* 45 + (28.54 x 107 4)v™ 1285 (4.3) where v = specific volume, ft°/1b, and T = temperature of fluid, °F. The heat transfer coefficient for the salt film on the outside sur- face of the tubes is determined by using the method proposed by 0. P. Bergelin et al.*’® The experimental data* are presented as correlations between a heat transfer factor (J) and the Reynolds number, with the Reynolds number defined by the expression 31 N. = EQE 4.4) Re ny where dO = outside diameter of tube, ft, G = mass velocity of the fluid, lb/hr-ftg, and B = viscosity at temperature of bulk fluid, 1b/hr-ft. The shell side of the steam generator exchanger is divided into two types of flow regions by the segmental baffles. These are the cross-flow and window regions, and the heat transfer factor is determined for each. The heat transfer factor for the cross-flow region (JB) is given by the expression 2/3 0+14 _ hB Cgub uo T8 = Co |k . (4-3) p B " where hB = heat transfer coefficient for cross-flow region, Btu/hr-ftZ.°F, Cp = gpecific heat, Btu/1b.°F, 4 GB = mass velocity of fluid in cross-flow region, 1lb/hr-ftZ, = viscosity at temperature of bulk fluid, 1b/hr.ft, ~ o = thermal conductivity, Btu/hr-ft-°F, and n, = viscosity of fluid at temperature of outside surface of tube, Ib/hr.ft. The heat transfer factor for the window region is given by the expression h (Cn 2/3 p 40-14 ] =—¥ [Ppb -9 4.6) w CG |k 1 (- pm b where hW = heat transfer coefficient for window region, Btu/hr-ftZ.°F, and G = mean mass velocity, 1b/hr- ft=. The mean mass velocity is given by the expression _ 1/2 G_ (GBGW , 4.7) where Gw = mass velocity of fluid in window region, 1b/hr- ft=. Equations for determining values of J were fitted to the graph of J versus NRe given in Fig. 11 of Ref. 4 for use in the SUPEX computer program. The 32 values of J given by Eqs. 4.8 and 4.9 are used in Eqs. 4.5 and 4.6 to determine the heat transfer coefficients for the cross-flow and window regions (hB and hw)' For 100 < N_ < 800, J = O.571(NRe)'°'456 (4.8) Re and For 800 < N, < 10°, J Re 0.346(NRe)‘°'582 (4.9) In Bergelin's method,4 the heat transfer coefficient for the shell side of the exchanger is a linear combination of the heat transfer coefficients for the cross-flow and window regions weighted by the amount of heat transfer surface in each region and corrected for bypass leakage. Because of the large baffle-spacing-to-shell-diameter ratio (approximately 2.7) required for the steam generator exchanger, an additional correction factor is applied to the shell-side heat transfer coefficient. The total shell-side heat transfer coefficient (ho) is given by the expression o.138/h + BaB hwaw + aB aw h - 0.77B(§Z) , (4.10) where B = bypass leakage factor recommended by Bergelin,? y = distance from the center line of the shell to the centroid of the segmental window area, ft, X = baffle spacing, ft, h, = heat transfer coefficient for cross-flow region, Btu/hr.ftZ-°F 3 a, = area of heat transfer surface in cross-flow region per unit length, ft2/ft, hW = heat transfer coefficient for window region, Btu/hr-ft2-°F, and a = area of heat transfer surface in window region per unit length, ft2/ft. The values of specific heat and thermal conductivity for the coolant salt are treated as constants, independent of temperature, and are included in the input information for the SUPEX computer program. The density and viscosity of the salt are treated as functions of temperature as determined by Eqs. 4.11 and 4.12. 33 o = 141.38 - 0.02466(T) (4.11) and p o= 0.2122 exp[fi%fifl , (4.12) where o = density of coolant salt, 1b/ft=, T = temperature of salt, °F, and n = viscosity of salt, lb/hr-ft. The thermal resistance of the tube wall is calculated for each increment of tube length by using the thermal conductivity of Hastelloy N evaluated at the average temperature of the tube wall for each particular increment. The thermal resistance of the tube wall is given by the expression =.EQ_(1n EQ) (4.13) T\ where Rw = thermal resistance of tube wall, hr-ft2'°F/Btu, d0 = outside diameter of tube, ft, k, = thermal conductivity of tube wall, Btu/hr.ft-°F, and di = inside diameter of tube, ft. The thermal conductivity of the tube wall is given by the expression kw = 0.006375'1‘W + 4.06 (4.14) where 'I'w = mean temperature of the tube wall, °F. The total thermal resistance, based on the outer surface area of the tube, is given by the expression d o R = t hidi 1 + ho + Rw . (4.15) The heat transferred per increment of exchanger length (AQ) is given by the expression 7d_n(AL) (AT ) Mg = = — (4.16) t 34 where = outside diameter of tube, ft, = number of tubes, = increment of tube length, ft, mean temperature difference between coolant salt and super- critical fluid for the particular increment, °F, and = total thermal resistance given by Eq. 4.15. gfiw EBE:SOQ‘ e pressure drop per increment of tube length for the supercritical fluid inside the tubes is given by the expression e - 4EEDLE ) where f = friction factor, AL = increment of tube lengtfi, ft, di = inside diameter of tube, ft, G = mass velocity of fluid inside tube, 1b/hr-ftZ, 8, = gravitational conversion constant, lbm-ftllbf-hre, and o = density of fluid inside tube, 1b/ft>3. The friction factor is given by the expression4 p. 19-32 £ = 0.00140 + 0.125( 7% (4.18) 1 The pressure drops on the shell side of the steam generator exchanger are calculated by using the equations recommended by Bergelin.® The pressure drop across the i-th cross-flow region is given by the expression . O.6rB(_E§_) 4.19) Bi 144 2gcp ? where = number of restrictions in cross-flow region, GB = mass velocity of fluid in cross-flow region, 1b/hr.ft=, and o = density of fluid, 1b/ft>. 35 The pressure drop across the i-th baffle window is given by the expression . (2 +0.6r ) & 4. 20) Wy 144 Zng ’ ’ where r. = number of restrictions in window region and G = mean mass velocity (given by Eq. 4.7), 1b/hr-ft=. The total pressure drop on the shell side of the exchanger is given by the expression N+1 N AP =B AP+ Z AP s (4.21) s p By W i=1 i=1 where B_ = bypass leakage correction factor for pressure recommended by P Bergelin* and N = number of baffles. Detailed stress calculations are not included in the SUPEX computer program, but an approximate value of the allowable temperature drop across the tube wall based on thermal stress considerations is determined for each increment of tube length. This value of allowable temperature drop can be compared with the value of the temperature drop across the tube wall determined in the heat transfer calculations to provide some guid- ance in selecting design parameters. The thermal stresses are treated as secondary stresses. Based on the requirements set forth in Section IIT, Nuclear Vessels, of the ASME Boiler and Pressure Vessel Code; the permissible wvalue for the thermal stresses is given by the expression Arh = arL < 38, - 8 s (4.22) where = hoop and longitudinal stress components caused by temper- 0. o A > Th™ AT L ature differences across the tube wall, psi, S allowable stress intensity based on rules prescribed in Section III of the ASME Boiler and Pressure Vessel Code, psi, and 36 S = total stress intensity resulting from primary membrane stresses plus secondary stresses from all sources other than thermal stresses, psi. The value of S was conservatively estimated to be about 26,000 psi. The tube wall material is Hastelloy N, and for TW < 1015°F, Sm = 24,000 - 7.5(TW) (4.23) and for 1015°F < T, < 1100°F, Sm = 57,000 - 4O(TW) . (4.24) Based on data reported by J. F. Harvey,> the hoop and longitudinal stresses resulting from temperature differences across the tube wall are given by the expression _QE(AEW) 2d° d AT = ATOL T 3 | —;-——Tg( ) s (4.25) In _9) dT - df 2(1 - v) 3 i where a = coefficient of thermal expansion, in./in.-:°F, E = modulus of elasticity for Hastelloy N, psi, AT . = temperature drop across tube wall, °F, v = Poisson's ratio, d = outside diameter of tube, in., and d. = inside diameter of tube, in. The estimated value of S and Eqs. 4.22, 4.23, 4.24, and 4.25 are used in the SUPEX computer program to calculate the allowable value of AEW. The values of E and & are determined in the computer program from Eqs. 4.26 and 4.27. E = [31.65 - 0.005(Tw)3 X 108 (4.26) and o = [0.0031(Tw) + 5.91] x 1078 . (4.27) Although detailed stress calculations are not included in the SUPEX computer program, a preliminary stress analysis of the steam generator exchanger was made by hand. This preliminary analysis was based on the 37 requirements of Section III, Nuclear Vessels, of the ASME Boiler and Pressure Vessel Code; and the hand calculated values are compared with allowable values in Table 4.2. The allowable stress values were taken from data in code case interpretations 1315-3 (Ref. 16) and 1331-4 (Ref. 17). Table 4.2. Preliminary Stress Calculations for MSBR Steam Generator . . . a . Maximum stress intensity, psi Tube Calculated P = 13,900; (Pm + Q) = 30,900 Allowableb Pm = 15,500; (Pm + Q) = 46,500 Shell Calculated = 5800; (Pm + Q) = 13,200 Allowable® = 8800; (P +Q) = 26,400 Maximum tube sheet stress, psi Calculated <17,000 Allowabled 17,000 %The symbols are those of Section III of the ASME Boiler and Pressure Vessel Code where Pm = primary membrane stress intensity, psi, Q = éecondary stress intensity, psi, Sm = allowable stress intensity, psi. bBased on a temperature of 1038°F for the inside surface of the tubes; this represents the worst stress condition. “Based on the maximum or highest temperature of the coolant salt of 1150°F. dBased on a temperature of 1000°F for the steam and use of a baffle on the shell side. 4.3 Description of SUPEX The equations described in Subsection 4.2 are used in the SUPEX pro- gram to size the steam generator exchanger for the specified input data. A flow diagram of the SUPEX program, a list of the input required, and a list of the output received from the computer are given in Appendix D. 38 In the SUPEX program, the total heat to be transferred in the exchanger is divided into a specified number of equal increments. For each increment, heat balance relations for the coolant salt and the supercritical fluid and the heat transfer equations are used to determine the change of temperature for each stream and the tube length required. The pressure drop in the supercritical fluid for each increment and the pressure drop in the coolant salt for each baffle space are calulated and summed. | Two major iteration loops are contained in the SUPEX program. First, the baffle spacing is assumed and iterations are made until the total calculated shell-side pressure drop agrees with that specified. Internal to this loop, the number of tubes in the exchanger is estimated, and iterations are made to give the total tube-side pressure drop speci- fied. A simplified flow diagram of the SUPEX program, a complete list- ing of the program, and a list of terms used in the program are given in Appendix D. Output from the program includes the number of tubes, inside diam- eter of the shell, length of the exchanger, baffle spacing, number of baffles, total heat transfer area, and the apparent overall heat transfer coefficient. The method of calculation used in the program permits the total length of the tubes to differ from the total length of the baffle space by a fraction of the baffle spacing. Both lengths are given in the output, as are the heat transfer area and apparent heat transfer coefficient for each length. The output also includes pertinent informa- tion for each baffle spacing and tube increment. To illustrate the use of the SUPEX program, the computer input data for the MSBR steam generator superheater exchanger described in Subsec- tion 4.1 and the output data printed by the computer are included in Appendix D. The time required for a typical IBM 360/91 computer run of this program is about 30 seconds. 39 4.4 Evaluation of SUPEX The problem of stability in the steam generator superheater was considered. As indicated by K. Goldman et al.t® and by L. S. ’I‘ong,19 instabilities in steam generators can arise from two sources. First, a true thermodynamic instability can exist where, for a given pressure drop across the tube, the fléw rate through the tube may be changed from one steady-state value to another by a finite disturbance. Second, a system instability that is caused by resonant conditions in the fluid can exist. Data related to the first type of instability have been reported by L. Y. Krasyakova and B. N. Glusker,®° and data related to the second type of instability have been reported by E. R. Quandt®' and by L. M. Shotkin.®? A qualitative evaluation of these data indicates that the mass flow rate, pressure drop, and heat flux used in the horizontal U-tube and U-shell design will result in stable operation. Operation of a test module will provide further information about the stability of this design concept. An analysis was made to evaluate the various uncertainties involved in the SUPEX computer program. Tolerances were placed on the physical properties of the coolant salt, the heat transfer coefficients, and on the pressure-drop correlation. The program was run for various cases to determine the quantitative values of the favorable and the adverse effects of the uncertainties. The favorable effects were defined as decreased heat transfer area, decreased shell diameter, and decreased total tube length. The adverse effects were defined as increased values for these same three parameters. The selection of these parameters was based on the belief that the heat transfer area is indicative of the total cost of the exchanger, the diameter of the shell is indicative of the stress prob- lem, and the total length of the tubes is indicative of the physical size of the exchanger. The range of uncertainties studied included the physical properties of the coolant salt with a deviation of 12% for the specific heat and density and a deviation of +10% for the viscosity and thermal conductivity, the tube-side and shell-side heat transfer coefficients with a deviation of + 20%, and the pressure-drop correlation with a deviation of +10%. 40 Scrutiny of the shell-side heat transfer coefficient revealed that positive deviations (increases) in the specific heat and thermal conduc- tivity of the coolant salt and negative deviations (decreases) in the density and viscosity of the salt will produce favorable effects, while opposite deviations will produce adverse effects. A negative deviation (decrease) in the calculated pressure drop will produce favorable effects, while a positive deviation (increase) will produce adverse effects. The results of this analysis in terms of percentage changes relative to the design case are given in Table 4.3. Case 1 is for an increased specific heat and density of the coolant salt and a decreased viscosity and thermal conductivity. Case 2 is for deviations opposite to those of Case 1. Cases 3 and 4 are for increased and decreased, respectively, shell-side heat transfer coefficients; Cases 5 and 6 are for increased and decreased, respectively, tube-side heat transfer coefficients; and Cases 7 and 8 are for decreased and increased, respectively, calculated pressure drops. Case 9 for overall favorable conditions is for the com- bined effect of all favorable changes, and Case 10 for overall adverse conditions is for all adverse changes. Cases 1, 3, 5, and 7 represent favorable changes; while Cases 2, 4, 6, and 8 represent adverse changes. Table 4.3. Percentage Deviations Resulting From Calculational Uncertainties Related to MSBR Steam Generator Exchanger Heat Total Transfer Shell Tube Case Conditions Area Diameter Length 1 Favorable physical properties -8.2 -1.4 -5.6 2 Adverse physical properties +7.6 +1.2 +5.2 3 Increased shell-side heat transfer -10.1 -1.6 -7.0 4 Decreased shell-side heat transfer +13.5 +2.1 +8.8 5 Increased tube-side heat transfer -2.3 -0.5 -1.3 6 Decreased tube-side heat transfer +4.,2 +0.9 +2.3 7 Decreased calculated pressure drop -2.6 -0.5 -1.6 8 Increased calculated pressure drop +1.8 +0.7 +0.5 9 Overall favorable -21 -4 -15 10 Overall adverse +30 +5 +18 10. 11. 12. 13. 41 REFERENCES C. G. Lawson, R. J. Kedl, and R. E. McDonald, '""Enhanced Heat Transfer Tube for Horizontal Condenser With Possible Application in Nuclear Power Plant Design,' Transactions of the American Nuclear Society, Vol. 9, No. 2 (1966). C. G. Lawson, Oak Ridge National Laboratory, personal communication to C. E. Bettis, Oak Ridge National Laboratory. H. A. Mclain, '"Revised Primary Salt Heat Transfer Coefficient for MSBR Primary Heat Exchanger Design,' ORNL internal correspondence MSR-67-70, July 31, 1969. 0. P. Bergelin, G. A. Brown, and A. P. Colburn, "Heat Transfer and Fluid Friction During Flow Across Bank of Tubes -V: A Study of a Cylindrical Baffled Exchanger Without Internal Leakage,' Trans. ASME, 76: 841-850 (1954). 0. P. Bergelin, K. J. Bell, and M. D. Leighton, ''Heat Transfer and Fluid Friction Druing Flow Across Banks of Tubes -VI: The Effect of Internal Leakages Within Segmentally Baffled Exchangers,'" Trans. ASME, 80: 53-60 (1958). B. Cox, "Preliminary Heat Transfer Results With a Molten Salt Mixture Containing LiF-BeF»-ThF,-UF4 Flowing Inside a Smooth, Horizontal Tube,'" ORNL internal document CF-69-9-44, September 25, 1969. E. N. Sieder and G. E. Tate, 'Heat Transfer and Pressure Drop of Liquids in Tubes,'" Industrial and Engineering Chemistry, 28(12): 1429-1435 (1936). H. W. Hoffman and S. I. Cohen, ''Fused Salt Heat Transfer, Part III: Forced Convection Heat Transfer in Circular Tubes Containing the Salt Mixture NaNOp-NaNOz-KNOg,'" USAEC Report ORNL-2433, Oak Ridge National Laboratory, March 1960. H. A. McLain, "Revised Correlations for the MSBR Primary Salt Heat Transfer Coefficient,'" ORNL internal correspondence MSR-69-89, September 24, 1969. D. A. Donochue, '"Heat Transfer and Pressure Drop in Heat Exchangers," Industrial and Engineering Chemistry, 41(11): 2499-2511 (November 1949). J. R. McWherter, '"MSBR Mark I Primary and Secondary Salts and Their Physical Properties,’ ORNL internal correspondence MSR-68-135, Rev. 1, February 12, 1969. H. S. Swenson, C. R. Kakarala, and J. A. Carver, "Heat Transfer to Supercritical Water in Smooth-Bore Tubes,'" Transactions of the ASME, Series C: Journal of Heat Transfer, 87(4): 477-484 (November 1965). J. H. Keenan and F. G. Keyes, Thermodynamic Properties of Steam, John Wiley and Sons, New York, 1936. 14. 15. 16. 17. 18. 19. 20. 21. 22. 42 E. §. Nowak and R. J. Grosh, "An Investigation of Certain Thermodynamic and Transport Properties of Water and Water Vapor in the Critical Region,' USAEC Report ANL-6064, Argonne National Labora- tory, October 1959. J. F. Harvey, Pressure Vessel Design, D. Van Nostrand Company, New Jersey, 1963. Case 1315-3, 'Nickel-Molybdenum-Chromium-Iron Alloy," Interpreta- tions of ASME Boiler and Pressure Vessel Code, The American Society of Mechanical Engineers, New York, April 25, 1968. Case 1331-4, "Nuclear Vessels in High-Temperature Service,'" Interpre- tations of ASME Boiler and Pressure Vessel Code, The American Society of Mechanical Engineers, New York, August 15, 1967. K. Goldman, S. L. Israel, and D. J. Nolan, 'Final Status Report: Performance Evaluation of Heat Exchangers for Sodium-Cooled Reactors,' Report UNC-5236, United Nuclear Corporation, Elmsford, New York, June 1969. L. S. Tong, Chapter 7 in Boiling Heat Transfer and Two-Phase Flow, John Wiley and Sons, New York, 1965. L. Y. Krasyakova and B. N. Glusker, "Hydraulic Study of Three-Pass Panels With Bottom Inlet Headers for Once-Through Boilers," Teploenergetika, 12(8): 17-23 (1965), (UDC 532: 621.181.91.001.5). E. R. Quandt, "Analysis and Measurement of Flow Oscillations,” Chemical Engineering Progress Symposium Series, Vol. 57, No. 32, 1961. L. M. Shotkin, '"Stability Considerations in Two-Phase Flow,'" Nuclear Science and Engineering, 28: 317-324 (1967). APPENDICES 45 Appendix A PHYSICAL PROPERTY DATA The design properties of the fuel salt used in the concept of a single-fluid MSBR and incorporated in the PRIMEX computer program are given in Table A.l. The design properties of the coolant salt used in the MSBR concept and incorporated in the PRIMEX, RETEX, and SUPEX com- puter programs are given in Table A.2; and the design properties of Hastelloy N used in the MSBR concept and incorporated in these compfiter programs are given in Table A.3. Values for the density, viscosity, and thermal conductivity of the fuel and coolant salts were taken from data reported in Ref. A.1l. The value given for the heat capacity of the fuel salt is taken from Ref. A.2, and the value given for the heat capacity of the coolant salt is taken from Ref. A.3. These references are listed below. A.1. Oak Ridge National Laboratory, "Molten-Salt Reactor Program Semi- annual Progress Report August 31, 1969," USAEC Report ORNL-4449, February 1970. A.2. 0Oak Ridge National Laboratory, '"Molten-Salt Reactor Program Semi- annual Progress Report August 31, 1968," USAEC Report ORNL-4344, February 1969. A.3. Oak Ridge National Laboratory, '"Molten-Salt Reactor Program Semi- annual Progress Report February 29, 1969," USAEC Report ORNL-4254, August 1969. 46 Table A.1. Design Properties of MSBR Fuel Salt Fuel salt components 7LiF-BeFa—ThF4—UF4 Composition, mole % 71.7-16-12-0.3 Approximate molecular weight 64 Approximate melting point, °F 930 Vapor pressure at 1150°F, mm Hg <0.1 Density,” g/cm3 o = 3.752 - (6.68 x 10-%)T°C 1b/ft3 o = 235.0 - 0.02317T°F At 1300°F p = 204.9 1b/ft3 At 1175°F p = 207.8 1b/ft3 At 1050°F o = 210.7 1b/£ft® Viscosity, Centipoise = 0.109‘exp g?;o 1b/ft-hr n o= 0.2637(exp %%%2) At 1300°F n = 17.29 1b/ft-hr At 1175°F n = 23.78 1b/ft-hr At 1050°F n = 34.54 1b/hr-ft Heat capacity,® Cp = 0.324 Btu/1b-°F + 47 Thermal conductivityd At 1300°F k = 0.69 Btu/hr-°F-ft At 1175°F k = 0.71 Btu/hr.°F.ft At 1050°F k = 0.69 Btu/hr-°F.ft aFigure 13.6 on page 147 of Ref A.l. Drable 13.2 on page 145 of Ref A.1. “Page 163 of Ref. A.2. dFigure 9.13 on page 92 of Ref. A.1. The value of k shown is for salt with about 5% less LiF than in the reference salt. Addition of LiF would increase the average value to about 0.72 to 0.74. The established and conservative value of 0.71 was used in the calculations for the MSBR concept. 47 Table A.2. Design Properties of MSBR Coolant Salt Coolant salt components NaBF4—NaF Composition, mole % 92-8 Approximate molecular weight 104 Approximate melting point, °F 725 Vapor pressure at 1150°F, mm Hg 252 Density,a -4 g/cm3 p = 2.252 - (7.11 X 10 ")T°C Ib/ft3 p = 141.4 - 0.0247T°F At 1150°F o = 113.0 1b/ft3 At 1000°F p = 116.7 1b/ft3 At 850°F o = 120.4 1b/ft3 Viscosity, Centipoise n = 0.0877(exp ifio 1b/ft-hr B = 0.2121(exp iggz At 1150°F p=2.60 1b/ft-hr At 1000°F n = 3.36 1b/ft-hr At 850°F n=4.61 1b/ft-hr Heat capacityc Cp = 0.360 Btu/1b.°F + 2% Thermal conductivity,d At 1150°F k = 0.23 Btu/hr.°F.ft At 1000°F k = 0.23 Btu/hr. °F-ft At 850°F k = 0.26 Btu/hr.°F.ft a b Figure 13.6 on page 147 of Ref. A.l. Table 13.2 on page 145 of Ref. A.1l. CPage 168 of Ref. A.3. dFigure 9.13 on page 92 of Ref. A.l. 48 Table A.3. Design Properties of Hastelloy N Composition, wt % Nickel Balance Molybdenum 12 Chromium 7 Iron 0 to 4 Manganese 0.2 to 0.5 Silicon, maximum 0.1 Boron, maximum 0.001 Titanium 0.5 to 1.0 Hafnium or niobium 0 to 2 Cu, Co, P, S, C, W, Al 0.35 Density, 1b/ft3 At 80°F 557 At 1300°F 541 Thermal conductivity, Btu/hr-ft.°F At 80°F 6.0 At 1300°F 12.6 Specific heat, Btu/lb-.°F At 80°F 0.098 At 1300°F 0.136 Thermal expansion per °F At 80°F 5.7 x 107° At 1300°F 9.5 x 107° Modulus of elasticity, psi At 80°F 31 x 10° At 1300°F 25 x 109 Tensile strength, psi At 80°F ~115,000 At 1300°F ~75,000 Maximum allowable design stress at 1300°F, psi At 80°F 25,000 At 1300°F 3500 Melting temperature, °F 2500 49 Appendix B THE PRIMEX PROGRAM The PRIMEX computer program is outlined in block-diagram form in Fig. B.1. The input data required for the program are given in Table B.1, and the output received from the program are given in Table B.2. A complete listing of the main program and its two subroutines is fol- lowed by definitions of the intermediate variables used in the program. To illustrate the use of the PRIMEX program, the input and output for the MSBR primary heat exchanger discussed in Subsection 2.1 of this report are presented as printed by the computer. 50 & C K ) READ AND PRINT INPUT DATA v ASSUME BAFFLE SPACING © >} ASSUME SHELL DIAMETER O, 2 CALCULATE NUMBER OF TUBES, FUEL AND COOLANT FLONS AND VARIOUS GEOMETRIES @ 2 ASSUME EXPANSION RADIUS REQUIRED FOR ACCEPTABLE STRESSES v START WITH FIRST INCREMENT FROM HOT SIDE OF HEAT EXCHANGER I=1 v ASSUME TEMPERATURE OROP FOR THE INCREMENT 0, >y EVALUATE ALL PHYSICAL PROPERTIES AT AVERAGE TEMPERATURE OF INCREMENT v CALCULATE PRESSURE DROPS AND HEAT TRANSFER COEFFICIENTS FOR THE INCREMENT, USING CORRECT CORRELATION FOR DIFFERENT REGIMES v CALCULATE HEAT RATE AND TEMPERATURE OROPS OF THE INCREMENT Fig. B.1l. Simplified Flow Diagram of the PRIMEX Computer Program. 51 DO INCREMENT TENPERATURE DROPS AGREE WITH OUR ASSUMPTION ? CHANGE ASSUMED INCREMENT TEMPERATURE DROP DOES END TEMPERATURE OF INCREMENT EQUAL TO SPECIFIED END TEMPERATURE OF HEAT EXCHANGER G0 TO NEXT INCREMENT I=1+1 CALCULATE STRESSES IN TUBES ARE ALL STRESSES ACCEPTABLE ? CHANGE ASSUMED EXPANSION RADIUS DOES TOTAL TUBE SIDE PRESSURE DROP ACCEPTABLE CHANGE ASSUMED SHELL DIAMETER ? Fig. B.l. (continued) 52 DOES TOTAL SHELL SIOE PRESSURE DROP ACCEPTABLE CHANGE ASSUMED BAFFLE SPACING ARE THERE ADDITIONAL CASES FOR PARAMETER STUDY ? PRINT OUTPUT v (: END _:) Fig. B.1l. (continued) 53 Table B,1, Computer Input Data for PRIMEX Program Card Columns Format Variable Term Units A 1-10 E10.4 Heat load required HEATL Btu/hr 11-20 F10.0 Allowable tube-side pres- PRDT 1b/ft? sure drop 21-30 F10,0 Allowable shell-side PRDS 1b /2 pressure drop 31-40 F10.0 Tube-side inlet pressure TPIN 1b/ft? 41-50 F10.0 Shell-side outlet pressure SPOUT 1b/ft® B 1-10 F10.0 Coolant outlet temperature CTO °F 11-20 F10.0 Fuel inlet temperature FTO °F 21-30 F10.0 Fuel outlet temperature ETF °F 31-40 F10.0 Coolant inlet temperature ETC °F C 1-10 F10.0 Leakage factor for heat LK transfer correlations 11-20 F10.0 Leakage factor for pres- PLK sure drop calculations 21-30 F10.0 Tube material conductivity WCOND Btu/hreft«°F 31-40 F10.0 Arc of bent tube for ther- ARC Degrees mal expansion 41-45 15 Number of pair points in ICNPT Stress intensity table for tube material D ,0s. 1-10 F10.0 Stress intensity at CTM CASM psi temperature DicypT 11-20 F10.0 Temperature CTM °F E 1-10 F10.0 Radius of coolant central RAS ft downcomer 11-20 F10.0 Distance between shell DTR ft wall and tube bundle 21-30 F10.0 Maximum anticipated heat RASMAX ft exchanger radius 31-35 15 Number of cases to be run KASES 36-40 15 Index one if enhanced KENTB tubes are used 41-45 I5 Index one if stress anal- KTBST ysis is included 4 R”,E. 1-10 F10.0 Outside diameter of tubes DIA ft . 11-20 F10.,0 Tube wall thickness WTHK ft FKASES 21-30 F10,0 Radial pitch RPI ft 31-40 F10.0 Circumferential pitch BCPI ft 41-50 F10.0 Inner baffle cut CUT3 % of area 51-60 F10.0 Outer baffle cut CUT4 7% of area 54 Table B.2. Output Data From PRIMEX Computer Program Term Variable Units THEATO Total heat actually transferred Btu/hr HTPERC Percentage of required heat load actually transferred QC Coolant (shell-side) mass flow rate 1b/hr QF Fuel (tube-side) mass flow rate lb/hr TTDSO Total tube-side pressure drop psi SPPERC Percentage of allowed tube pressure drop actually used TTDTU Total shell-side pressure drop psi TPPERC Percentage of allowed shell pressure drop actually used RAS8 Radius of heat exchanger shell ft BSOTI Distance between baffles ft VOL Fluid volume contained in tubes ft2 AREA Total heat transfer area in heat exchanger fto SNT Total number of tubes TUBLEN Actual tube length ft HEXLEN Heat exchanger length from lower tube sheet ft to upper nozzle of tubes STRLEN Straight section length of tubes ft EXPRAD Radius of tube bends for thermal expansion ft BRL1 Modification factor for Bergelin's heat transfer correlation PSTO Primary stresses on outer surface of tubes psi PQSTO Combined primary and secondary stresses on psi outer surface of tubes PQFSTO Combined primary, secondary, and peak psi stresses on outer surface of tubes PSTI Primary stresses on inner surface of tubes psi PQSTI Combined primary and secondary stresses on psi inner surface of tubes PQFSTI Combined primary, secondary, and peak psi stresses on inner surface of tubes SAVT Shell average temperature °F TAVT Tube average temperature °F 55 Table B.2 (continued) Term Variable Units TCI(I) Coolant outlet temperature from increment I °F TCO(I) Coolant inlet temperature from increment I °F CWT (1) Average tube wall temperature at coolant side °F TFI(I) Fuel outlet temperature from increment I °F TFO(I) Fuel inlet temperature from increment I °F FWT(I) Average tube wall temperature at fuel side °F TWDT (1) Average temperature drop across tube wall in °F increment I VMI(I) Fluid average velocity in outer window in ft/sec increment I VM2(1) Fluid average velocity in overlapping baffle ft/sec zone in increment 1 VM3 (1) Fluid average velocity in inner window in ft/sec increment 1 VWO1(I) Fluid velocity across tubes in outer edge of ft/sec baffle in increment T VW03 (1) Fluid velocity across tubes in inner edge of ft/sec baffle in increment T PDSO(I) Shell-side pressure drop for increment I 1b /ft? PDTO(1) Tube-side pressure drop for increment I lb/ftg RENTO(I) Tube-side Reynolds number for increment I PRNTO(TI) Tube-side Prandtl number for increment I RENSO1 (1) Reynolds number in outer window increment I RENSO02 (1) Reynolds number in overlapping baffle zone in increment I RENSO03 (1) Reynolds number in inner window in increment I HTO(I) Tube-side heat transfer coefficient in Btu/hr-ft2-°F increment I AHSO(I) Shell-side heat transfer coefficient in Btu/hre ft° +°F increment I UOA(T) Overall heat transfer coefficient in Btu/hr-ft2-°F increment I HEAT (1) Heat transferred in increment I Btu/hr *%FTN 1001 1002 1003 1604 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1C15 1016 1617 1018 1019 The PRIMEX Program listing ’L'E’G’M- PROGRAM MSBRPE-Z2 TYPE REAL LK s LAWO1l 4 LAWO3 DIMENSION TFOCT75), TCIC(T7E)4VML(T75) 4VM2(T75) yVWC1(T75)VWC3 (751}, IRENTO(75 ), PRNTO(75) 4RENSOL(75),RENSO2¢(75) yRENSC3(75), 2VM3(T75) 4 PDSO(75)sNT(100)4BJ(3)yHSOL(T75) yHSC2(75) +HSO3 (75) , BAHSO(T75) yHTO(T75) sUCALTS) 4 TCOLT5) o TFI (750 4HEAT(T75) s TWDT(T75) 4PDTO(75),y TUBLN{T75), VI(75)9sV2(T75)+V3(T75) 4VWL(T5) sVW3(T75), 5 R(100), FACT(100), TCPI{100), TOTAL(100) +CASM(E) LCTM(6) 6 CHWT(75)sFWT(T75),AVWT(75) FORMAT( E10.4, 4F10.0) FORMAT( 4F10.0) FORMAT( 4F10.0,15) FORMAT(2F10,4) FORMAT( 3F10.0,315) FORMAT( 6F10.0) FORMAT (1H197X 91HI 4 8Xy3HCTMy TXy4HCASM//(4X41542F12.21)) FORMAT(22HOHEAT LOAD REQUIRED = +F12.0+2X,8H{(BTU/HR)) FORMAT (43HOALL OWABLE TOTAL TUBE-SIDE PRESSURE DRCP = 4F10.0+2Xy 1 10H(LB/SQ-FT) ) FORMAT (44HCALLOWABLE TCTAL SHELL-SIDE PRESSURE CRCP = ,F10.0,2X, 1 10H{LB/SQ-FT) ) FORMAT(23HOTUBE INLET PRESSURE = 4F10.0492X,1CH(LB/SQ-FT)) FORMAT (24HOSHELL OUTLET PRESSURE =¢F10.0,2X,10H(LB/SQ-FT)) FORMAT(33HOHIGH TEMP. OF SHELL SIDE FLUID =,F104242Xs3H(F)) FORMAT(33HOHIGH TEMP. OF TUBE SIDE FLUID = 4F10.2:2X+s3H(F)) FORMAT(32HCLOW TEMP. OF TUBE SIDE FLUID = 4F10.242Xs3H(F)) FORMAT({32HOLOW TEMP., OF SHELL SIDE FLUID =,F1C.2¢2Xs3H{(F))} FORMAT(32HOHEAT TRANSFER LEAKAGE FACTOR = ,4F10.5) FORMAT (27THOPRESSURE LEAKAGE FACTCR = LF10.5 ) FORMAT(35HCCONDUCTIVITY OF TUBE WALL METAL = +F10.5+2X, 1 13H(BTU/HR-FT-F) ) MSBRP MSBRP MSBRP MSBRP MSBRP MSBRP MSBRP MSBRP MSBRP MSBRP MSBRP MSBRP MSBRP MSBRP MSBRP MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR 10 20 30 31 32 33 34 35 36 40 50 60 70 80 90 100 110 120 121 130 131 140 150 160 170 180 190 200 210 220 221 9¢ 1C20 FORMAT(37HOARC OF FOUR BENDS FOR FLEXIBILITY = ,F10.2 42X, 1 9H(DEGREES)} 1021 FORMAT(34HOINSIDE RADIUS OF OUTER ANNULUS = yF10.5,2X+6H(FEET)) 1022 FORMAT(41HODISTANCE BETWEEN SHELL WALL AND TUBES = 1 +F10.5¢2X,6H(FEET) ) 1023 FORMAT(4SHOMAXIMUM ANTICIPATED QUTER RADIUS CF EXCHANGER = , 1 F10.542X+s6H(FEET) ) 1024 FORMAT(23HONUMBER OF CASES RUN = ,414) MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR 1025 FORMAT(25HOUSE OF ENHANCED TUBES = +14,2X+32H(ONE IF ENHANCED TUBEMSBR 1S ARE USED)) 1026 FORMAT(1HO,36HUSE OF STRESS ANALYSIS SUBRCUTINE = , 1 I442X419H(ONE IF TO BE USEDI}} 1027 FORMAT(29HOOUTSIDE DIAMETER OF TUBES = +F10.5,2Xy O6H(FEET) ) 1028 FORMAT(27HOWALL THICKNESS OF TUBES = +F10e5+2Xy O6H(FEET) ) 1029 FORMAT(1EHORADIAL PITCH = 4,F10.542Xy 6H(FEET)) 1030 FORMAT{25HOCIRCUMFERENTIAL PITCH = 4F10.542Xy 6H(FEET}) 1031 FORMAT(22HOINNER BAFFLE CUT3 = ,Fl0.5,2Xys 10H(PER CENT} } 1032 FORMAT(22HOOUTER BAFFLE CUT4 = 4F10.542Xy 1O0H(PER CENT) ) 1033 FORMAT(25H1TOTAL HEAT TRANSFERED = 4F12.0+2X,8H(BTU/HR), 1 2Xy IH( 9+ F5.1+9H PERCENT}) 1034 FORMAT(29HOMASS FLOW RATE OF COOLANT = ,F10.0,2X, 7H(LB/HR} ) 1035 FORMAT(26HOMASS FLOW RATE OF FUEL = +F10.042Xy 7H(LB/HR} ) MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR 1036 FORMAT(34HOSHELL-SIDE TOTAL PRESSURE DROP = F1l0.292Xy 9H(LB/SQIN)IMSBR 1 12X ¢1H(4F5.1y9H PERCENT)) MSBR 1037 FORMAT(33HOTUBE-SIDE TCTAL PRESSURE DROP = 4F10.242X, S9H(LB/SQIN),MSBR 1 2Xy IH( 4 F5.149H PERCENT) ) 1038 FORMAT(24HONOMINAL SHELL RADIUS = 4FT7.4+2X+4H(FT)) 1039 FORMAT(2¢HOUNIFORM BAFFLE SPACING = +FT74442X4H(FTY}) 1040 FORMAT(4OHOTUBE FLUID VOLUME CONTAINED IN TUBES = ¢F7.2+1X, 112H(CUBIC FEET)) 1041 FORMAT(1FHO,46HTOTAL HEAT TRANSFER AREA BASED ON TUBE CeDe = o 1 F12.24+2Xs EH(SQFT) ) 1042 FORMAT(25HOTOTAL NUMBER OF TUBES = ,Fé.0) 1043 FORMAT(Z21HOTOTAL TUBE LENGTH = ,F6.2 92X +s4H(FT}) 1044 FORMAT(29HOHEAT EXCH. APPROX. LENGTH = F6.2+2Xs6H(FEET)) 1045 FORMAT(35HOSTRAIGHT SECTICN OF TUBE LENGTH = sF6.242X +4H(FT)) MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR 1046 FORMAT(38HORADIUS GF THERMAL EXPANSION CURVES = +F6.2+2Xy6H(FEET) IMSBR 230 231 240 250 251 2 60 261 270 280 281 290 291 300 310 320 330 340 350 360 361 370 380 390 391 400 401 410 420 430 431 440 441 450 460 470 480 490 LS 1047 1048 1 2 1049 1 8X94HPDSO 18Xy 4HPDTO/ /32X 6HFT/SEC33X s THLB/SQFT//(1X41347F12.4)) FORMAT (3 1IHOBERGLIN MODIFICATION FACTOR = ,Ff5.2) FORMAT (1HO 42Xy 1HI» 7TX¢3HTCI ¢9X¢3HTCOyGXs3HCWT 99X, IXy 3FFWT ¢ 8Xy 4HTWDT//11 Xy 1HF 911X IHF 911X 9o1HF 411X, BHTFI+9Xs3HTFOy 1FFy 11Xy IHF 9 11X 1HF 311X 1HF//7 (1 X913 47ELZe4)) FORMAT(1HO 92X 1HE» GXy2HV1 y 9X42HVZ +9X+2HV3 49X¢3HVWL +9X+3HVW3 1050 FORMAT(1HO+2Xy1HIL 95Xy 5HRENTO » 7Xy SHPRNTO ¢ 7X96HRENSCL 96 X9 6HRENS G2, 16Xy 6HRENSO3, 7TX33HHTO, 8X y4HAHSO,9X y3HUCA +8 Xy4HHEAT// 77 X, 2 1051 1052 1053 1 1054 FORMAT(1HO,36HP+Q STRESS AT TUBE OD AND TUBE ID = 1 2 1055 FORMAT(1HO,38HP+Q+F STRESS AT TUBE OD AND TUBE 1D 1 2 13HBTU/HR/SQFT/F 413Xy EHBTU/HR//(1X41349EL12.41)) FORMAT(27HOTUBE WALL AVERAGE TEMP. = +F10.2) FORMAT (28HOSHELL SIDE AVERAGE TEMP., = 4, F10.2) FORMAT(1HO,34HP STRESS AT TUBE 0D AND TUBE ID = SH{LB/SQIN}//18H( SHOULD NOT EXCEED+F10424+3H 1)) ' 2F10.241X, 2F104291X,9H(LB/SQIN) //1BH{SHOULD NCT EXCEED,F10.2, 3H 1)) 2F10.291Xy9H{LB/SQIN) //18H(SHCOULD NCY 3H ) READ IN AND PRINT OUT INPUT DATA KEY7= 1 VM1(1)=0. VM2(1)=0. VM3(1)=0. VWO1(1)=0. VWO3{1l)=C. RENSOL1(11=0. RENSO2(1)=0. RENSO3(11=0. HS01(1)=0. HSO02(1)=0. HSO3(1)=0. HEF 1 1. HEFO l. -9 EXCEED+F10a2 ? MSBR MSBR MS BR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR 500 510 511 512 520 521 530 531 532 540 550 56C 561 570 571 572 580 581 582 650 660 610 620 630 640 650 660 610 680 690 700 716 720 730 740 810 8¢ READ READ READ READ READ 1001, 1002, 1003, 1005, CONTINUE READ PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT: PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT 1006, HSFCT=1O IF(FTO.LT.CTO) 1008, 1C09, 1¢10, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, RA5, DIA, HEATL, CT0, LKy HEATL PRDT PRDS TP IN SPOUT CTO FTO ETF ETC LK PLK WCOND ARC RAS DTR RA 8MAX + KASES KENTB KTBST DIA WTHK RPI BCPI CuT3 CuT4 + TPIN, SPOUT FTC, ETF, PLK s WCONDyARC ,ICNPT 1004, (CASM(K) 4CTM(K) yK=1,ICNPT) DTRy RABMAX,KASES,KENTB,KTBST WTHK, HSFCT==-1. 1007+ (KyCTM(K)4CASM{K) yK=1 ,ICNPT) MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB 760 770 780 790 800 810 820 830 840 850 860 870 880 890 500 910 920 930 940 G50 960 970 980 990 10Co 1010 1020 1030 1040 1050 10 60 1C70 10 80 1650 39 BEGIN GECMETRY CALCULATIONS FOR SINGLE ANNULLS CCUNTER FLOW DISC AND DOUGHNUT BAFFLED HEAT EXCHANGER ARCR= C.017452%ARC ATUBE = (3.14159% (DIA**%2.0))/4.0 GFTT = 1./3600. GFT = 1./144. DIAI=DIA-2.0%WTHK FATUB =(3.14159%(DIAI**2.,0))/4.C KEYl = 0 PERC1 = 0.99 IF{KEY1l. GT.C)IBSOI=0.5*(BSL+BSH) KEYZ2 = C PERCZ2 = C.99 RA8BL =RA5 RABH=RA8BMAX RA8=0.5%¥(RASL +RABH ) RJB={(RAB8-RA5-2.*%DTR}/RPI+1. I1J8=RJ8 RIJ8=1J8 IF(RJB-RIJB~0e5) 4y 445 J8=1J8 TRPI=(RA8~RAS5+-2.*%DTRI/(RI1J8-1.) CPI=BCPI*RPI/TRPI GO TO 6 J8=1J8+1 TRPI=(RA8-RAS5-2.*DTR)/RIJE8 CPI=BCPI*RPI/TRPI DO 7 1I=1,J8 ROI)=RAS54DTR+TRPI*(I-1} FACT(I)=6,28318*%R( 1) NT(I)=FACT(I}/CPI TCPI(II=FACT(I)/NT(I) IF(I.EQ«1)TOTALCII=NT(I) IFC(INE.1)TOTALCTI)=TOTALCI-1)+NT(I) NTO=TOTAL(J8) SNT=NTO RAS52=RA5%%2 RAB2=RA8%*%2 MS8B MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB 1660 1670 1120 1130 1140 1150 1160 1170 1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1210 1320 1330 1340 1350 1360 137C 1380 1390 1400 1410 1420 1430 1440 1450 1460 1470 09 RA6=(RA52+CUT4*(RAB2-RA52))%**,5 J6={RA6~R(1) }/TRPI+1, RAG=R(JEI+.5%TRPI RA7=(RAB82-CUT3*(RA82-RAE2) ) *%,5 J7=(RA7T-R(1)}/TRPI+1. RAT=R(J7)+.5%TRPI RA62=RA6X*x2 RAT2=RA7*%2 RB1=0,5%(J8-J7) RB2=J7-J6 RB3=0.5%J6 SUM1=TOTAL(J8}-TOTAL(JT7) SUM2=TOTAL(JT)-TOTAL(J6) SUM3=TOTAL(Jé€) ISUM1=5SUM1 ISUMZ2=SUM2 ISUM3=5UM3 BSMAX=1.5%((RAB~(RAB~RAT7) /24 )=(RA5+(RA6-RA5)/2.)) BSMIN=0. 2% (RA8~RA5) IF(BSMIN.LT.0.1667)BSMIN=0,1667 APO1=3.14159%(RA82-RAT2)-ATUBE*SUMI] AP03=3,14159%(RA62-RA52)-ATUBE*SUM3 LAWO1=6.28318%RA7T-¢S*DIAX(NT(JTI+NT(JIT+1)) LAWO3=6. 2831 8%RA6~S*DIAX(NT(J6)4NT(J6+1)) HW=2.*WCOND/ (DIA*(ALOG(DIA/DIAI))) CSPHAV=0.36 FSPHAV=0.324 QC=HEATL/(CSPHAV*(CTO-ETC)) QF=HEATL/( FSPHAV*( FTO-ETF)) GTO = QF/(NTO*FATUB) KEY3=0 XPRMAX=6,.,0 XPRMIN= 0. EXPRAD= Q.5%(XPRMIN+XPRMAX) IF(KTBST.EQ.Q)EXPRAD=1.77 IF(KEY1l.EQ.0)BSH=B SMAX IF(KEY1.EQ.0)BSL=BSMIN MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 1630 1640 1650 1660 1670 1680 1690 1700 1710 1720 1730 1740 1750 1760 1770 1780 1790 1800 1810 1820 1830 1840 19 10 11 IF(KEY1.EQ.O)BSOI=0.5*%(BSL+BSH) CURVES=0,069813%ARC*k EXPRAD+ Q.4*%(RAB-RAS)+,25%BS0I IT =0 KFINAL=0 I=1 TSUM=0. SSUM=0. THEATO = TPDTO TPDSC TFO(I)=F TCI(I}=C TIF=-5.0 TiIC=-5.0 CDTF=0. FDTF=0. BSO = BSOI BRL1 BSO/({(RAB-(RA8-RAT7)/2.)-(RAS+ (RA6-RA5)/2.1) GBRL C.7T7*BRL1**(-,138) AWO1 BSO*LAWC1 AWO3 BSO*LAWO3 AWl SQRT(AWC1*APOL) AW?2 (AWO1+AWO3) /2. AW3 SQRTLAWO3*AP03) GSO1 QC/AW1 GS02 QC/AW2 GSO3 QC/AW3 BSO=CURVES EQVBSO= CURVES+ 13.*%(DIA+DIAIL) KEY 4=0 KEY5=0 ATC .0 0 0 it oH 0 0. c. 10 10 Wi oot TCI(I) + (TIC/2.0) CFT ATC +CDTFXHSFCT ATF TFO(I)+TIF/2, FFT=ATF-FOTF*HSFCT FI=1 TUBULN(I) =(FI-1.)*BSOI+CURVES CVIS=0.2121%EXP(4032./(460.,+ATC)) Hon MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS8B MS B MS B RY MSB MSB MSB MSB MSB MSB MSB MSB MS B MSB MSB MS8 MSB 1850 1860 1870 1880 1890 1500 1910 1920 1930 1940 1950 1960 1970 1980 199C 2000 2010 2020 2030 2040 2G50 2060 20760 2C 80 2090 2100 2110 2120 2130 2140 2150 2160 2180 22C0 2210 2220 <9 C 12 13 14 15 1 1 1 CVISW=0.2121*%¥EXP(4032./(460,+CFT)) CDEN=141.37-0.02466*ATC CCON=0.240 CSPH=0.36 FVIS=D0.263T*EXP(7362./(460.+ATF})) FVISW=0.263T7T*EXP(7362./(460C.+FFT)) FDEN=234.97-0.02317*ATF FCON=0.70 FSPH=0.224 VISK = (CVIS/CVISWI}*%0.14 FVISK=(FVIS/FVISWI**0,14 DCVIS CIA/CVIS CCDEN 1. /CDEN QCCDEN = QC*CCDEN o CALCULATE REYNOLS AND PRANDTL NUMBER TUBE SIDE RENTO(I)=DIAI*GTO/FVIS PRNTO( 1) =FVIS*FSPH/FCON IF(KENTB+EQe¢ 1. AND.RENTO(I) .GT.1001. IHEF I=14+((RENTO(I)-10004) 79000, ) **0. 5 POTO(I )=(,0028+. 25%RENTO%**(~,32) }*¥EQVBSC*GTO**2*HEFI1/ (DIAI*FDEN*4171824C0. ) CALCULATE HEAT TRANSFER CCEFF TUBE SIDE HTO(I)=FCON/DIA* 0217 (RENTO(I ) **,8) *(PRNTO(I)*%43333 )*FVISK*HEFI GO 10 15 IF(RENTO(I).LT.2100.) GC TO 14 HTO(I) = FCON/DIA*,089% (RENTO(I ) **,6666-125,)%(PRNTO(I)*%,3333)% FVISK*HEFI*(1e+43333%(DIAL/TUBLN(I) )**,6666) GO TO 15 HTO(I) = FCON/DIA*(4.36*(0.025*RENTO(Il*PRNTO(I)*DIAI/TUBLN(I) )/(1.+0.0012*RENTO(I }*PRNTO(I ) *DIALI/TUBLN(I))) IF(I.EQ.1)GO TO 16 CALCULATE FLOW AREAS SHELL SIDE VWO1(I) = QCCDEN/AWOL VWO3(I) = QCCDEN/AWO3 VML(I) = GSO1*CCDEN VM2(I) = GSO2%CCDEN VM3(I) = GSO3%CCDEN eAND.TeNEel) MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS 8 MSB MS8B MSB MSB MSB MSB MSB MSB MSB 2230 2240 2250 2260 2270 2280 2290 2300 2310 2320 2330 2340 2350 2360 2550 2380 2390 2400 2401 2410 2411 2640 2430 2440 2450 2460 2461 2470 2480 2481 2490 2480 2510 2520 2530 2540 2550 t9 16 17 CALCULATE PRESSURE DROPS SHELL SIDE DP1 (1.4.6*%RBY)IXCDEN*VML(I }*%2 DP2 s 6¥RB2*¥CLEN®VM2( I )*%2 DP3 (1.+.6*%RB3)*CDEN®VM3(] }*%*2 RENSOL(TI) GSG1*DCVIS RENSOZ(I) GS02*DCVIS RENSO3(I) GSO3*DCVIS IF(KENTB.EQe1«AND.RENSC2(I)eGT.1001.) oo " ton PDSO(I) = (DP1+DP2+DP3)*PLK*HEFQ0/834624000. IF(I.EQ.2)PDSO(1)=PDSO(2) CALCULATE BJ FACTOR AND SHEL SIDE COEFFICIENT BJ(1) =(0.346%RENSOL(I)**{-0,382))%GBRL BJ(2) =(0.346%RENSO2(I ) **(-0,382) )*GBRL BJ(3) =(0.346%¥RENSO3(I)*%*(~-0.382) )*GBRL HSOL1(I) = (LK*CSPH*GSO1*BJ(1 I *( (CCON/(CSPH*CVIS) )*¥,66) )*VISK HSO2{I) = (LK*CSPH*GSO2*BJ(2)*( (CCON/(CSPH*CVIS))*%x,66))*VISK HSO3(I}) = (LK*CSPH*GSO3%BJ(3)*((CCON/(CSPH*CVIS) )*%k,66))*VISK AHSOC(TI)=(((HSOLCT)*SUML1 )+ (HSC2(I)*SUM2)+(HSO3(I )*SUM3))/SNT)*HEFO GO T0 17 PDSO(I)=0, APO=3.14159%(RA82-RA52)~SNT*ATUBE EQVDIA=4 .*AP0O/(3.,14159%SNT*D[A+6,24318%(RAB+RA5)) GS0=QC/APO RENSO =GSO*DCVIS PRESO =CVIS*CSPH/CCON AHSO(I)=0.128%CCON*VISK*(12.*EQVDIA*RENSO 1 ¥%0,6 1 *PRESO *%¥0.33/DIA UOA(I)=1.0/0(1.0/AHSO(I ) +(1.C/HTC(I))+(1.0/HW)) A = QF*FSPH B = QC*CSPH D = UOA(I)*SNT*BSO *3,1415S*DIA P = =HSFCT*(D*(A-B))/(A*B) PBAR = EXP(P) C = (B-A)*PBAR TCOCI) = ((TCI(II*(B*PBAR-A))=-(TFC(I ) *AX{PBAR-1.})))/C MSB MSB MSB MS8 MSB MSB MSB MSB MSB MSB MS 8 MS B MSB MSB MS B MSB MSB MSB MSB MSB MSB MSB MS B MSB MSB MSB MSB MSB MSB MSB MS8 MSB MSB MSB MSB 2590 2570 2580 2590 2600 2610 2620 2630 2631 2640 2650 2730 2670 2680 2690 2700 2710 2720 2730 2740 2750 21760 2770 2780 2790 2800 2810 2811 2820 2830 2840 2850 2870 2880 2890 79 18 19 IF((ABS(CYIF-TIF)eLE«{3e0))sAND. (ABS(CTIC~TIC).LE.(3.0)))G0O TO 18 =((TCOCTI-TCICI)I®*B/AY + TFOC(I) = (HEAT(I)/NTO)*ALOG(DIA/DIAL)/(2.0%3,14159%BS0O*WCOND) TFI(CI) HEAT(I) ==AX(TFI(I) - TFO(I)) TWDT(I) CTIF = TFI(I)-TFO(I) CTIC = TCO(I)-TCI(I) TIF = CTIF TIC = CTIC KEY5=KEYS+1 IF(KEY5.,GT .50)G0 TQO 37 GO TO 11} THEATO TPDTC TPDSO IF(I1.EQe 2) TPDSO=TPDSO+PDSO(1) COTF=(((HEAT(I)}) THEATO + HEAT( TPDTO + PDTO(I) TPDSO + PDSO(I) FDTF=CDT F*AHSO(I) /HTO FWT(1) CwrT(I) AVWT(I) TSUM=TSUM+AVWT(I) SSUM=SSUM+ATC [F(KFINAL.EQel .AND.I.EQ.IT) GO TO 20 IFCC(ABS(ETF=-TFI(I) M) LE.((ABS(TFI(I)-TFO(I)))/2.0)).0R. =ATF-FDTF*HSFCT =ATC+CDTF*HSFCT =0 5% (FWT(1) I) /NTO)/BSO) /7(3.14159%DIA*AHSC(1)) (I} +CWT(I)) 1 (TFI(I)L.LE.ETF)) GO TO 169 I=1+ 1 IF(I.GT.75) GO TO 30 IF(I.EQ.2) ATC1=ATC TFOC(I) TCI(I) B8S0=BSOI EQVBSO=B SO KEY4=KEY 4+] IF(KEY4.GT .501G0 TO 36 GO TO 10 KFINAL=1 IT=1 FIT -— - IT TFI(I-1) TCO(I-1) MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS B MSB MSB MSB MS B MSB MSB MSB MSB MSB MS8B MSB MSB - MSB MSB MSB MSB MS B MSB MSB 2900 2910 2920 2930 2940 2950 2960 2970 2980 2990 aco0c 3010 3020 3030 3040 3090 3100 3130 3140 3150 3050 3060 3061 3070 3080 3160 3170 3180 3190 3200 321¢ 3220 3230 3240 3250 3260 €9 20 21 22 23 24 DCURVE=CURVES*((HEATL-THEATO) /HEAT(1)}) CURVES=CURVES+DCURVE GO TO 9 TUBLEN=( FIT~1. )*BSOI+CURVES HEXLEN=( FIT-1.)%BSOI+4.*EXPRAD*SIN{ARCR) +DCURVE+0Q.25*BSMAX STRLEN=(FIT=1. }*BSOI+DCURVE+.25%BSMAX ITF( KTBST.EQ.Q)} GO TC 24 T1=FWT(1) T2=CWT (1) PDTO1=PDTO(1) PDS01=PDSO(1) - TSUM=TSUM-AVWT (1) PN e SSUM=SSUM-ATC1 TAVT=(CURVES*AVWT(1)+BSOI*TSUM) /TUBLEN SAVT=((HEXLEN-BSOI*(FIT-1e) ) *ATCL+BSOI*SSUM) /HEXLEN CALL TUBSTR(TPIN,SPOUT,PDTO1l ,PDSO1,TPDSO»yT1,T2, HEXLEN, EXPRADyDIAT 4DIAWARCHETF4+FTO+ETC 4CTO4SAVT,,TAVT, T11eT124T13,T244T254T364T737,T738,749,T7410,0T, BN,ASM, ST+STPySQPySLPRySLPGySLLCySLLI »STTO,STTI +TM,CASM,CTM, PlsP2+SAsR1,R2,TLsRB, AAl,AA2,AA3,AA4,AAS5,BE1,BB2, 883,8B4,+BB5) KEY3=KEY3+1 IF(KEY3.GT.50)0G0 TO 35 IF(T24.LT.0.0,0R.T12.LT.0.0) GO TO 22 IF(T24.GT.(.08*%ASM) AND.T12.GT. (. C8%ASM)) GO TO 23 GO TO 24 | XPRMIN=EXPRAD GO 70O 8 XPRMAX=EXPRAD GO T0 8 . VOL = 0.7854%(DIATI**2,0)*NTO*TUBLEN CHECK OF TUBE AND SHELL PRESSURE DROPS KEYZ2 = KEYZ2 + 1 IF(PERC2.LE.Q0.1) GO TO 33 IF(TPDTO.LT.(PERC2*PROT)} GO TO 25 IF(TPDTO.GT.PRDT) GO TO 26 GO TO 27 ‘ MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS8 MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB M5B MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB 3270 3280 3290 3300 3310 3320 3330 3340 3350 3360 3370 3380 3390 3400 3410 3420 3421 3422 3423 3424 3425 3430 3440 3450 3460 3470 3480 3490 3500 3510 3520 3250 3540 3550 3560 3570 3580 99 25 26 27 28 29 30 1057 IF(RAB.LE.(RAS +0.005)) GO T0O 34 RABH =RAS8 IF(KEY2.NE.320)GO TO 3 RA8BL=RA8BL-C,?2 PERC2 = PERCZ2 - (.C1 KEYZ2=1C GO TO 3 IF(RA8.GE.(RABMAX-0C.005)) GO TO 34 RA8L =RAS8 IF(KEY2.NE.30) GO 7O 3 RABH=RA8H+0./2 PERC2 = PERC2 - 0.01 KEYZ2=10 GO TO 3 KEY1l = KEY1l + 1 IF(PERCL.LE.O.1) GO TO 22 IFC(TPDSO.LT.(PERC1*PRDS)) GO TO 28 IF(TPDSO.GT.PRDS)IGO TO 29 GO 7O 38 IF(BSOI.LE.(BSMIN+0,005))G0 TO 31 BSH =BSOI IF(KEY1.NE.30)GO TO 2 BSL=BSL-0.1 PERC1 = PERCl - (.01 KEY1=10 GO TO 2 IF(BSOI.GE.(BSMAX-0.,005})G0 TG 31 BSL =BSOI ‘ IF(KEY1.NE.30) GO TO 2 BSH=BSH+0.1 PERC1 = PERC1 - 0.01 KEY1=10C GO TO 2 PRINT EXIT SIGNALS PRINT 10°%1,BSO0 FORMAT(3GH1BAFFLE SPACINGS EXCEEDE 75 WITH BSC GO TO 38 1F5.242X94H(FT) ) MSB MS 8B MS8 MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS8 MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB 3590 3600 3610 3620 3630 3640 3650 3660 3670 3680 3690 3700 3710 3720 3730 3760 3770 3780 3790 3800 3810 3820 3830 3840 3850 3860 3870 3880 3890 39C0 3910 3920 3930 3640 3650 3960 3970 3980 L9 31 1058 32 1059 33 1C60 34 1061 35 1062 36 1063 37 1064 38 39 PRINT 10E2 FORMAT(2CHIBSOI = MAX. OR MIN.) GO TO 38 PRINT 1059 FORMAT(48H]1 PERC1 FOR SHELL PRESSURE DROP IS LESS THEN 0.1) GO TG 38 PRINT 1060 FORMAT(48H1 PERC2 FOR TUBE PRESSURE DRGP IS LESS THEN 0.1) GO TO 38 PRINT 1061 FORMAT(29H1 SHELL RADIUS = MAX. CR MIN.) GO TO 38 PRINT 1062, KEY3 FORMAT(6HLIKEY3= ,15) GO TO 38 PRINT 1063, KEY4 FORMAT(6H1KEY4= ,15) GO TO 38 PRINT 10¢4, KEYS5 FORMAT(6H1KEY5= ,15) GO TO 38 END OF CASE, PRINT QUTPUT DO 39 I = 1,17 VI(I) = VMI(I)*GFTT V2{I) = VM2(I)*GFTT V3(I) = VM3{I)*GFTT VW1(I) = VWOL(I)*GFTT VW3(I) = VWO3B(I)*GFTT CONTINUE TTDSO = TPDSO*GFT TTDTO = TPDTO*GFT TPPERC=TPOTO%*100./PRDT SPPERC=TPDSO*100./PRDS HTPERC=100.*THEATO/HEATL AREA=3,14159*DIA*SNT*TUBLEN MSB MSB MSB MSB MSB MS8 MSB MSB MSB MSB MSB MSB MSB MSB MSB MS B MSB MSB MSB MSB MSB MSB MSB MSB MSB MS8 MS8B MS8 MSB MSB MS8B MSB MSB MSB MSB MSB 3990 4000 4010 40 20 4030 40 40 4050 4C €0 4C70 40 80 4090 4100 4110 4120 4130 4140 4150 4160 4170 4180 4190 3810 3820 4220 4230 4240 4250 4260 4270 4280 4290 4300 4310 4320 4330 4340 89 C C 40 ASM3=3,%ASM PSTO=AAl PQSTO=AAZ2 PQFSTO=AA3 PSTI=BB1 PQSTI= BB4 PQFSTI=BB5 PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINY PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT 1 PRINT 1033, THEATO, HTPERC 1024, QC 1025, QF 1036,TTDSO, SPPERC 1027, TTDTO, TPPERC 1038,RA8 1039,BS01 1040,VCL 1041, AREA 10424 SNT 1043, TUBLEN 10444 HEXLEN 1045, STRLEN 1046 ,EXPRAD 1047, GBRL 1051 ,TAVT 1052 4 SAVT 1053,PSTO,PSTI,+ASM 1054,PQSTOL.PQSTI yASM3 1055,PQFSTO,PQFSTI 4 SA 1048y (L2 (TCICI)oTCOCI)4CWTLL) » TWDTCI) Da1=1,1IT) 10494 (T4 (VI(I)sV2(T)4yV2(I) 4 VWI(I)VW3(I)},PDSO(I),PDTO(I))}, 1 [=1,1IT) PRINT 10Z20,(I, (RENTO(I)PRNTO(I) +RENSC1(I),RENSC2(I),RENSG3(I), IHTOCI )y AHSO(I) JUCA(I) +HEAT(I)) +I=1,1IT) LOOP FOR ADDITIONAL CASES IF REQUIRED CONTINUE TEICL) +TFC(I) oFWT(I), MS8 MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS B MSB MSB MSB MSB MSB MSB MSB MSB MSB MS8B MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB 4350 4360 4370 4380 4390 4400 4410 1640 4430 4440 4450 4460 4470 4480 4490 4500 4510 4520 4530 4540 4550 4560 4570 4580 4590 4600 4610 4620 4630 46 31 4640 4641 4650 4651 4240 4250 468C 69 4] CcC CcC cC KEY7=KEY7+1 IF(KEY7.GT.KASES)IGO TO 41 GO TO0 1 wm PN CONTINUE END SUBROUTINE TUBSTR(TPINySPOUT.+PDTC1,PDSC1sTPDSOsT1,T2, HEXLEN, EXPRADDIATI 4yDIAJARCETF4FTOLETC4CTOySAVTTAVT, Tll!TlZvT].B'TZ‘f’TZS, T36,T371T38 1T49 'Tli'lO'DT' BF'ASM' ST+STP+SQP 9 SLPRySLPG+SLLOySLLI +STTOLSTTI 4TM,CASHF,CTM, PlyP2¢SAyR1,4,R2,TLyRBy AAl,AA2,AA3,AA4,AA5,BB1,BB2, BB3,BB4,BB5) DIMENSION CASM(6),CTM(6) GFT=1./144. Pl=(TPIN-.5%¥PDTO1l )*GFTY P2=(SPOUT +.5%PDSO1 }*GFT R1=64*%DIAI R2=6.*DIA TL =12 .%HEXLEN RB=12.*EXPRAD A=0.017452*ARC MSB 4690 MSB 4700 MSB 4710 MSB 4720 MSB 4730 TUBST TUBST TuBST TUBST TUBST TUBST TUBST TUBST TUBST TUBST TUBST TUBST TUBST TUBST TUBS DETERMINE AVERAGE CHANGE IN TEMPERATURE OF SHELL(DTS) AND TUBE(DTT) DTS = SAVT-70. DTT = TAVT-7C. CALCULATE PRESSURE AND TEMPERATURE DIFFERENTIAL ACROSS TUBE WALL, DP = P1-P2 DT = T1-T2 AND AVERAGE TEMPERATURE OF TUBE WALL TM = (T1+T21})/72. TUBS TUBS TUBS TUBS TuBS TUBS TUBS 10 11 12 13 14 15 20 30 50 60 70 80 S0 100 110 120 130 140 150 160 170 180 0L CC CcC cC cc CcC cC CC CALCULATE MOMENT OF INERTIA OF TUBE CRGSSECTICN{AMI) AMI = 0.7853G68%(R2**¥4-R1%*%*4) CALL SUBROUTINE TO DETERMINE ALLCWABLE STRESS(ASV) CALL LAGR (CASMyCTM,ASM,TMy2,46 v+ IERR) ESTABLISH MATERIAL PROPERTIES CONSTANTS SA= 25000.0 EM = 25C00000.0 PR = 0,3 TE = 0.CN00078 SE = C.0C00076 CALCULATE AXIAL LOAD AND MOMENT DUE TO LCNGITUCNAL EXPANSION DY = TLX(TE*DTT-SE*DTS) RM = (R2+R1)/2. TW = R2-R1 AL = TW*RB/RM*%x2 AL2 = AL%%Z2 AK = (1.+12.%AL2)/(10.+12.%AL2) AA = 2.%A P = 25000000.*AK*AMI*DY/(RB**3% (AAXCOS(AA) -3, *SIN(AA) +4,.%A)) BM = P*RB*(1.-CO0S(A)) CALCULATE Q STRESS DUE TO P SQP = -P/(6.28318%RM*Th) CALCULATE Q STRESS DUE T0O M Bl = 6/ (Detb*AL2) B2 = BM/(AK*AMI) B3 = (R2/RM)*%x2 B4 = (R1/RM)*%x2 B5 = 1.5%RM*B2¥%AL*B1 SLLO = R2*BZ2*(1.-B1*B3) SLLI = R1*B2*(1.-B1*B4) STTO = B5%(1.-2.%B3) STTI = B5%(1l.~2.%B4) CALCULATE F STRESS DUE TO TUBE WALL TEMPERATURE CROP ST = 13G.,%DT SLI = -S7 ST = -S7 SLO = ST STO = ST TUBS TUBS TUBS TUBS TUBS TUBS TuBS TUBS TUBS TUBS TUBS TUBS TUBS TuBS TUBS TUBS TUBS TuBS TUBS TuBS TuBS TUBS TUBS TUBS TusS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS 190 200 210 220 230 240 250 260 270 28C 290 300 310 320 33C 340 350 3€0 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 1L CC cC CC cC cC CC cC cC cC cC cc ccC CALCULATE STRESSES DUE TO PRESSURE HOOP STP = DP*RM/TW LONGITUDNAL SLPR = STP/2. SLPG = 0 RADIAL SRPI = =-P1 SRPO = =~P2 P STRESS TuBE OD BEND OD All =AMAX1{(STP,SLPRySRPC) Al2 =AMIN1{(STP+SLPR+SRPC) AAl Al1l-A12 T11 ASM- ABS(AA]l) P+Q STRESS TuBE OD BEND 0D Al3 =AMAX1(STP+STTO,SLPR+5QP+SLLG,SRPO) Al4 =AMINL(STP+STTO,SLPR+SQP+SLLC,SRPO) AAZ2 = Al2-Al4 Tl2 = 3%ASM- ABS(AAZ2) P+Q+F STRESS TUBE OD BEND 0D Al5 =AMAX1(STP+STTO+STO+SLPR+SQP+SLLC+SLO,SRPC) Al6 =AMIN1(STP+STTO+STOsSLPR+SQP+SLLO+SLO.SRPC) AA3 = Al15-Al¢ T13 = SA - ABS(AA3) P STRESS TUBE OD BEND 1ID SAME AS P STRESS AT TUBE CD BEND 0D -- T11) P+Q STRESS TUBE OD BEND ID A22 =AMAX1{STP+STTO,SLPR+SQP-SLLC,4SRPO) A23 =AMINL{STP4+STTO,SLPR+35QP-SLLC,SRPD) AAG = A22-A23 T24 = 3%ASM- ABS{AA4) P+Q+F STRESS TUBE 0D BEND ID A24 =AMAX1{STP+STTO+STOsSLPR+SQP-SLLO+SLO,SRPOI A25 =AMINI(STP+STTO+STO,SLPR+SQP-SLLO+SLO,SRFC) AAS = A24-A25 T25 = SA - ABS(AA5) TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TusS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TuBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 5 GFT 81 Magnitude of longitudinal stress resulting from BM on outside diameter of tube, psi. Magnitude of longitudinal stress resulting from BM on inside diameter of tube, psi. Magnitude of hoop stress resulting from BM on outside diameter of tube, psi. Magnitude of hoop stress resulting from BM on inside diameter of tube, psi. Temperature differential across tube wall, °F. Tube-side pressure, psi. Shell-side pressure, psi. Allowable stress intensity for cyclic analysis, psi. Inside radius of tube, in. Outside radius of tube, in. Length of tube (difference in elevation of tube ends; HEXLEN in PRIMEX main program), in. Radius of flexibility bend segments, in. Maximum primary (P) stress intensity on outside surface of tube at bend OD, psi. Maximum primary and secondary (P + Q) stress intensity on out- side surface of tube at bend OD, psi. Maximum peak (P + Q + F) stress intensity on outside surface of tube at bend OD, psi. Maximum primary and secondary (P + Q) stress intensity on out- side surface of tube at bend ID, psi. Maximum peak (P + Q + F) stress intensity on outside surface of tube at bend ID, psi. Maximum primary (P) stress intensity on inside surface of tube at bend OD, psi. Maximum primary and secondary (P + Q) stress intensity on inside surface of tube at bend OD, psi. Maximum peak (P + Q + F) stress intensity on inside surface of tube at bend OD, psi. Maximum primary and secondary (P + Q) stress intensity on inside surface of tube at bend ID, psi. Maximum peak (P + Q + F) stress intensity on inside surface of tube at bend ID, psi. Conversion factor, feet to inches. Arc of four bend segments in flexibility bend, radians. DTS DTT DP AMI EM PR TE SE DY RM ™ AL AL2 AK AA P 82 Average change in temperature of the shell, °F. Average change in temperature of the tubes, °F. Pressure differential across tube wall, psi. Moment of inertia of tube cross section, in.% Modulus of elasticity for tube and shell material, psi. Poisson's ratio for tube and shell material (0.3). Coefficient of thermal expansion for tube material, in./in.°F. Coefficient of thermal expansion for shell material. Difference in thermal expansion of tubes and shell, in. Mean radius of tube wall, in. Thickness of tube wall, in. Dimensionless parameter in Wahl's factor AK. Square of AL. Wahl's rigidity multiplication factor. Two times A. Axial load resulting from restrained thermal expansion, 1lb. B1, B2, B3, B4, B5 Repeated factors used in calculating stresses result- SLI STIL SLO STO SRPI SRPO All Al2 Al3 Al4 ing from BM. Longitudinal stress on inside diameter of tube resulting from temperature differential across tube wall, psi. Hoop stress on inside diameter of tube resulting from tempera- ture differential across tube wall, psi. Longitudinal stress on outside diameter of tube resulting from temperature differential across tube wall, psi. Hoop stress on outside diameter of tube resulting from tempera- ture differential across tube wall, psi. Radial stress on inside diameter of tube resulting from pressure, Ppsi. Radial stress on outside diameter of tube resulting from pres- sure, psi. Maximum value of primary (P) stress on outside surface of tube at bend OD, psi. Minimum value of primary (P) stress on outside surface of tube at bend 0D, psi. Maximum value of primary and secondary (P + Q) stress on out- side surface of tube at bend 0D, psi. Minimum value of primary and secondary (P + Q) stress on out- side surface of tube at bend OD, psi. Al5 Al6 A22 A23 A24 A25 B11l B12 B13 B1l4 B15 B1l6 B23 B24 B25 B26 83 . Maximum value of peak (P + Q + F) stress on outside surface of tube at Minimum tube at Maximum Minimum value of primary and side surface of tube at bend value of peak (P +Q Maximum tube at Minimum tube at Maximum at bend Minimum at bend Maximum surface Minimum surface Maximum tube at Minimum tube at Maximum surface Minimum surface Maximum tube at Minimum tube at bend OD, psi. value of peak (P + Q bend 0D, psi. value of primary and side surface of tube at bend bend 1D, value of peak (P + Q bend 1D, value of primary (P) 0D, psi. value of OD, psi. primary (P) + F) stress on outside surface of secondary (P + Q) stress on out- ID, psi. secondary (P + Q) stress on out- ID, psi. + F) stress on outside surface of + F) stress on outside surface of stress on stress on value of primary and secondary of tube at bend 0D, psi. value of primary and secondary of tube at bend OD, psi. inside surface inside surface (P + Q) stress (P + Q) stress of tube tube inside inside value of peak (P + Q + F) stress on inside surface of bend OD, psi. value of peak (P + Q + F) stress on inside surface of bend OD, psi. value of primary and secondary (P + Q) stress on inside of tube at bend ID, psi. value of primary and secondary (P + Q) stress on inside of tube at bend ID, psi. value of peak (P + Q + F) stress on inside surface of bend 1D, psi. value of peak (P + Q + F) stress on inside surface of bend ID, psi. Computer Input for Reference MSBR Primary Heat Exchanger I CTM CASM 1 800.00 18CC0.00C 2 S00.00 18C00.00C 3 1000.00C 17CCn.00 4 1100.0C 130€0.00 5 1200.00 6CC0.00 6 1300.00 3500.00 HEAT LOAD REQUIRED = 18997565808. (BTL/HR) ALLOWABLE TOTAL TUBE-SIDE PRESSURE DROP = 18720. (LB/SQ-FT) ALLOWABLE TOTAL SHELL-SIDE PRESSURE DROP = 16727. (LB/SQ-FT) TUBE INLET PRESSURE = 25920« (LB/SQ-FT) SHELL OQUTLET PRESSURE = 4896. (LB/SG-FT) HIGH TEMP., OF SHELL SIDE FLUID = 115C.00 (F) HIGH TEMP. OF TUBE SIDE FLUID = 130C.00 (F) LOW TEMP. OF TUBE SIDE FLUID = 1050.C0 (F) LOW TEMP. OF SHELL SIDE FLUID = 850.0C (F) HEAT TRANSFER LEAKAGE FACTOR = ¢.8CC00 PRESSURE LEAKAGE FACTOR = - 0.52C00 CONDUCTIVITY OF TUBE WALL METAL = 11.60000 (BTU/HR-FT-F) %8 ARC OF FQOUR BENDS FOR FLEXIBILITY = 60.00 (DEGREES) INSIDE RADIUS OF OUTER ANNULUS = 0.83330 (FEET) DISTANCE BETWEEN SHELL WALL AND TUBES = C.03125 (FEET) MAXIMUM ANTICIPATED OUTER RADIUS OF EXCHANGER = 6.000C0 (FEET) NUMBER OF CASES RUN = 1 USE OF ENHANCED TUBES = 1 (ONE IF ENHANCED TUBES ARE USED) USE OF STRESS ANALYSIS SUBROUTINE = 1 (ONE IF TO BE USED) OUTSIDE DIAMETER OF TUBES = 0.03125 (FEET) WALL THICKNESS OF TUBES = 0.00292 (FEET) RADIAL PITCH = 0.06250 (FEET) CIRCUMFERENTIAL PITCH = 0.06250 (FEET) INNER BAFFLE CUT3 0.40000 (PER CENT) H OUTER BAFFLE CUT4 0.400C0 (PER CENT) ¢8 Computer Output for Reference MSBR Primary Heat Exchanger TOTAL HEAT TRANSFEREL = 189956480C. (BTU/HR) (100.0 PERCENT) MASS FLOW RATE OF COOLANT = 17590736. (LB/HR) MASS FLOW RATE OF FUEL = 23454320. (LB/HR) SHELL-SIDE TOTAL PRESSURE DROP = 116.16 (LB/SQIN) (10C.0 PERCENT) TUBE-SIDE TOTAL PRESSURE DROP = 125.€1 (LB/SQIN) ( 99.7 FERCENT) NOMINAL SHELL RADIUS = 2.83¢4 (FT) UNIFORM BAFFLE SPACING = 0.9256 (FT) TUBE FLUID VOLUME CONTAINED IN TUBES = 67.38 (CUBIC FEET) TOTAL HEAT TRANSFER AREA BASED ON TUBE G.D. = 13037.C2 (SAFT) TOTAL NUMBER OF TUBES = 58%G6. TOTAL TUBE LENGTH = 22.52 (FT) HEAT EXCH. APPROX. LENGTH = 21.31 (FEET) STRAIGHT SECTION OF TUBE LENGTH = 18.325 (FT) RADIUS OF THERMAL EXPANSION CURVES = 0.86 (FEET) BERGLIN MODIFICATICN FACTOR = 0.80 TUBE WALL AVERAGE TEMP. = 1113.04 SHELL SIDE AVERAGE TEMP. = 10C7.83 98 P STRESS AT TUBE OD AND TUBE ID = SHOULD NGT EXCEED 3912. 53 P+Q STRESS AT TUBE OD AND TUBE ID = SHOULD NGT EXCEED 11737, 58 P+Q+F STRESS AT TUBE OD AND SHOULD NCT EXCEED i Vo0 Wmd N - TCI F N.1150E C.1129E D0.1115E 0.1101€E 0.1087E 0.1074E 0.1060E 0.1046E 0.1032E 0.1018E 0.1004E 0.9895E 0.9754E 0.9614E 0.9474E 0.9334E 0.9194E 0.9054E 0.8915E 0.8776E C.8638E 04 04 04 04 04 04 C4 04 04 Q4 04 03 03 03 03 03 03 03 03 03 03 25000. TCO F 0.1129E 0.1115E 0.1101E 0.1087E 0.1074E 0.1060E 0.1046E 0.1032E 0.1C18E 0.1004¢E 0.9895E 0.9754E D.9614E 0.9474E 0.9334E 0.9194E 0.9054E 0.8915E 0.8776E 0.8638E 0.8500E 00 04 04 C4 04 C4 C4a 04 04 04 04 03 03 03 03 03 03 03 03 c3 03 03 €73.9C ) 11£39.02 ) TUBE ID = 13C06.32 ) CWT TFI F F C.1254E 04 0.1282E 0.1184E 04 0.1271E 0.1172E C4 0.1259E C.1159E 04 0.1248E 0.1146E 04 0.1236E C.1133E 04 0.1225E 0.1119E 04 0.1213E 0.1106E 04 0.1201E 0.1093E 04 0.1190E 0.1080E 04 O.1178E 0.1067€ 04 0.1166E 0.1054E 04 0.1155E C.104CE 04 0.1143E 0.1027E 04 0.1131E 0.1014E 04 0.1119E 0.1001E 04 0.1108E C.9874E 03 0.1C96E 0.S742E 03 0.1085E C.S610E 03 0.1073E 0.9479E 03 0.1061E C.9348E 03 0.1050E 6364593 (LB/SCIN) 8317.50 (LB/SGIN) 10551.26 (LB/SQIN) 04 C4 04 04 C4 04 04 C4 C4 04 04 04 04 04 C4 C4 04 C4 04 04 04 TFGC F 0.1300E 0.1282E 0.1271E 0.1259E 0.1248E 0.1236E 0.1225¢E 0.1213E 0.1201E 0.1190E 0.1178E 0.1166E C.1155E 0.1143E 0.1131E 0.1119E 0.11C8E C.1096E 0.1085E 0.1073E 0.1061E 04 04 04 C4 04 04 04 04 04 04 04 04 Ca 04 04 04 04 C4 04 04 04 FWT F C.1271E C.1229E 0.1216E 0.1204E 0.1191¢€ 0.1178E 0.1165E 0.1152E 0.1139E 0.1126E 0.1112E 0.1099¢E 0.1086E 0.1073E 0.1059E 0.1046E 0.1033E 0.1C19E 0.1006E 0.9929E 0.9796E 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 03 63 TWDT F 0.1681E 0.45C9E 0.4495E O0.4512E 0.4526E 0.4538E 0.4549E C.4557E 0.4564E 0.4568E 0.4571E 0.4571€E 0.4569E 0.4566E 0.4560E 0.4551E 0.4541¢E 0.4529E 0.4514E 0.4497E 0.4479E 02 02 2 02 02 02 02 02 02 02 02 02 02 02 c2 02 02 02 02 C2 02 L8 Vo~ N - vl 0.0 6.1660 6.1475 6.1292 6.1109 6.0927 6.0745 6.0565 6.0384 6.0205 6.0027 5.9849 5.9673 5.9497 5.9323 5.9150 5.8979 5.8808 5.,8639 5.8472 5.8306 vz C.C * 7.0071 6.9861 6.5653 6.9445 6.9238 6.5032 6.8826 6.8621 6.8418 6.8215 6.8013 6.7613 6. 7415 6.7219 6.7024 6. 6830 6. 6638 6. 6448 6. 6260 V3 FT/SEC 0.0 6.7T107 6.6905 6.670¢€ 6.6507 6.6306 6.6112 6.5915 6.5719 6.5523 6.5329 6.513¢ 6.4944 €.4753 Ee45€4 6.4375 6.4189 6.40032 6.3819 6.3637 6.3457 VW1 0.0 6.4319 6.4126 6.3935 6. 3554 6.3365 6.3176 6.2G88 6. 2801 6.2615 6.2430 6.2246 6. 2063 6.1881 6. 1701 6.1522 6.1344 6.1168 6.0994% 6.0821 VW3 0.0 T.6953 T.6722 7.64G3 T.6265 7.6038 7.5812 7.5586 7.5361 745137 T.4914 T«4693 Te4413 T«4254 T.4036 7.3821 7.3394 7.3183 T.2974 T.2768 PDSO LB/SQFT 851.3384 851.3384% 845,2434 839,1812 833.1099 827.0310 820,9490 814.8638 808.7805 802.6997 796.6255 790.5603 784.5063 T7T78.4670 T72.4438 716644417 760.4609 7154.5051 T48.5771 742.6804 736.8167 PDTO 3430.7144 834.3669 82646611 818.9949 811.3169 803.6326 795.9424 788.2510 780.5627 772.8799 765.2080 757.5488 749.9067 742.2856 734.6880 727.1172 719.5779 712.0718 704.6025 697.1743 689.7888 88 VO~NOWVMPH WN -~ RENTO 0.1129E 0.1090¢E C.1059E 0.1029E 0.9998E 0.9706E 0.9418E 0.9134E 0.8854E 0.8578E 0.8307E 0.8041E 0.7779E 0.7523E 0.7271E 0.7025€ 0.6784E 0.6548E 0.6318E 0.6094E 0.5874E PRNTO 0.8172€ 0.8463E 0.8707¢ 0.8960E 0.9225¢E 0.9503¢E 0.9794E 0.1010E 0.1042€E 0.1075E 0.1110¢ 0.1147E 0.1186¢€ 0.1226¢ 0.1268E 0.1313€ 0.1360E 0.1409E 0.1460E 0.1514¢E 0.157CE 01 0l 0l 01 ol o1 01 02 02 02 02 02 c2 02 02 02 02 02 02 02 RENSOL 0.0 0.2908E C.2843E 0,2779E C.2715E 0.2651E 0.2587E C.2523E 0. 2460E 0.2397E C.2335€ 0.2273E C.2211€ 0.2150E C.2089E C.2029E C.1970E 0.1912¢E 0.1854E 0.1797E 0.1740E RENSO2 0.0 0.3304E 0.3231FE 0.3158¢ 0. 3085E 0.3012€E 0. 2940E 0. 2868E 0.2796E 0.2724E 0.2653E 0.2583E 0.2513¢ D.2443E 0.2374E C.2306E 0.2239¢E 0.2172E 0.2107€E 0.2042E 0.1978E RENSC3 0.0 0.3164E 0.3094E 0.3024E 0.2954E 0.2885€ 0.2815E 0.2746E 0.2677E€ 0.2609E 0.2541E 0.2473E 0.2406E 0.2340E 0.2274E 0.2209E 0.2144E 0.2080¢E 0.2018E 0.1955E 0.1894E HTO 0.2958E 0.3421F 0.3317E 0.3244E 0.3172€E 0.3100€E 0.3029E 0.2959E C.2889E 0.2820E 0.2751€ 0.2684E 0.2617E 0.2551E 0.2485E 0.2421E 0.2357¢ 0.2295E 0.2233E 0.2172¢E 0.2112E AHSO 0.5273E 0.2605¢ 0.2552E 0.2526E 0.2500E 0.2474E 0.2448E 0.2421E 0.2395¢E 0.2368E C.2341E 0.2314E 0.2287E 0.2259E 0.2232E 0.2204E 0.2177E 0.2149E 0.2122E 0.2094E 0.2067E BTU/HR/SQFT/F 03 04 04 04 04 Ca 04 04 04 04 UoA 0.3980E 0.1048E 0.1029E 0.1018E 0.1C06E 0.9950E 0.9833E 0.9716E 0.9597E 0.9476E 0.9355€E 0.9233E 0.9109E 0.8985E 0.8860E 0.8733E 0.8607E 0.8479E 0.8351E 0.8223E 0.80S4E HEAT BTU/HR 0.1332E 0.8775¢€ 0.8748E 0.8780E N.86C7E C.8832¢ 0.8853E 0.8869E 0.8882E 0.8890E 0.8895E 0.8896E 0.8892E 0.8885€ 0. 8873E 0.8857E 0.8837E 0.8813E 0.8785¢ 0.8752E 0.8716¢ 68 90 Appendix C THE RETEX PROGRAM The RETEX computer program is outlined in block-diagram form in Fig. C.1. The input data required for the program are given in Table C.1, and the output received from the program are given in Table C.Z2. A complete listing of the main program is followed by definitions of the intermediate variables used in the program. To illustrate the use of the RETEX program, the input and output for the MSBR steam reheater exchanger discussed in Subsection 3.1 of this report are presented as printed by the computer. 91 . (s ) () >y READ AND PRINT INPUT DATA v ASSUME BAFFLE SPACING ® >3 ASSUME SHELL DIAMETER ® -y CALCULATE NUMBER OF TUBES, FUEL AND COOLANT FLOWS AND VARIOUS GEOMETRIES v START WITH FIRST INCREMENT FROM HOT SIDE OF HEAT EXCHANGER I=1 v ASSUME TEMPERATURE DROP FOR THE INCREMENT () > EVALUATE ALL PHYSICAL PROPERTIES AT AVERAGE TEMPERATURE OF INCREMENT v CALCULATE PRESSURE DROPS AND HEAT TRANSFER COEFFICIENTS FOR THE INCREMENT, USING CORRECT CORRELATION FOR DIFFERENT REGIMES v CALCULATE HEAT RATE AND TEMPERATURE DROPS OF THE INCREMENT Fig. C.1. Simplified Flow Diagram of the RETEX Computer Program. 92 00 INCREMENT TEMPERATURE DROPS AGREE WITH OUR ASSUMPTION NO YES DOES END TEMPERATURE OF INCREMENT EQUAL TO SPECIFIED END TEMPERATURE OF HEAT EXCHANGER NO YES DOES TOTAL TUBE SIDE PRESSURE DROP ACCEPTABLE ? NO YES DOES TOTAL SHELL SIDE PRESSURE DROP ACCEPTABLE ? NO Fig. C.1. (continued) CHANGE ASSUMED INCREMENT TEMPERATURE DROP GO TO NEXT INCREMENT I 1-1 CHANGE ASSUMED SHELL DIAMETER CHANGE ASSUMED BAFFLE SPACING 93 ARE THERE ADDITIONAL CASES FOR PARAMETER STUDY ? PRINT OUTPUT (: END :) Fig. C.1. (continued) 94 Table C.1. Computer Input Data for RETEX Program Card Columns Format Variable Term Units A 1-10 E10.4 Heat load required HEATL Btu/hr 11-20 F10.0 Allowable tube~side pres- PRDT 1b/ft3 sure drop 21-30 F10.0 Allowable shell-side pres- PRDS 1b/ft? sure drop B 1-10 F10.0 Coolant outlet temperature CTO °F 11-20 F10.0 Fuel inlet temperature FTO °F 21-30 F10.0 Fuel outlet temperature ETF °F 31-40 F10.0 Coolant inlet temperature ETC °F C 1-10 Fl1l0.0 Leakage factor for heat LK transfer correlations 11-20 F10.0 Leakage factor for pres- PLK sure drop calculations 21-30 F10.0 Tube material conductivity WCOND Btu/hrefte°F D 1-10 F10.0 Radius of coolant central RAS ft downcomer ‘ 11-20 F10.0 Distance between shell DTR ft wall and tube bundle 21-30 F10.0 Maximum anticipated heat RABMAX ft exchanger radius 31-35 I5 Number of cases to be run KASES 36-40 I5 Index one if enhanced KENTB tubes are used E ,Es, 1-10 F10.0 Outside diameter of tube DIA ft cee 11-20 F10.0 Tube wall thickness WTHK ft EKASES 21-30 F10.0 Triangular pitch TPIP ft 31-40 F10.0 Inner baffle cut CUT3 % of area 41-50 F10.0 OQuter baffle cut CUT4 % of area 95 Table C.2. Output Data From RETEX Computer Program Term Variable Units THEATO Total heat actually transferred Btu/hr HTPERC Percentage of required heat load transferred QC Coolant (shell-side) mass flow rate 1b/hr QF Fuel (tube-side) mass flow rate 1b/hr TTDSO Total tube-side pressure drop psi SPPERC Percentage of allowed tube pressure drop ~ actually used TTDTU Total shell-side pressure drop psi TPPERC Percentage of allowed shell pressure drop actually used RA8 Radius of heat exchanger shell ft BSOI Distance between baffles ft VOL Fluid volume contained in tubes ft2 AREA Total heat transfer area in heat exchanger ft° SNT Total number of tubes TUBLEN Actual tube length ft GBRL Modification factor for Bergelin's heat transfer correlation SAVT Shell average temperature °F TAVT Tube average temperature °F TCI(I) Coolant outlet temperature from increment I °F TCO(I) Coolant inlet temperature from increment I °F CWT(I) Average tube wall temperature at coolant side °F TFI(I) Fuel outlet temperature from increment I °F TFO(I) Fuel inlet temperature from increment I °F FWT(I) Average tube wall temperature at fuel side °F TWDT (1) Average temperature drop across tube wall in °F increment I V1(I) Fluid average velocity in outer window in ft /sec increment I V2(I) Fluid average velocity in overlapping baffle ft /sec zone in increment T V3(I) Fluid average velocity in inner window in ft/sec increment I 96 Table C.2 (continued) Term Variable Units VW1(I) Fluid velocity across tubes in outer edge of ft/sec baffle in increment I VW3(I) Fluid velocity across tubes in inner edge of ft/sec baffle in increment I PDSO(I) Shell-side pressure drop for increment I 1b/ft° PDTO(I) Tube-side pressure drop for increment I 1b/ft? RENTO(I) Tube-side Reynolds number for increment I PRNTO(I) Tube-side Prandtl number for increment I RENSOL (1) Reynolds number in outer window in increment T RENSO2 (1) Reynolds number in overlapping baffle zone in increment I RENSO3(1I) Reynolds number in inner window in increment I HTO(I) Tube~side heat transfer coefficient in Btu/hr-ft2-°F increment 1 AESO(I) Shell-side heat transfer coefficient in Btu/hr-ft2'°F increment 1 UOA(TI) Overall heat transfer coefficient in Btu/hr-ft2°°F increment I HEAT(I) Heat transferred in increment I Btu/hr The RETEX Program Listing *¥FTNyLs E+ Gy M, PROGRAM MSBRPE-2 MSBRP TYPE REAL LK s LAWC1 , LAWC?Z - MSBRP DIMENSION TFO(130),TCI(130),VMI(130),VM2(130),VWC1(130),VWO3(130),MSBRP 1 RENTO(130},PRNTO(130) ,RENSOL1(130),RENSO3(130), RENSC2(130}, MSBRP 2 VM3 (13C),PDSCG(130)4NT(100},B4(3),HS01(130)4,HS02(1301),HSO3(120}),MSBRP 3AHS0(1301),HTC(120),UCA(130),TCO(130),TFI(120),HEAT(130),TWDT(130),MSBRP 4 PDTO(1301,TUBLN(130),V1(130),V2(130}),V23(130),VW1(130}),VW3(130), MSBRP 5 R(100),FACT(1CO),TCPI(100),TCTAL(L100} MSBRP 6 CWT(130),FWT(130),AVWT (1320} MSBRP 1001 FORMAT( E10.4, 2F10.C) MSBRP 1002 FORMAT( 4F10.C) MSBRP 1002 FORMAT( 3F10.0]) MSBRP 1004 FORMAT( 3F10.0,215) MSBRP 1005 FORMAT( 5F10.0) MSBRP 1006 FORMAT(22HOHEAT LOAD REQUIRED = 4F12.04+2X,EH(BTU/HR) ) MSBRP 1007 FORMAT (43HOALLCWABLE TCTAL TUBE-SIDE PRESSURE DROP = ,F10.0,2X, MSBR 1 10H(LB/SQ~FT) ) MSBR 1008 FORMAT(44FOALLCWABLE TCTAL SHELL-SIDE PRESSURE DROP = ,F1l0.042X, MSBR 1 1O0H(LB/SQ-FT}) ) MSBR 1009 FORMAT(33FHCHIGH TEMP, CF SHELL SIDE FLUIC =,F10.2,2X+3H(F)) MSBR 1010 FORMAT(32HOHIGH TEMP., CF TUBE SIDE FLUIL = JF10.2:2X,3H(F)} MSBR 101! FORMAT(32HOLCW TEMP. CF TUBE SIDE FLUID = LF10.2,2Xs3H(F)) MSBR 1012 FORMAT(32HOLGW TEMP. CF SHELL SIDE FLUIC =4F10.2:2X,3H(F}) MSBR 1013 FORMAT(32FOHEAT TRANSFER LEAKACE FACTOR = ,F10.5) MSBP 1014 FORMAT(27FOPRESSURE LEAKAGE FACTOR = ,F10.5 ) MSBR 1015 FORMAT(25FOCCNCUCTIVITY OF TUBE WALL METAL = 4,F10.5,2X, MSBR 1 13H(BTU/HR-FT-F) ) MSBR 1016 FORMAT(34FOINSIDE RACILS OF CUTER ANNULULS = 2F10.5,2Xs6H(FEET)) MSBR 1017 FORMAT(41HFOCISTANCE BETWEEN SHELL WALL AND TUBES = MSBR 1 +F1045+42X%,€6H(FEET}) MSBR 1018 FORMAT (4SHOMAXIMUM ANTICIPATED QUTER RADIUS OF EXCHANGER = , MSBR 1 F1O0e542X46H(FEET) ) MSBR 10 20 30 31 32 33 34 35 36 &9 50 60 70 80 g0 100 101 110 111 120 130 140 150 160 170 180 181 150 200 201 210 211 L6 C 1019 FORMAT (23HONUMBER OfF CASES RUN = ,14) MSBR 1020 FORMAT(25F0USE GOF ENHENCED TUBES = ,14,2X,32H(0ONE IF ENHENCED TUBEMSBR 1S ARE USEC)) 1021 FORMAT(Z2SEQOCUTSIDE CIAMETER OF TUBES = LFI1C0.5,2Xs G6H(FEET) ) 1022 FORMAT(27FOWALL THICKNESS OF TUBES = ,FiC.%42Xy 6H{FEET) ) 1023 FORMAT(Z2O0FCTRIANGULAR PITCH = , ' F10.542Xy G6H(FEETH) 1024 FORMAT(22FOINNER BAFFLE CUT3 +yF10.5,2Xs 10H(PER CENT) 1} 1025 FORMAT(22FCCUTER BAFFLE CUT4 sy F10.542Xy 10H(PER CENT) ) 1026 FORMAT(Z25FR1TCTAL HEAT TRANSFERED = 4yF1l2.042X,8H(BTU/HR), ] eXelFH{4F5.1,9H PERCENT)) 1027 FORMAT (29FOMASS FLOW RATE OF CCOLANT = ,F1C.0y2X, 7TH(LB/HR) ) 1028 FORMAT(26KCMASS FLOW RATE OF FUEL = 4F10.04+2Xs 7H(LB/HR) ) 0 MSBR MSBR MSBR MSBE MSBR MSBF MSBR MSBR MSBR MSBR 1029 FORMAT(24F0OSHELL-SIDE TOTAL FRESSURE DRCP = ,F10.2,2Xy SH(LB/SQIN)MSBR 1 12X 9 IH(,FE.,1,SH PERCENT)) MSBR 1020 FORMAT(33+OTUBE~-SIDE TCTAL PRESSURE DROP = ,F10.242X, SH(LB/SCIN),MSBR 1 2XyIF(,F5.1,SH PERCENT)) 1031 FORMAT(24FCNCMINAL SFELL RADIUS = 4FT7.4,42X34H(FT)) 1032 FORMAT(26HCUNTFORM BAFFLE SPACING = 4FTe b4y 2Xy&4HIFTY) 1032 FORMAT(40FOTUBE FLUID VOLUME CCNTAINED IN TUBES = 2F7.2+1X, 112H(CUBIC FEET)) 1034 FORMAT(1HC,4€6HTOTAL HEAT TRANSFER AREA EASED CN TUBE 0.De = 1 Fl2.24+2XEH(SQFT)) 1025 FORMAT(25FOTCTAL NUMBER CF TUBES = ,Fé.C} 1036 FORMAT(Z21HOTCTAL TUBE LENGTH = +F6es292X4H(FT)) 1037 FORMAT(ZZHCBWINDOW 1 CROSSFLOW = 4F5.2,2Xy€H(SQFTY)) 1038 FORMAT(31+0OBERGLIN MCDIFICATICN FACTOR = ,F5.2) 1029 FORMAT(1HC2X 31HI s 7X+2HTCI 46X, 3HTCCy9Xy3HCWT 49X, 2HTFI 9X,3HTFO, 16X s BHFWT § EXy4HTWDT// 11Xy 1HF 3 11X31HF,11 X, 1HF,11X, 2 IHF 311X, 1HF 3 11X IHFy 11X 1FF//(1X, 13, TE1Z24 %)) 1040 FORMAT (L1HGC,2Xs1HI s 7X33HVMI ,G Xy ZHVMZ2 49X 4 2HVM2 48X, 4HVWO1 +8Xs4HVWO3, 1 8X44HPDSC,8X4HPDTO/ /32X, 6HFT/SEC33X,THLB/SQFT//(1X413,7F12.4)) 1041 FORMAT(1HC,2X 31HI 35Xy SHRENTC, 7X35HPRNTO 47X +6HRENSOY1 46X 46HRENSCZ, 16Xy 6HRENSC3 37X 43HHT O 38X 9 4HAHSO 39Xy 3HUCA 3 8X 44HHEAT//TT7X y 2 13HBTU/HR/SQFT/F +13Xs6HBTU/HR//{1X,12,6E12.4)) 1042 FORMAT(27HOTUBE WALL AVERAGE TEMP, = LF10.2) 1043 FORMAT (28FOSHELL SIDE AVERAGE TEMP., = , F1l0.2) MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MS BR MSBR MSBR MSBR MSBR MSBR MSBR MSBR & 9 MSBR MSBR 220 230 231 240 250 260 270 280 290 291 300 310 320 321 330 331 340 350 360 361 370 37% 380 360 400 410 420 421 422 430 431 440 441 4472 460 650 86 READ IN AND FRINT OUT INPUT LCATA KEY7= 1 VM1(1)=0. VM2(1) =0, VM3 (1) =0, VWO1(!)=0. VW0O3(1)=0, RENSO1(1)=0. RENSOZ2(11=0,. RENSO32(1) =0. HS01(1)=0. HS03(1)=0. READ 1001y HEATL, PRDT, PRDS READ 1002, CTO,y FTO, ETF, ETC READ 1003, LK, PLK,WCCND READ 1004, RA5, DTR, RABMAX,KASES,KENTB CONTINUE ‘ READ 1005, CIA, WTHK, TRIP, CuT3, CUT4 HSFCT=1. IF(FTOLLT.CTC) HSFCT=-1, PRINT 100&, FEATL PRINT 1007, FRCT PRINT 100€&, PRLCS PRINT 100¢, CTC PRINT 1010, FTC PRINT 1011, ETF PRINT 1012, ETC PRINT 1012, LK PRINT 1014, PLK PRINT 101£%, WCCND PRINT 101€, RAE PRINT 1017, CTR PRINT 101E&, RAEMAX PRINT 101¢S , KASES PRINT 102C, KENTB MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBK MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR 660 490 500 510 520 530 540 550 560 570 580 590 600 81C 620 630 640 €50 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 66 PRINT 1021, CIA MSBR 830 PRINT 1022, WTFK MSBR 840 PRINT 1022, TR1P MSBR 850 PRINT 1024, CUT3 MSBR 860 PRINT 102%, CUT4 MSBR 870 MSB 1650 BEGIN GEOMETRY CALCULATICNS FCR SINGLE ANNULUS COUNTER FLOW MSB 1660 DISC AND COUGHNUT BAFFLEC HEAT EXCHANGER MSB 1670 ATUBE = (3.14159% (DIA*%2,01)/4.0 MSBR 910 GFTT = 1. /3€00, MSBR 920 GFT = 1./144. MSBR 930 DIAI=DIA-2.0%WTHK MSBR 940 FATUB =(2.14156%(DIAI**2,00)/4.0 MSBR 950 KEY1l = O MSBR 960 PERC1 = 0.99 MSBR 970 IF(KEY1. GT.0)BSOI=0. 5*(BSL+BSH) MSBF 980 KEY2 = 0 MSBR 990 PERCZ2 = 0.99 MSB 1000 RABL=RAS5 _ MSB 1010 RABH=RA8MAX MSB 1020 RA8=0. 5% ({RABL +RA8H ) MSB 1030 NTO = 4, 0¥ ((RAB**2,0)-(RAS*%2,0) )/ (Ll.12*(TRIP*%2.0})) MSB 1040 RAS52=RA5%*%2 MS8 1050 RAB2=RAB**2 MSB 1060 RA6=(RAS24CUT4*(RAB2-RA52) ) %*,5 MSB 1070 RA7=(RA82-CUT3*(RABZ-RA52) )**, & MSB 1080 RA62=RA6**2 MSB 1090 RA7Z2=RA7T**2 MSB 1100 APO1=3.1415G%( (RA8)**2,0-(RAT7)*%2, 0)%(1.0- (ATUBE/ MSB 11190 1(0, 866*( (TRIP)I*%2,0) 1)) ) MSB 1111 APO3=2,1415G%( (RA6 ) **2,0-(RA5)**2,0)*(1.C~(ATUBE/ MSB 1120 1(0. 866 TRIP**2.01) 1)) : MSB 1121 PLAV = (0.955%TRIP MSB 1130 RBl = (RAE-RA7)/(1.86¢*TRIP) MSB 1140 RBZ2 = (RA7-RA6)/(0.Q33%TRIP) MSB 1150 RB3 = (RA6-RA5)/(1,86€%TRID) MSB 1160 001 LAWO1=3.1415G6%2,0%FAT*(1.0-(DIA/PLAV)) LAWO3=3. 14156%2. 0%RA6*(1.0-(DIA/PLAV)) ISUM]L = 4,0*((RA8%*¥2,C)-(RAT*%2,0))/(1.12%(TRIP*%¥2,0)} SUM1 = TSUM] ' B ISUM2 = 4. 0*((RAT*%2_ 0)~-(RA6*%2,0))/(1.12%(TRIP*%2,01)) SUM2 = TSUM2 ' ISUM3 = 4,0*((RAGF*2,C)I=(RAS**2,0)} )1 /(1. 12%(TRIP*%24,0)) SUM3 = TSUM3 SNT = IStV + ISUM2 + ISUM3 BSMAX=1. 5*( (RAB-(RAE-RA7)/2. )-(RAS4(RA6-RA5)/2.)) BSMIN=0. 2*(R28-RA5) IF(BSMIN.LT.0.,1€67)BSMIN=0.1667 HW=2.*WCOND/ (D IA*(ALOG(DIA/DIAI)})} CSPHAV=0., 326 FSPHAV=0, £57} QC=HEATL/ (CSPEAVX(CTO-ETC)) QF=HEATL/ (FSPHAVX(FTO-ETF}) GTO = QF/(NTC*FATUB) CONTINUE IF(KEY1l. EC. 0 )BSH=BSMAX IF(KEY1l. EC.CIBSL=BSMIN IF(KEY1.EC.OIBSCI=0.5*(BSL+BSF) IT =0 KFINAL =0 I=1 TSUM=0, SSUM=0,. THEATO = (. C TPDTO = 0 TPDSO = O TFO(I)=FT TCI(INI=CTC KEY4 = 0 TIF=-5.0 TIC=-5.0 CDTF=90. FDTF=0. BSO = BSO1 MSB MSB MSB MSB MSB MSB MS8 MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS8 MSB mMs8 MSB MSB MS8 MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB 1170 1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320 1330 1340 1350 1360 1370 1380 1390 1400 1410 1420 1430 1440 1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 101 BRL1 = GBRL = 0. 77*BRLI**(-.138) AWOl = BSC*LAWC1 AW03 = BSC*LAWC3 AWl = SQRT(AWC1*APQOL) AW2 = (AwO1+AW03)/2. AW3 = SQRT(AWC3*APC3) GSO1 = QC/AWl GS02 = QC/AwW2 GSO3 = QC/An3 ATC = TCI(I) + (TIC/2.0) CFT = ATC +CCTF*HSFCT ATF = TFC(I)+TIF/2. FFT=ATF-FLCT F¥HSFCT FI=1 TUBLN(I) = FI*BSOI CVIS=0.2121*%EXF(4032./(460.4ATC)) CVISW=0, 2121*EXP(4032. /(460.4CFT}) CDEN=141.427-C. C2466%ATC CCON=0.24C CSPH=N,3¢ FVIS=0.0¢€2 FVISW = 0.0€2 FDEN = 0,7622 FCON = 0,.,02¢ FSPH . £271 VI SK (CVIS/CVISWI**(0,14 FVISK=(FVIS/FVISW) %0, 14 DCVIS = CIA/CVIS CCDEN = 1,.,/CCEN QCCDEN = CC*CCCEN CALCULATE REYNCLS AND PRANDTL NUMBER TUBE SIDE RENTO(IV=CIAIXCTO/FVIS PRNTO(I)=FVIS*FSPH/FCCN HEFI=1.+((RENTC(I)~10C0.)/900C. )**0.5 TF(KENTB«NEL1IFEFI=1, PDTO(I )=(.0028+.25%RENTO**(-,321) )% (CIAT*FLCEN*417182400.) BSC/((RAB-(RAB-RAT7)/2.)-(RA5+(RAE-RAS)/2.)) BSC*GTC**x2%xHEFI/ MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS8 MS 8 MSB MSB MSB MSB MS8 MSB MSB MS8B MSB MS8B MSB MSB MSB MSB MS 8 MS8B MSB MSB MSB MSB MS8 MSB MSB MS8 1550 1560 1570 1580 1590 1600 1610 1620 1630 1640 1650 1670 1690 1700 1710 1720 1730 1740 1750 1760 1770 1780 1790 1800 1810 1820 1830 1840 1850 2550 1870 1880 1890 13500 1510 1911 0T g 10 il 1 1 CALCULATE HEAT TRANSFER COEFF TUBE SIDE HiO(T)=FCON/CT A%, 022 7% (RENTO(T )**4 8)*% (PRNTC( I )%%*,2333)}*FVISK*HEFI GO TO 10 IF(RENTO(I).LT,.2100.) GO TO 9 HTO(I) = FCON/CIA%, O89%(RENTO(I)}**%,666=-125., y*(PRNTO(] I**,3333)* FVISK¥HEFI*(1,4.2233%(DIAI/TUBLN(I) )**,666€) GO 70 10 HTO(I} = FCON/CIA*(4.36+(0.025%RENTO(I)#PRNTO(I)*DIATI/TUBLN(I) }/(14+C.COLZH*RENTO(I)*PRNTO(I)*DIATI/Z/TUBLN(I) ) CONTINUE CALCULATE FLCW AREAS SHELL SIDE VWO1(I) = QCCCEN/AWC1 VWO3(1) = CCCCEN/AWC3 VM1(I) = GSC1*CCDEN VM2 (I} = CSG2*CCDEN VM3(1) = CSC3*CCDEN CALCULATE PRESSURE DRCPS SHELL SIDE DP1 (1.4, EXRELYXCDEN*VMI (T )*>*2 DpP2 e 6%RB2*CLENXVM2 (I )*%*2 DP3 (1. 4. E*RE3)*CDEN®VMI(T I*x%2 RENSO1(I) = CGSC1*DCVIS RENSO2(TI} CSC2*%DCVIS RENSN3(1) GSC3*DCVIS HEFO=1,40.3*((RENSOZ2(1)-1000, )/900C, }**C.5 IF(KENTB, NEL 1 }IHEFDO=1. PDSO(I) = (CF1+4DPZ+DP2)*PLK*FEFC/834624C00. CALCULATE BJ FACTOR ANC SHEL SIDE COEFFICIENTY BJ(1) =(0.24€*RENSOL(I)**(~-0.2E82) V*GBRL BJ(2) =(0.324€*RENSOC2(I¥1**(-0.3€2))*GBRL BJ(32) =(0e246*RENSOZ(I1**(~-0.2€2) )%*GBRL it un Hn HSO1(I) = (LK¥CSPH®(GSC1*BJ(LI*((CCCN/(CSPH*CVIS) )I**,66))*VISK HSO2(I) = (LK*CSPH*CSC2%BJ(2)*((CCON/ (CSPH*CVISH b**, 66 ) 1*VISK HSO3(I) = (LK*CSPH*GSC3*BJ(3)*((CCCN/(CSPH*CVIS) b**,66))*VISK AHSO(I b=( ((HSCI (T} *SUMLI+(HSC2(T)*SUM2 )+ (HST2(T)*SUM3) )/ SNT ) *HEFC GO TO 12 CONTINUE MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS8 MSB MSB MSB MSB MsSB MSB MSB MSB MSB MSB MS8B MS8 MSB MSe MSB MSB MSB MS8 2640 1930 1940 1850 1960 1961 1570 1680 1981 1590 2480 2010 2020 2030 2040 2050 2590 2070 2080 20690 2100 2110 2120 2130 2140 2150 273¢C 2170 2180 2190 2200 2210 2220 2230 2240 2250 £01 UDA(TI)=14C/((140/AHSO(I} )4+ (L.O/HTO(I})+(1.0/HW)) MsB8 22690 A = QF%FSFH MSR 2270 B = QC*CSFHE MSB 2280 D = UDA(I I*SNT*BSO #3,14159*CIA MSB 2290 P = “HSFCT*(C*(A-B) )/ (A%B) PBAR = EXPI(P) MSB 2310 C = (B-A)*PBAR MSB 2320 TCO(I) = ((TCI(I}x(B*PBAR-A))-(TFO(I)%*A*(PRAR-1.)})/C MSB 2330 TFICI) =((TCC(I)=-TCI(I))I*B/A) + TFO(1) MSB 2340 HEAT(I) =-A%(TFI(I} - TFO(I}) MSB 2350 TWDT(I) = (FEAT(I)/NTC)*ALOG(DIA/DIAI }/(2.0%2,.14159%BSQ0%*WCOND) MSB 2360 CTIF = TFI(I)-TFO(I) MSB 2370 CTIC = TCC(IN-TCIC(I) MSB 2380 IF((ABS(CTIF-TIF)uLE«(1le5))aANDs (ABS(CTIC-TIC)I.LE. (1.5)))G0O0 TC 13 MSB 2390 TIF = CTIF MSB 2400 TIC = CTIC MSB 2410 GO TO 6 MSB 2420 THEATO = THEATC + HEATI(I) - MSB 2430 TPDTO = TEDTC 4 PDTO(I) MSB 2440 TPDSO = TFDSC + PDSO(1) MSB 2450 COTF=( ({HEAT(I)) /NTC)/BSO)/(3.14159%D[A%AHSO(I}) MSB 3090 FOTF=CDTF*AHSC(I) /HTC(1I) MSB 3100 FWT(1) =ATF-FCTF*HSFCT CWT(I) =ATC+CLCTF*HSFCT AVWHT(I) =0.5%{(FWT(I) <+CWT(I}) MSB 3130 TSUM=TSUM+AVWT(I) MSB 2140 SSUM=SSUM+ATC MSB 2560 IF(KFINAL.EQs1.AND.1.EQeIT) GO TO 15 MSB 2460 IF(({(ABSCETF-TFI(I)))a LE«{ (ABS(TFI(II-TFC(I}))/2e0))140R. MSB 2470 1 (TFI(I). LE.ETF))} GO TQ 14 MSB 2471 I=T+1 MSB 2480 IF{I.GT,129)GC TO 23 MSB 2490 TFO(I) = TFI(1I-1) MSB 2570 TCI(I) = TCO(I-1) MSB 2580 BSO=8S01 MSB 2550 GO TO 6 MSB 2600 H01 15 16 17 18 19 20 21 KFINAL=1 IT=1 FIT = IT GO TO 5 TUBLEN= FIT%BSCI TAVT=TSUM/FIT SAVT=SSUM/FIT CONTINUE VOL = 0., 7854*(CTAI *%2,0)*NTOXTUBLEN CHECK OF TUBE AND SHELL PRESSURE DROPS KEYZ2 = KEYZ2 + 1 IF(PERC2.LE.O.1) GO TC 26 IF{TPDTO. LT« (PERC2%PRCT)) GO TC 18 IF(TPDTO. CT.PRCTY GO TC 19 GO TO 20 IF(RAB4LE.(RAS +0.0C8) ) GC TQ 27 RABH =RAS8 IF(KEY2«NE.20)CGC TO 3 RASBL=RA8BL-0.2 PERC2 = PERC2 - 0.01 KEYZ2=10 GO 7O 2 IF(RA8.GE.(RASBNMAX-0. 005})) GC TC 27 RABL =RAESg IF(KEY2.NE.2C) GO TO 3 RASBH=RABH+0,2 PERC2 = PERCZ2 - 0.0C1 KEYZ2=10 GO TO 3 KEYl = KEY1 + 1 IF(PERC1.LE.O.1) GO TC 2% IF(TPDSOLLT. (PERCI1*PRLCS)) GO TC 21 IF(TPDSO0.CT.PRLSIGO TC 22 GO TO 28 IF(BSOI-LE. (BSVMIN+O.QCENIGO TQ 24 BSH =BSCI1 IF(KEY1.NE.2C)ICC TO 2 MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS8 MSB MSB MSB MSB MSB MSB 2610 2620 2630 2640 2650 2680 2690 3250 2710 2720 2730 2740 2750 2760 2770 2780 2760 2800 2810 2820 2830 2840 2850 2860 2870 2880 2890 2900 2910 2920 2930 2940 29650 2960 2970 G01 22 23 1044 24 1045 25 1046 26 1047 27 1048 28 BSL=BSL-0.1 PERC1 = PERC1 - 0.01 KEY1l=10 GO T0 2 IF(BSOI.GE. (BSVAX-0.0C5) IGO0 TO 24 BSL =BSOI IF(KEY1.NE.2C) GO TO 2 BSH=BSH+0.1 PERC1 = PERC1 - 0.01 KEY1=10 GO TO 2 PRINT EXIT SIGNALS PRINT 1044,BSO FORMAT (39F1BAFFLE SPACINGS EXCEEDE 129 WITH BSO =4F5.242Xy4H(FT)) GO TO 28 PRINT 104¢ FORMAT (20F1BSOT = MAX., OR MIN. ) GO TO 28 PRINT 104¢ FORMAT (48+1 PERC1 FOR SHELL FRESSURE DRCP IS LESS THEN 0.1} GO TO 28 PRINT 1047 FORMAT(48H1 PERC2 FOR TUBE PRESSURE DRCP IS LESS THEN 0.1) GO TO 28 PRINT 104¢€ FORMAT (2GF1 SHELL RADIUS = MAX. OR MIN,) GO TO 28 END OF CASE, FRINT QUTPUT DO 29 T = 1,IT7 VI(I) = VMI(I)*GFTT V2{I)}) = VM2(II*GFTT V3(I) = VM2(I)*GFTT VW1(I) = VWOL(I)*GFTT VW3 (I) = VWC2(I)*kGFTT MSB MS8 MSB MSB MS8B MSB MSB MSB MSB MSB MSB MS8 MSB MS8 MSB MSB MS8 MSB MSB MSB MSB MSB MSB MSB Ms8 MSB MSB MSB MSB MSB MsB MSB MSB MSB MSB MS8 2980 2990 3000 3010 2020 3030 2040 2050 3060 2070 3080 3640 3650 3110 3120 3130 3140 3150 3160 3170 2180 3190 3200 3210 3220 3230 3240 3250 3810 3820 3280 3290 3300 2310 3320 3330 901 29 30 31 1 1 1 CONTINUE TTDSO TFEDSC*CFT TTDTO TEDTC*CFT TPPERC=TPLTO*100,/PROT SPPERC=TPLCSC*1C0./PRDS HTPERC=10C. *THEATO/HEATL AREA=341415S*CIA*SNT*TUBLEN PRINT 102¢é,TFEATOyHTPERC PRINT 1027, QC PRINT 1028, CF PRINT 102<,TTDSC,SPPERC PRINT 103C, TTCTO, TPPERC PRINT 1031,RA8 PRINT 1032,BSCI PRINT 1032,VCL PRINT 1034, AREA PRINT 103%5,SNT PRINT 103¢&,TUBLEN PRINT 103€&, GBRL PRINT 1042 ,TAVT PRINT 1043 ,SAVT PRINT 1036, (I (TCI(I)sTCOCI)9CWT(I)y TFI(I) TFO(I)4FWT(I), TWET(I) },I=1,IT) PRINT 104C,{I,(VYCT1},v2(T),V2(I),VWI(I) VW2(T),PESO(I),PDTO(I)), I=1,IT) PRINT 1041,(I, (RENTCG(I)4PRNTC(I),RENSO1(I),RENSO2(T),RENSQO3(T), HTO(TI} +AHSO(I) JUOCA(IV},HEAT{(I)),I=1,1T) LOOP FOR ADCITIONAL CASES IF REQUIRED CONTINUE KEY7=KEY7+1 IF(KEY7.GT.KASESIGO TC 31 GO 70 1 CONTINUE END MSB MSB MSB MS8 MSB MSB MSB MSB MSB MSB MS8B MSB ‘MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS8 3340 3350 3360 32370 3380 3390 2400 1640 2420 3430 3440 2450 3460 3470 3480 3490 3500 3510 3520 3530 3540 3550 3560 3561 3570 3571 3580 3581 4240 4250 3610 3620 3630 3640 2650 3660 L0T 108 Intermediate Variables The intermediate variable terms used in the RETEX computer program are as defined for the PRIMEX program except for the two terms defined below. TRIP Uniform triangular pitch, ft. PLAV 0.955*TRIP used in calculating the effective cross~-flow area between the tubes, ftZ2. Computer Input for Reference MSBR Steam Reheater Exchanger HEAT LOAD REQUIRED = 125CC0CC0O. {(BTU/HR) ALLOWABLE TOTAL TUBE-SIDE PRESSURE DRCP = ©220. (LB/SQ-FT) ALLOWABLE TOTAL SHELL-SICE PRESSURE CROP = 8¢€40. (LB/SQ-FTI HIGH TEMP., OF SHELL SIDE FLUIC = 1180.00 (F) HIGH TEMP, OF TUBE SIDE FLUID = 1000.00 (F) LOW TEMP., OF TUuBE SIDE FLUIC = 6£0.00 (F} LOW TEMP., OF SHELL SIDE FLUIO = 850.00 (F} HEAT TRANSFER LEAKAGE FACTCR = 0.80000 PRESSURE LEAKAGE FACTOR = C.5200C CONDUCTIVITY OF TUBE WALL METAL = 11,6000C (BTUL/HR-FT-F) INSIDE RADIUS CF OUTER ANNULUS = C.0 (FEET) DISTANCE BETWEEN SHELL WALL AND TUBES = 0.C4167 (FEET) MAXIMUM ANTICIPATED OUTER RADIUS OF EXCHANGER = 5.CC00C (FEETI NUMBER OF CASES RUN = 1 USE OF ENHENCED TUBES = C (ONE IF ENHENCEC TUBES ARE USED) OUTSIDE DIAMETER OF TUBES = 0.0625C (FEET) WALL THICKNESS OF TUBES = €C.00292 (FEET) TRIANGULAR PITCH = 0.C8232 (FEET) INNER BAFFLE CUT2 C. 200C0 (PER CENT) OUTER BAFFLE CUT4 €. 200C0 (PER CENT) 601 Computer Output for Reference MSBR Steam Reheater Exchanger TOTAL HEAT TRANSFERED = 12€488992. (BTU/HR) (101.2 PERCENT) MASS FLOW RATE OF COOLANT = 1157407. (LB/HR) MASS FLOW RATE OF FUEL = €41075. (LB/HR) SHELL-SIDE TOTAL PRESSURE CROF = 59.52 (LB/SQIN} ( 99.2 PERCENT) TUBE-SIDE TOTAL PRESSURE DRCP = €9.85 (LB/SQIN} ( 69.5 PERCENT) NOMINAL SHELL RADIUS = (C.E828 (FT) UNIFORM BAFFLE SPACING = 0.,7205 (FT) TUBE FLUID VALUME CONTAINEC IN TUBES = 30.€6C (CUBIC FEET) TOTAL HEAT TRANSFER AREA BASEC ON TUBE CeD. = 237¢€.5€¢ (SQFTH TOTAL NUMBER OF TUBES = 400. TOTAL TUBE LENCTH = 20.z€¢ (FT} BERGLIN MODIFICATION FACTOR = 0.75 TUBE WALL AVERAGE TEMF. = G42.v CALCULATE THE GEOMETRIC FACTORS NECESSARY TO CALCULATE THE BERGELIN FACTORS, THEN CALCULATE THE BERGELIN FACTORS. == CALCULATE THE TUBE SIDE MASS FLOW RATE FOR AN INTEGER NUMBER OF TUBES. CALCULATE THE GEOMETRIC PARAMETERS ASSOCIATED WITH THE NUMBER OF RESTRICTIONS IN THE WINDOW AND CROSS FLOW REGIONS. SET TOTAL PRESSURE DROPS, TOTAL BAFFLE SPACINGS AND TOTAL TUBE LENGTHS TO ZERO. Fig. D.1. Simplified Flow Diagram of the SUPEX Computer Program. 116 DIVIDE THE TOTAL AMOUNT OF HEAT TO BE TRANSFERRED INTO EQUAL AMOUNTS FOR EACH INCREMENT. v BASED ON THE TOTAL HEAT TRANSFERRED IN AN INCREMENT, CALCULATE THE DELTA-T AND DELTA-H FOR THE SHELL: SIDE FLUID FOR ANY INCREMENT. CALCULATE THE SHELL SIDE FILM RESISTANCE FOR THE GIVEN BAFFLE. @) YES YES 62 Pye BEGIN THE INCREMENT CALCULATION BY CALCULATING THE TUBE SIDE FLUID TEMPERATURE AT THE END OF THE INCREMENT. v CALCULATE THE LOG-MEAN-DELTA T FOR THE INCREMENT CALCULATE THE TUBE WALL RESISTANCE CALCULATE THE TUBE SIDE FILM RESISTANCE CALCULATE THE LENGTH OF THE INCREMENT CALCULATE THE TUBE SIOE DELTA-P FOR THE INCREMENT CALCULATE THE ALLOWABLE OELTA-T ACROSS THE TUBE WALL BASED ON STRESS CONSIDERATIONS CALCULATE THE SHELL SIDE DELTA-P FOR THE PARTICULAR BAFFLE SPACE SUM THE TUBE SIDE DELTA-P'S SUM THE TUBE LENGTHS v NO CHECK TO SEE IF ALL OF THE N-INCREMENTS HAVE BEEN USED. _i::>’--' - CHECK TO SEE IF THE NEXT INCREMENT WILL BE IN A NEW BAFFLE :: NO SPACE. Fig. D.1. (continued) 117 CALCULATE THE DIFFERENCE BETWEEN THE TOTAL TUBE SIDE DELTA- P (SDPT) AND THE ALLOWABLE TUBE SIDE DELTA-P (DELPTA) YES v NO CHECK TO SEE IF SDPT IS WITHIN 3% OF DELPTA _j::>>--=- w ADJUST THE NUMBER OF TUBES IN THE EXCHANGER (NUMT) v CALCULATE THE DIFFERENCE BETWEEN THE TOTAL SHELL SIDE DELTA- P (SDPS) AND THE ALLOWABLE SHELL SIDE DELTA-P (DELPSA) YES NO CHECK TO SEE IF SOPS 1S WITHIN 3% OF DELSA ADJUST THE BAFFLE SPACING (BS(K)) ALL OF THE HEAT HAS BEEN TRANSFERRED--THE TOTAL PRESSURE DROPS ON BOTH TUBE AND SHELL SIDE ARE WITHIN LIMITS. WE HAVE AN ACCEPTABLE SOLUTION. WRITE OUT THE RESULTS. Fig. D.1. (continued) *(5) 118 Table D.1. Computer Input Data for SUPEX Program Card Columns Format Variable Term Units 1 1-10 F10.,5 Tube outside diameter DTO in, 11-20 F10.5 Tube wall thickness THK in. 21-30 F10,5 Tube pitch P in. 31-40 110 Number of increments N 2 1-10 F10.1 Salt inlet temperature TH1 °F 11-20 F10.1 Salt outlet temperature TH2 °F 21-30 F10.1 Steam inlet temperature TC1 °F 31-40 F10.1 Steam outlet temperature TC2 °F 3 1-10 F10.1 Steam inlet pressure PC1 psi 11-20 F10.1 Steam exit pressure PC2 psi 21-30 F10.1 Allowable total shell- DELPSA psi side pressure drop 31-40 F10.5 Bypass leakage factor for BLFP pressure drop 4 1-20 E20.6 Mass flow rate of steam WwC 1b/hr 21-40 E20.6 Mass flow rate of salt WH 1b /hr 41-60 E20.6 Total heat transfer rate QT Btu/hr 61-70 F10.5 Bypass leakage factor BLFH for heat transfer 5 1-10 F10.5 Specific heat of salt CPH Btu/1be°F 11-20 F10.5 Thermal conductivity of TCH Btu/ftehr«°F salt (hot £fluid) 21-30 F10.5 Estimated number of GNB baffle spaces 6 1-10 F10.5 Fractional window cut PW 11-20 F10.5 Estimated total tube SXG ft length 21-30 F10,5 Estimated baffle spacing BSG ft 119 Table D.2, Output Data From SU?EX Computer Program Term Variable Units For Each Baffle Space J Baffle number IBK(J) Increment number of first increment which lies completely in baffle space J DELTW(J) Calculated temperature drop across tube wall °F DELTWA(J) Allowable temperature drop across tube wall °F based on allowable stress TWALL (J) Temperature of wall material °F DELPS(J) Calculated shell-~-side pressure drop for the psi baffle space DHOT(J) Mean density of hot fluid (salt) for the 1b/ft? baffle space VHOT (J) Mean viscosity of hot fluid (salt) for the 1b/ftehr baffle space For Each Increment I Increment number X1 Tube length for the increment ft TH(I) Temperature of hot fluid (salt) °F TC(I) Temperature of cold fluid (steam) °F PC(I) Pressure of cold fluid (steam) psi DELP(I) Tube pressure drop for the increment psi RI(T) Thermal resistance of inside film for the hr-°F/Btu increment RW(TI) Thermal resistance of wall material for the hr-°F/Btu increment RO(I) Thermal resistance of outside film for the hr-°F/Btu baffle space in which the increment lies RT(I) Total thermal resistance between hot and hr-°F/Btu cold fluids for the increment For the Entire Exchanger NUMT Total number of tubes NBS Total number of baffle spaces BSL Length of a baffle space ft DS Inside diameter of exchanger shell in, 120 Table D.2 (continued) Term Variable Units SDPT Total pressure drop in tubes psi SDPS Total pressure drop in shell psi DTLME Log-mean delta-T °F SX Total tube length ft AREAX Total heat trénsfer area based on total tube fto length UEQX Overall heat transfer coefficient based on Btu/hr-ftB-°F total tube length SBS Total baffle space length ft AREAB Total heat transfer area based on total ft2 baffle space length UEQB Overall heat transfer coefficient based on Btu/hre ft? «°F total baffle space length The SUPEX Program Listing *¥FTNyL oGy EsM, PROGRAM SUPEX SUPEX 10 TYPE REAL NEW SUPEX 20 DIMENSION TC(2C1)s TH(201) 4PC(201) HC (201}, SUPEX 30 1DELPS(10C) yRW(201),RI(201),RO(100),RT(201),U(201), SUPEX 31 2X(201) yDELP(201),DELTWA(100) ;DELTW(100) sIBK(100) SUPEX 32 3DHOT(50) 3 VHOT( 50 ), TWALL (50) SUPEX 33 CALL SVH(1,P,T,V,H) SUPEX 40 READINPUTTAPES0,1007,DTCs THK 4P 4N | SUPEX 50 READINPUTTAPE50,1008, TH1,TH2,TC1,TC2 SUPEX 60 READINPUTTAPES0,1009,PC14PC2,DELPSA,BLFP SUPEX 70 READINPUTTAPES0, 10104 WC s WH, QT ,BLFH SUPEX 80 READINPUTTAPES0,1012,CPH, TCH,GNB SUPEX 90 READINPUTTAPE5041011,PWsSXG,BSG SUPE 100 DELPTA=PCLl-PC2 SUPE 110 LOP1=0 SUPE 120 LOP2=0 | SUPE 130 LOP3=0 SUPE 140 LOP4=0 SUPE 150 LOP5=0 SUPE 160 LOP6=0 SUPE 170 LOP7=0 SUPE 180 LOP8=0 SUPE 190 LOP9=0 SUPE 200 LOP10=0 SUPE 210 LOP11=0 SUPE 220 DELTH=QT/(WH%CPH) SUPE 230 DTPB=DEL TH/GNB SUPE 240 CALL RITEL(DTOsTHK,PsNsTHL,TH2,TC1,TC2,PC1,PC24DELPTADELPSAJWC, SUPE 250 1 WHyQT4CPHyTCHPW,BLFP,BLFH,GNBBSG,SXG) SUPE 251 BSL = BSG SUPE 260 DTI=(DT0-2.0%THK )/ 12.0 SUPE 270 P=P/12.0 SUPE 280 DTO=DT0/12.0 SUPE 290 1¢1 TCAV=(TC1+TC2)/2.0 PCAV=(PC1l+PC2)/2.0 CALL SVH(2,PC1l,TC1l,SPV1,DUM) CALL SVH(2,PC2,TC2,SPV2,DUM) CALL SVH(2,PCAV,TCAV,SPVAV,DUM) SPVG=(2,0%(SPV1+SPVAV}+SPV2})/5.0 CALL VISCOS(TC1,PC1l,VISI) CALL VISCOS{TCZ2,PC2,4VIS2) CALL VISCOS(TCAV,PCAV,VISAV) VISG=(2.0%(VIS1+VISAV)+VIS2})/5.0 CFG=C.014 THETAL = 0.8 PERCL = (THETAL = O0.5*SINF(2.0*THETAL)}/3.14159 THETAU = 1.5707 PERCU =(THETAU - O0.5%SINF(2.0*%THETAU))/3.14159 NEW = THETAL + (PW -PERCL)*(THETAU -THETAL)/(PERCU —-PERCL) PNEW = (NEW — C.5%SINF(Z.0%NEW))/3.14159 EPNEW=ABSF(PW-PNEW) IF(EPNEW-0.001)444,2 THETAL =NEW PERCL = PNEW LOP11=LOP11+1 IF(LOP11-10)1,1,3 WRITEOUTPUTTAPES1,1022,L0P11 601080 THETAC = THETAL G=3600.0%SQRTF((DELPTA*64.4%144.0%DTI)/(CFG*xSXG*SPVG) ) REG=CTI*G/VISG CFC=(0.00140+(0.125/(REG**0.32)}1*4,C DIFA=ABSF(CFC-CFG) IF(DIFA~Q.05%CFC )9+ 9,6 CFG=CFC LOP1=L0OP1+1 IF(LOP1-10)8,8,7 WRITEOUTPUTTAPES1+1013,L0P1 G0TO080 SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 el i1 12 13 14 15 CONT INUE GOTOS NUMT=XINTF(WC*4.0/ (G*3,1416%DTI%*%*2)) BNUMT=FLOATF(NUMT) LOP10=0 DS=P*SQRTF(4.0%BNUMT*0,866/3.1416) XBAR = (DS/2.0}*{THETAC - O0.5%SINF(2,0%THETAC) (2. 0%(SINF(THETAC) )*%3,0)/3.0)/(THETAC-0.5*SINF({2.0%*THETAC)) BRL1 = BSL / (DS-2.C*XBAR) GBRL = O0.77*BRL1**(-0,138) AW=PW*3,1416%DS*%¥2/4,0 AX=(3. 1‘1‘16*05**2/400’”A“ THETA=(1.50%(3.1416-(4.0%AX/DS*%2)) ) **%0.333 AXC=(3.1416-THETA+(SINF(2.0%*THETA)/2.0) )*DS**2/4.0 DIFB=ABSF(AXC-AX) ' IF(DIFB-0.02%AX)15,15,12 THETAZ2=(1.50%(3.1416-(4.0%AXC/DS#*%2) ) )*%0,333 AXC2=(3.1416~THETAZ2+(SINF(2.0%THETA2)/2.0))*DS**2/4,0 THETA=( AX-AXC)*( THETA2-THETA) /(AXC2-AXC )+ THETA LOP2=L0P2+1 IF(LOP2-10)14414,13 WRITEOUTPUTTAPES51,1014,L0P2 6GOT080 CONT INUE GOTO1l1 GC=4.0%WC/(BNUMT*3 ,1416*DT[*%*2) XB=DS*COSF(THETA)/ 2.0 CNB=2.0%XB/(0.866%PpP} XH=(DS/2.0)-XB CNW=(XH/ (0 866*P))~-1.0 XC=DS*SINF(THETA) PCFB=(P-DTO) /P SBK=PCFB*{(DS+XC) /2.0 SW=PW*BNUMT#*(0.866%P¥%2-(3,1416*%DTO**2/4,0) ) SDPT=0.0 SDPS=0.0 LOP8=0 SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE 660 670 680 690 700 710 720 721 730 740 750 760 770 780 790 800 810 820 8 30 840 850 860 870 8 80 890 900 910 920 930 9 40 950 960 970 980 990 SUP 1000 SUP 1010 £Cl 16 17 18 19 20 21 MS=1 SX=0 $SBS=0 TC(1)=TCZ2 TH(1)=TH1 RWK=0TO*LOGF(DTO/D0TI)/2.C PC(1)=PC2 CALL SVH(24PC2,TC24DUM,HC(1)) BN=FLOATF(N) QX=QT/BN DECT=QX/ (WH*CPH) DECH=QX/WC I=1 K=1 SB = SBK#*BSL LOPT7=0 TCON=TH(I}-DTPB/2.0 DENH=141+38E+4+0C-2.466E~02%TCON VISH=0.2122E+CO*EXPF(4032.CE+00/ (TCON+460.0E+00) ) DHOT (K} =DENH VHOT(K)=VISH CON1=(CPH*VISH/TCH)**0.667E+00 GM=WH/ SB RECB=CTO*GM/VISH IF(RECB-800.0}17,18,18 HJB=0.571/(RECB*%0,456) GOTO019 HJB=0.34€¢/(RECB**0.382) HB=HJB*CPH*GM/CON1 GW=WH/SW GS=SQRTF (GM*GW) RECW=DTO*GS/VISH IF(RECW-800.,0)20,421,21 HJW=04571/(RECW**( 4456 G0T022 HJW=0.34€6/(RECW**(0,382) SUP SuUP SUP SUP SUP SUP SUP SupP SUP SUP SuUP SUP SupP SUP SUP SuUP SUpP SuUP Sup SUP SUP SUP SupP Sup SUP SUP SUpP SUP SuUP Sup SUP SUP SUP Sup SUP SUP 10 20 1030 1040 1050 1C60 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320 1330 1340 1350 1360 1370 7C1 22 23 24 25 26 27 28 29 30 31 32 33 HW=HJW*CPH*GS/CON1 HO=(HB*( 1,02, 0%PW)+HW*(2.0%PW) ) *BLFH HO = HO*GBRL RO(K)=1.0/HO TH{I+1)=TH(I)-DECT LOP5=0 HC(I+1)=HC{I)-DECH DELPP=0.0 PC(I+1)=PC(I)+DELPP LOP3=0 LOP4=0 TC(I+1)=TC(I)-DECH CALL SVH(2,PC(I+1),7C(I+1),DUM,HCG) EH=ABSF(HC(I+1)-HCG) IF(EH-0,001%HC(1I+1))31,21,26 TRIAL=TC(I+1) HRIAL=HCG TCOI+L)=TC(I+1)+(HC(I+1)-HCG)*(TC(I)-TC(I+1))/(HC(I)-HCG) CALLSVH(2,PC(I+1)sTC(I+1)+DUM,HCG) EH=ABSF(HC(I+1)-HCG) IF(EH-0.001*HC (I+41)1}31,31,28 TNEXT=TC(I+1)}+(HC(I+1)-HCG)*(TC(I+1)-TRIAL)/(HCG-HRIAL) TRIAL=TC(I+1) HRIAL=HCG TCOE+1)=TNEXT LOP3=L0OP3+1 IF(LOP3-10)30,30,29 WRITEQUTPUTTAPES1,1015,L0P3 GOTU80 GOT027 DENOM=(TH(I+1)-TC(I+1 ) /(TH(I)-TC(I)) TDEN=ABSF(DENCM-1.0) IF(TBEN-C.05) 32,33,33 DELTLM=0.5E+00%(TH(I+1)-TC(I+1)+TH(I)~TC(I)) GO TO 34 SUP SUP SUP Sup Sup SUP SUP SupP SupP SUP SUP SuUP SUP SUP SUP SUP SUP SUP SUP SuUP SuU°p SUP SUP Sup SUP SUP SuUP SUP SUP SUP SUP SUP SUP SUP SUP DELTLM=(TH(I+1)=TCCI+1)-TH(I)+TC(I)) /LOGF ({TH(I+1)=TC(I+1))/(TH(I)SUP 1-TC(I))) SUP 1380 1390 1400 1410 1420 1430 1440 1450 1460 1470 1480 1490 1500 1510 152¢C 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 1630 1640 1650 1660 1670 l168C 1690 1700 1710 1720 1730 1731 GC1 34 35 36 CONTINUE TM=(TC(I+1)+TC(IL))/2.0 PM=(PC(I+1)+PC(I))/2.0 CALL SVH(2,PM,TM,SPVB,HFB) PM=(PC({I+1)+PC(I))/2.0 CALL VISCOS(TM,PM,VISB) TW=TM+0, 23%DELTLM TCW=0,006375%TW+4, 06 RW{I)=RWK/TCW DTFM=0.1%DELTLM TMS=TM+DTFM CALL SVH{2,PM,TMS, SPVIHFI) CALLCONDT(TMS,PM,TCFI) CALL VISCOS(TMS,PM,VISFI) CRE=(CTI*GC/VISFI)*%0,923 CPR=(((HFI-HFB)/(TMS=-TM))*=(VISFI/TCFI))**0.613 CSV=(SPVB/SPVI ) *%%0, 231 HI=0.00459%(TCFI/DTI)}*CRE*CPR*CSV RI(I)=DTO/(HI%DTI) RT(IV=RO(K)I+RW(I)+RI(I) DYFMC=RI{(I)*DELTLM/RT(I) IF(ABSF{DTFM-DTFMC)-0.03%DTFMC)39,39,36 DTFM2=(DTFM+DTFMC ) *,5 TMS2=TM+DTFM2 CALL SVH(2,PM,TMS2,SPVI2,HFI2) CALL CONDT(TMS2,PM,TCFI2) CALL VISCOS(TMS2,PM,VISFIZ) CRE2=(DTI*GC/VISFi2)%*0,.923 CPR2=(((HFI2~HFB)/( TMS2-TM} I *(VISFI2/TCFI2))*%0,613 CSV2=(SPVB/SPVI2}%%0,231 H2I=0.00459%TCFI2%CRE2%CPR2%CSV2/DTI R2I=CTO/ (H2I*DTI) R2T=RO(K)+RW(I)+R2I DTFMC2=R2I*DELTLM/R2T SLOPE=(DTFMC-DTFMC2)/(DTFM-DTFM2) DTFM=(DTFMC-(SLOPE%DTFM) ) /(1.0-SLOPE) SUP Sup SUP SUP SUP SUP SUP SUP SUP SUP SUP SuUP SUP SuUP SUP SUpP SUP SUP Sup SUP SUP SUP Sup SuUP SUP SUP SUP SUP Sup SUP Sup Sup SUP SUP SuUP SUP 1740 1750 1760 1770 1780 179C 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 9¢1 37 38 39 40 41 42 43 44 45 46 47 LOP4=L0OP4+1 IF(LCP4-10)38,38,37 WRITEOUTPUTTAPES1,1016,L0P4 GOTO8C CONTINUE GOTO35 UlII=1.0/RT(I) X{I)=QX/(BNUMT=*3,1416*DTO*U(T)*DELTLM) RE=DTI*GC/VISB CFI=0.00140+0.125/ (RE*%*0, 32) DELP(I)=(4.0%CFI*X(I)/DTI)%GC*%2,0%SPVB/(64.4%3600,%%2,%144,0) DIFC=ABSF(DELP{(I}-DELPP) IF(DIFC-C.O5%DELP(I}))43+43,40 DELPP=DELP(I) LOP5=L0OP5+1 IF(LOP5-10)42,42,41 WRITEQOUTPUTTAPESL1,1017,L0P5 GOTO080 CONT INUE GOT0Z24 IF(MS)53,53,44 IBK(K)=1I TW=(RI(I)+0 5 RW(TI)I*(THC(L)-TC(I))/RTLI)+TC(I) ALPHA=(0,0031%TW+5.6G1) ETW=31.,65-0.,005%TH CON2=ALPHA*ETW/{(1l.4*LOGF(DTG/DTI )} CON3=1,0-(2.0%DTO**2%LOGF(DTO/DTI)/(DTO**2-DT[*%*2)) CON3=CON3*(-1.) IF{TW=101543)45446446 B=24000.0 SL=7.5 GOTO47 B=57000.C SL=40.0 CON4=3,0%(B-SL*TW)-2600C.C TWALL(K) =TW DELTWA(K )=CON4/(CONZ2*CON3) DELTWIK)I=RW(II*(TH(TI-TC(I)}/RT(I) SUP SUP SupP SUP SuP SuUpP SUP SUP sSue SuPp SUP SUP Sue SUP SUP SuUpP SUP SUP SUP SUP SUP SUP SupP Sup SUP SUP SUP SUP SuUP SUP SUP SUP SUP SUpP SuUP SUP SuP SUP 2100 2110 2120 2130 2140 2150 2160 2170 2180 2190 2200 2210 2220 2230 2240 2250 2260 2270 2280 2290 2300 2310 2320 2330 2340 2350 2360 2370 2380 2390 2400 2410 2420 2430 2440 2450 2460 2470 Lel 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 IF(I-1151451,49 IF(N-I)51,51,50 BWN=1.0 GOTOS2 BWN=0,.,5 DELPSB=0.6*%CNB*{(GM/3600.0}**2/(64.4%144 .0%DENH) DELPSW=BWN*{2.04¢0.6%CNW)*(GS/3600.0)*%2/(64,4%144.,0%DENH) DELPS(K)=(DELPSB+DELPSW)*BLFP SDOPS=SDP S+DELPS(K) SBS = SBS+BSL SDPT=SOPT+DELP(I) SX=SX+X(1) [FIN-1)162462,54 I=I+1 IF(SBS-SX)58458455 MS=0 LOP7=LOPT7+1 IF(LOP7-30157457+,56 WRITEOUTPUTTAPES51,1018,L0P7 GOTO80 CONTINUE GO0TOZ23 MS=1 K=K+1 CONTINUE LOP8=LOP8B+1 IF(LOP8-30)61461,+60 WRITEQUTPUTTAPES51,1019,L0P8 GOTO80 CONT INUE GOTO16 EDPT=ABSF(SDPT-DELPTA) IF(EDPY~C.03%DELPTA 66466463 NUMT=XINTF(BNUMT*(SDPT/DELPTA)*%0,35) LOP9=L0OPS+1 IF{(LOPS~10)¢€5, 65,64 WRITEOUTPUTTAPES1,1020,L0CP9 G0TO80 SUP Sup SUP SUP SuP SuUpP SUP SuUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP Sue SuPpP SUP Sup SUP SuUp SUP Sup SUP SUP SUP SUP SUP SUpP SuUP SUP SUpP SUP SUP SUP 2480 2490 2500 2510 2520 2530 2540 2550 25€0 2570 2580 2590 2600 2610 2620 2630 2640 2650 2660 2670 2680 2690 2700 2710 2720 2730 2740 2750 2760 2770 2780 2790 2800 2810 2820 2830 2840 2850 8¢I 65 66 67 68 69 70 71 1001 FORMAT(1H19//+43X91HJ95Xs5H1ST-1+44X96HDELT-We3Xy8HDELT-W-A,3X, 6HT-WALL 93Xy 6HDELP-S+3Xs6HDENS-H+3 X4y6HVISC—-H) 1 1002 FORMAT(IH 54(1H=-)y3X946(1H=)s3XsT(1H=)43X,8(1H=)44(3X,6(1H=)),/) 1 1003 FORMAT(I5¢3XsI1€93XeF7e293X9FB84292(3X4F6.143X4F6.3)) 12 73 74 CONTINUE BSG=BSL GOTO10 EDPS = ABSF(SDPS - DELPSA) IF(EDPS - O O3%DELPSA)T70,70,67 BSL = BSL*SQRTF(SDPS/DELPSA) LOP10=LOP10O+1 IF(LOP10-10)€94+69,68 WRITEOQUTPUTTAPES1,1021,L0P10 GOTO80 CONTINUE GOTO15 CONTINUE CALL RITEZ2 J=0 JN=J+1 JNC=49+JN IF(JN.GT.K) GO TO 73 WRITEQUTPUTTAPES1,1001 WRITEQUTPUTTAPES1,1002 NBS = K DO 72 J=JNyKsl WRITEQUTPUTTAPES1,1003+JIBK(J)sDELTW(J) +DELTWA(J) yTWALL(J), DELPS(J)DHOT(J )+ VHOT(J) IF(J.EQ.JNC) GO TO 71 CONT INUE CONT INUE CALL RITE3 I=0 IN=I+1 INC=49+][N IF(IN & ORNL TM-2815 . Lundin . MacPherson MacPherson McCoy McLain McNees McWherter Meyer Moore Ne Ims Nicholson Perry Pickel Rosenthal ap Scott iman-Tov . Stoddart . Thoma Trauger Walker Watson Watts Weir Whatley White . Winsbro Young Central Research Library Document Reference Section GE Division Library Laboratory Records Department Laboratory Records, ORNL R.C. ORNL External Distribution Patent Office David Elias, USAEC, Division of Reactor Development and Technol- ogy, Washington, D. C. 20545. Ralph H. Jones, USAEC, Division of Reactor Development and Tech- nology, Washington, D. C. 20545. T. W. McIntosh, USAEC, Division of Reactor Development and Tech- nology, Washington, D. C. 20545. 158 97. M. Shaw, USAEC, Division of Reactor Development and Technology, Washington, D. C. 20545. 98-99. Division of Technical Information Extension. 100. Laboratory and University Division, USAEC, ORO.