” o 9 . -t} a) ORNL-TM-2952 Contract No.' W-'-7403-eng-26l REACTOR DIVISION PARAMETRIC SURVEY OF THE EFFECTS OF MAJOR PARAMETERS ON THE DESIGN OF FUEL~TO-INERT-SALT HEAT EXCHANGERS FOR THE MSBR A, P, Fraas and M, E, LaVérne NOVEMBER 1971 P . N O TI C E : : -‘-'l'his rcport 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, | 7'} makes sny warranty, express or implied, or assumes any -} legal Hability “or responsibility for the accuracy, com- ’ ‘pléteness or: usefulness of any information, apparatus, | . | product 6r process disclosed, or represents that its nse - P wonld not infrlnge private!y owned rights ' OAK RIDGE NATIONAL LABORATORY ' Oak Ridge, Tetinessee 37830 - operated by _ UNION CARBIDE CORPORATION “x\' ~ for the o ‘ U S ATOMIC ENERGY COMMISSION BISTRIBUTION OF THIS DOCUMENT g UNUWZM . » ) to about 825 ft for Flinak. Fabrication costs for a tube bundle will depend primarily on the num- ber of tubes in the bundle;'because this determines the number of header - welds required. Material costs will vary with tube length and the total tube cross~sectionallarear For the same set of parameter changes employed above with respect to fuel inventory, one finds virtually no change in the number of tubes and, thus, essentially an unchanged fabrication cost. Tube'length,'from Table 1, is,reduced‘by a factor of approximately O.45. The smaller tube'cross-sectional area contributes a further factor of 0.68, for an overall reduction_factor of about 0.3, that is, a reduction in mate- rial weight of nearly 70%. | - A substantial fraction of the above savings is predicated on the ability to increase the temperature difference between the fuel and inert salt from 100 to 150°F; Experience gained in the ANP Program with thermal stresses indicated that it is not difficult to assure a high degree of reliability and freedom from difficulties with thermal stresses if the temperature difference between the two fluid circuits does not exceed 100°F. However, with careful design it seems likely thet the temperature differ- ‘ence might be increased to]asrmuch as 150°F without deleterious effects provided that both”sfthorough"analysis_and near full-scsle'tests could be ~carried out. As can be shown from the equatlons in the analysis of this report for 8 given system and fluid temperature rise, the pumping power in either fluid circuit depends only on the salt properties and the pressure drop in dthat circuit being linear in the pressure drop. Thus, for a given fuel and inert salt combination, the pumping power can be reduced only by reduc- " ing the pressure drop For a given fuel and set of specified operating conditions, the pumping power can be reduced 10 to 20% by using Flinak in place of NaBF, in the secondary circuit. The savings in total heat ex- changer pumping power range from 10 to 20%, depending only on the ratio of the inert salt pressure drop to the fuel pressure drop. ANALYSIS The analysis presented in this section is predicated on the use of smooth, round tubes on an equilateral triangular pitch with axial fluid flow outside the tubes. Conventional, well-established relationships were used for the various heat balance, convective heat transfer, and pressfire drop equations employed. (Recent experiments with molten salt favor reducing the heat transfer coefficients about 15% from the values used here.) Design Bases and Criteria The analysis and parametric study presented in this report were carried out on the basis of a U-tube heet exchanger tube bundle having the tubes in an equilateral triangular pattern with the fuel salt flowing axially on the shell side and the inert salt (in the secondary circuit) in counterflow on the tube side as described in Ref. 1. A cross section of the exchanger configuration envisaged is shown in Fig. 1. However, as will be seen subsequently, the analysis is by no means limited to the particular configuration and conditions treated here but is applicablé to a much wider range of problems. | | The tubes were placed on an equilateral triangular pitch, rather than a square pitch, in order to increase the thickness of the fluid stream in the region between adjacent tubes because data from ANP heat exchanger tests had indicated that thin fluid ligaments between tubes 'lead to flow stratification and a loss in heat transfer performance. This effect was deduced from the curves in'Figs. 2 and 3, which were obtained with ANP heat exchangers.® ‘The tube spacers, consisting of "oombs" of flattened wire, employed in the ANP heat exchangers could be used with the equilateral triangular spacing considered hefe. That approach would yield &n increase in pres- sure drop by a factor of about 1.5 over that for the ideal case with no spacers. It seems likely that spiral wire spacers would lead to an ‘R ®© #) - RNL DWG T1-9163 ) i ’ " Fig. 1. Tube Bundle for One of the Six Fuel-to-Inert Salt Heat Ex- changers Employed in Pa.ra.llel in the Conceptual Design of Ref. 1 for a 2200 Mw(t) Reactor. | ORNL-LR-DWG 42878 100 , 4 MIXTUR Npgy WNpr) 420,023 (Nge) Nwu/(Npr)®4 TA EXTERNAL 10,000 Fig. 2. The Heat-Transfer Characteristics of a Molten Sa.lt When Flowing Inside Round Tubes (Yarosh, Ref. 2). ORNL—LR-DWG 42860 100 ORNL 1 = { IHE-8 ORNL { SHE-2 B2 IHE-8 OPE{ SHE 2 APE {1 SHE 7 APE 2 SHE7T OORNL{ TYPE e ORNL { IHE-3 o ORNL 2 IHE-3 10 B4 (LEG 1) IHE-3 B2 2) IHE-3 (Nnu/Npr)OA 100 » 1000 Nre 0,000 Fig. 3. The Heat-Transfer Characteristies of a Molten Salt Flowing on the Shell Side of Twelve Different Z-Tube Heat Excha.ngers Tested in Six Different Systems (Yarosh, Ref. 2). » o ) «} a) 7 increase in pressure dfbp Somewhat less than this and they might also have a somewhat more favorable effect on the heat transfer coefficient, but no clear-cut data are available, A definitive ansfier to these guestions would require testing of the exact geometry of the heat exchanger matrix contem- plated. | | | Similarly, the effects of varlous types of surface roughness designed to increase the heat transfer coefficiEnt,.in.fabt, aréfvery-difficult to predict and will also require tests of the éXact geometry contemplated in order to determine the extént to which the heat trahsfer coefficient is improved at the expense of an increase in préssure drop. Because it ap- pears that surface roughness frequently has not paid important dividends for cases of the type of interest here, and because of the uncertainties involved, it was decided to conduct the analysis assufiing bare, smooth tubes with no allowances for spacers, Incluéion'of:the latter would in- _créase the fuel pressure drop by around 30 to 50%, but should also in- crease the heat transfer coefficient somewhat so that, with an equilateral triangular tube pattern, the_éhélléside.heat transfer coefficient might - well be higher than for-the.corfesponding circular passages inside the round tubes. Derivatioh bf fieat Exchanger Equations We assume that the heat exchanger tube bundle is composed of round, smooth tubes with axial flgid flow outside the tubes. We neglect entrance effects and the shell-Side?firessure drop associated with the,tube spacers. Nomenclature for the analyéis[is given'in Table 2. ,Heat Balanfies The axial heat transport is given in terms of thé)maés flows, fluid temperature changes,'and'exéhangér geometry by g_é-GSAscpsaTS | | - (1) | and Table 2. Nomenclature R Q H o P Symbol Meaning Units A Axial flow area ft2 | Cp Specific heat | ' Btu/lbm'F Diameter . _ ft Blasius friction factor o ) Mass velocity | lb:m/hr'ft2 o Dimensional conversion constant .lbmft/lbf'hr2 | (4.170 x 108) h Heat transfer coefficient _Btu/hr-ftz-F k Thermal conductivity Btu/hr- £t.F L Tube length £t N Number of tubes AP Pressure difference l'bf/ft2 Q Heat transfer rate 7 Btu/hr Sy — S5 Shell-side coefficients and exponents - Ti - Ts Tube -side coefficients‘and'exponents AT | Film temperaturé difference ' F degrees &T Fluid axial temperature difference F degrees t Thickness ft i Viscosity lbm/hr- ft Density lbm/ft3 Subscripts | m Mean o Outside 8 Shell side t Tube side W Tube wall 2 Q= GMDtNC 0Ty - (2) The radial heat transport by convection and conduction through the ) two fluid films and the tube wall, respectively, is given by Q = n 0 e | e Q = b wD LNAT, , | (4) and C - = kwTrDmen/tu : (5) Convective Heat Transfer - The convective heat transfer relations employed here are those of Sieder and Tate? for laminar flow, and Colburn“ for turbulent flow. Both relations may be expressed in the form given by Eqs. 6 and 7, where the several coefficients and exponents are determined from Table 3 according - to the flow regime, 3 2ol o (s (e} o -} B i s B Tlc_vz EreE” o Temperature Difference BetWeen Fluids' ~ The overall temperature difference, AT between the two fluids is ~glven by the summation of the temperature differences through the two fluid films and the tube wall “ AT--_-.ATS "'_ATW +ATt . | (8) a) 10 Table 3. Coefficients and Exponents Used in Convective Heat Transfer and Friction Factor Equations Sy S Ss S, S5 Qutside tubes (shell side) Laminar flow 4/2/10 1/3 1/3 64 1 Purbulent flow 0.032 0 4[5 0.256 1/5 Ty Ts Ty T, Ts Inside tubes (tube side) Laminar flow 4/3/10 1/3 1/3 64 1 Turbulent flow 0.023 0 4[5 0.18 1/5 Note: The coefficient Sy for turbulent flow is obtained from Ref., 5, Pressure Drops The pressure drop on the shell side is given by the Blasius relation, L @2 P = f e —— (9a) s sDS 2gcos where the friction factor is defined, in terms of the shell-side Reynolds (%Ds)fss £ = S, o . | - (9b) Similerly, the tube-side pressure drop is determined from number, by L Gi AP, = f o= =2 (10a) t tD, 2g o, and ot s "} - 11 D, -T5 £, m(fl t b | (10b) ™ | The coefficients and exponents appearing in the expressions for the fric- tion factors also are determined from Table 2 according to the flow regime, Shell -Side Equivalent Diameter The equivalent diameter of the shell-side flow passage is determined from the definition, | D = —= S (11) Solution of the Equations Let us take as input parameters (independent variables) the total heat . transport ‘the pressure drops on the ‘shell and tube-sides, the tube size, the temperature phanges\in the,two fluid streams, and the overall_tempera- ture difference between_the'fiuids.- Then5,the foregoing set of 11 equa- tions is just sufficient to determine the two mass flows, the equivalent diameter and flow area on the .shell side, the overall length and number of tubes in the bundle, the three transverse temperature differences, and the ‘two heat transfer eoefficients,_ll dependent variables in all. ' _Reduction to a Single Equation' | Let us now eliminate the friction factors between Eqs. 9a and 9b and _,Vbetween Eqs. 10a and lOb Rewriting the remaining equstions with only known quantities on thelr right hand sides then ylelds S Q Ghy = O =57 - (12) ps 8 L e Q : S ( ) GN=Cp = — (3 t In2c_, st 4t pt Tt 12 _ Q hSLNATS =C3 = ?fi; » (14) Q h, INAT, = C, =~;fi; ’ (15) Qt | me=cs=ka, ,, - (16) mw . n pt-52-83182-53 ¢ (c k2)1/3 1/3- G 1) 578 s 6 ps s ? h L7263 = Cq = T{(C kz)l/ 3,1/3-T3-14T5+T; (18) £ pt t % t I ATS+ATW+ATt=o_3=AT, (19) o 1o 2g p AP 6> Ssp7 1S5y, o g = —SE & (20) s ' S5 : S4b 2-T 28 0, AP D2 Gy °L=Cyo = ) (21) t | - 4ty and -1.-1 _ T | L | AN D~ =Ca=7D . (22) The coefficients C; through C;; are defined by the groupings of input parameters appearing on the extreme right of each multiple equation. We now reduce the above set of 1] equations to the following single equation in tube-side mass flow, E E E th + C20Gt2 + CZlG‘bB —Co=0. _ (23) ¥ ) =) 13 - The coefficients and exponents appearing in Eq. 23 are, in general, rather complex combinations of the coefficients Cy through Cy; and the various coefficients and eprnegts obtained from Table 3, Details of the elimina- tion process will not bérpresented'here but are availgble in Appendix A. Equation 23 may be solved for the tube-side mass flow rate by an iterative process,ffollowing-which the remaining dependent variables may be determined by a series of back-substitutions. | 7 B In any iterative prdcess, the speed 6f‘convergence, in fact, perhaps convergence at all, dependS'on_having a good firét estimate of the value of the variable being soUght. Empifically;'the-followingrequation,was found to give a good initial estimate for the yalue’of_the tube-side mass flow rate. 1/E, o= odemrem] - Equation 24 fias'tested on a wide variety of-input parameters and, in most . cases, gave an initial value_for_the tubefside flowAwithin-2% of the final 'iterated value. Computer Solution Because of the obvious tedium, and the attendant error-proneness, ~involved in any sort of desk calculator solution of the above equations, a FORTRAN program was prepared for use on the Call-A-Computer (CAC) time- . sharing syStem.__Details_ofgthe program operation may be found in the appendices. In,particfilar,_a,chPUter-prepared printout of the complete program is presented in Appendix B, Appendix C contains samples of pro- gram input'and output,'togefihgrrwith instructions for uSé'Of the programQ o Exte£§ions of the.Analysié_ '-'Although the parametfic;étudy:presentedjlater'in this-repbrt aSéumes © an equilateral triangular tube pattern and fused salts in counterflow with equal temperature changes in the two streams, the basic analysis is not, in fact, so limited, as will be shown below. 14 6ther Fluids Equations 6 and 7 for the convective heat transfer.coefficients, although applied in the parametric study only to fused salts, are actually applicable to any fluid having a relatively high Prandtl number, For liquids of very low Prandtl number, such as liquid metals, Eqs. 6 and 7 must be modified, For example, one could employ the Lubarsky-Kaufman re- lation® for the Nusselt number in turbulent flow and the theoretical value of 4.36 in laminar flow. These changes involve only redefining the expo- nent on the Prandtl number in Egs. 6 and 7 to be a variasble rather than the present constant and extending Table 3. ‘Tube Patterns The basic equations, 1 though 11, contain no reference to tube pat- tern, per se. The implication is that, for a given set of input parameters, - the same solution set of dependent variables would be obtained for an equilateral triangular pattern as for, say, a square pattern. This, of course, involves the implicit assumption that the latter spacing is not such as to result in the performance deterioration dbserved in Figs. 1 and 2. S In order to determine tube spacing, one must employ an auxiliary rela- tion such as Eq. 25, A, = N(/352/2 — 1D2/4) - (25) which defines the tube spacing in terms of the shell-side flow area, the number of tubes, and the tube OD for an equilateral triangular pattern. Other Conditions Although applied in the parametric study only to a counterflow heat exchanger with equal temperature -changes in the two streams,_the present .analysis may be extended readily, both to parallel flow and to counterflow with unequal temperature changes, by the simple device of properly defin- ”ing the overall temperature difference. The appropriate quantity is the log mean temperature difference (IMTD), defined by~ - » ) o) 15 GTD — LTD IMTD = ——————— (26) ' log ——== GTD eLTD where GTD is the greater and LTD is the lesser of the two terminal tem- perature differences between the two streams. When the two temperature differences are equal, the IMTD becomes indeterminate and must be taken as equal to either of the two temperature differences, The existing com~ puter program uses these definitions. PARAMETRIC STUDY In this study, the U-tube configuration of Fig. 1 was employed, with the fuel salt flowing axially sround the tubes on the shell side and with the inert salt in counterflow inside the tubes. The heat.load was kept fixed and equal to that for one of the six heat exchangers for a 2200 Mw (t) reference design reactor.l The tube wall material was taken to be INCO 800 and the fuelxemployed was the lithium-beryllium-thorium-uranium - fuel salt in current use for reference design purposes at the time of writing. Two different inert salts, NaBF, and Flinak, were used in the secondary circuit. The. physical properties of the materials used were taken from Refs. 7 and 8 as tabulated in Table 4 The temperature rise in the inert salt and the temperature drop in the fuel in traversing the heat exchanger were kept constant at 250°F With a temperature difference between the two fluid streams of 100°F, the heat exchanger characteristics were calculsted for each of the two inert salts, using all combinations of three different shell side pressure _drops three different tube side pressure drops, and two different tube dismeters. The results are given in Table 5. For one of the tube sizes, the effects of changing the temperature difference between the fluid ' streams to 125 and 150°F were then investigated for the same set of pres- 'sure drops and inert salts used previously. Table 6 summarizes the re- sults from this set of calculations The input parameter variations used in this study are summarized in Table 7. 16 Table 4. Reference Design Conditions and the Physical Properties at Design Temperatures for the Materials Used ‘Reference Design Condition Fuel temperature in, °F | 1300 Fuel temperature out, °F | 1050 Inert salt in, °F : S 950 Inert salt out, °F 1200 - Tube material L INCO 800 Tube thermal conductivity, Btu/hr NTUBE | 105 DIMENSI@N DAT(20) ) 110 COMMON CLAM:CURT:SI152053054’55:Tl:T2:T3:T4:T5 115 PI = 3.1415926543 PI104 = Pl/4. 120 CURT = 147343 CLLAM = 44./10tCURT 125 TWOGC = 64.348%3600.123 C00 = 5*%PI/SQRT(3+) 130 | DAT(20) = DAT(20)+1.0 135 READ, NIN3 IFC(NIN)Y 21s21 140 READ» (JsDATCJY2I=1sNIN) 145 @ = DATCI1) 150 DPS = DAT(2)3 TSI = DAT(3)3 TSO = DAT(4) 135 CPS = DAT(S5)3 MUS = DAT(6)3 KS = DAT(7)3 RHOS = DAT(8) 160 DPT = DAT(9)3 TTI = DAT(10)3 TT® = DAT(11) 165 CPT = DAT(12)3 MUT = DAT(1335 KT = DAT(14)3 RHOT = DAT(15) 170 DO = DAT(16)3 TW = DATC17); KWALL = DAT(18) 175 RHOW = DAT(19)s ICASE = DAT(20) 180 PRINT 30, ICASE , 185 30FBRMATC/“CASE "» 13) 190 DPS = 144.%DPS3 DPT = 144.%DPT 195 DO DO/12+3 TW = TW/12+3 DT = DO-2+%THW 200 A0 = PI@A*DO*DO3 AT "= PIfiA*DT*DT: AW = AO-AT 205 DTS = TSI-TSO3 DTT = TTO-TTI 210 DT1 = TSI-TTQs DT2 = TS@-TT1 215 DM = (DO-DT)/LO@GC(DO/DT) 220 €08 = DTi: IF(DTI-DT2) 2,3,2 225 2 CO08 = (DTI—DT2)ILGG(DT1/DT2)- 230 3 CO0S5 = Q/PI : 235 CO1 = Q/(CPS*DTS)3 coz = QI(AT*CPT*DTT) 240 C03 = COS/D0s3 .CO4 = COS/DT3 CO5 = COS*TwW/ (DM*KWALL) 245 co6A = (CPS*KS:Z*MUSTtCURT , ' ' 250 CO7A = (CPT*KT?2*MUT)OCURT/DT 255 CO%9A = TW@GC*RHOS*DPS 260 C10A = TWGGC*RHGT*DPT*DT 265 Ci1t = PI@4xD03 C12 = CO1/C€CO02%C11%3 C13 = CO3/C05 270 C14 = C04/C053 C15- 602*008/005: N=0 R 275~ CALL STURB3 CALL TTURB; 1AS = IAT = - "280 4 CO6 = CO6A%S1/MUS+S3 ' 285 €07 = COTA*T!*DT?(TE+T3)IMUT?T3 290 €09 = CO%A/(S4*MUStSS) - 298 Cl0 = ClOA*(DT/MUT)fIS/T4 300 _Cté = C13/C063 c17 = 009/0103 018 = 0141007 ©.- 305 €19 = C15%C10 ~ 310 El = 3.-TS53 E4 = (S2- 1. )/3.; . 315 E2 = 3.-2.%52-S3+E4*(2.%T5+55) - 320 E3 = E1-T3+4T2%(T5-24) 325 ES = 1.-S2- sa+aq*c1.+ss>h* 330 €20 = C16%C10152%C171EASCIZIES L6 HEATX2 CONTINUED 335 340 345 350 355 360 365 370 375 380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535 540 545 550 555 S60 565 570 575 580 22FORMATC(//T7X"P DRGP T IN C21 = C18%C10tT23 GT = 0.9%(C19/(C20+C21))t(1./E2) DO S I =1, 10 » GT! = GT*El13 GT2 = GTtE23 GT3 = GT*ES3 G6T20 = C20%GT23 GT21 = C21%GT3 FUN = GT1+GT20+GT21-C19 : DER = (E1*GT1+E2*GT20+E3*GT213)/GT3 DGT = FUN/DER GT = GT-DGT3 IFC(ABS(DGT/GTX-1.E-5) 6 : 5 CONTINUE ' , PRINT» tt"NOT CONVERGED. DGT/GT ='"» DGT/GT 6 GSAGT = (C17*C121C1.+SS)*GTt(S5~T5))*1CURT GS = GT*GSOGTs DS = C12/GSOGT RET = GT*DT/MUT3 RES = GS*DS/MUS 1CT = 03 IFCRET-1502.) 73 ICT = 1 7 NT = 03 IFCIAT-ICT) 9,859 8 NT = 1 9 ICS = 03 IF(RES-994.) 103 ICS = 1 10NS = 05 IFC(IAS-ICS) 12,11,12 1INS = 1 o 12IF(NT*#NS) 13,13,18 13N = N+13 GO TO (14,15,16,17) N 14CALL TLAM 3 IAT = 03 GO TO 4 1SCALL SLAM 3 IAS = 03 GO TO 4 16CALL TTURB3 IAT = 13 G@ TO 4 17PRINT, °*ASSUMED AND CALCULATED REGIMES DO NQT,AGREEQ“ Go TO 1 | 18LTUBE = C10#GTt+(TS-2.)3 NTUBE = C02/GT _ AS = CO1/GS3 HS = CO6%(DS*GS)1S3#(DS/LTUBE)*S2/DS VS = GS/RH@S3 VT = GT/RHOT - - HPS = DPS*AS#VS/1.98E63 HPT = DPT#AT*NTUBE#VT/1.98E6 HT = CO7*GT+T3/LTUBE*T23 DTW = COS5/ (LTUBE*NTUBE) FDTT = Cl1A4%DTW/HTs FDTS = C13*DTW/HS S = SQRTC(COO*DO*C(DS+D0))? , BUNWT = LTUBE*(NTUBE*(AT*RHOT+AWX*RHOW) +AS*RHOBS) PRINT 205Q512.%D0s12¢%TWs12+%DT»KWALL»RHGW PRINT 22,DPS/144.,TSI,TS0,CPS>MUS,»KS,RHBS, +DPT/144¢>TTI>»TTO>CPT>MUT>KT»RHOT ‘ PRINT 24, NTUBESLTUBE,12.%S512.*DS>» +AS*L.TUBE s AT*LTUBE*NTUBE » AW*LTUBE*NTUBE »BUNWT PRINT 26,C08,DTWsFDTSsHSsFDTTHT PRINT 285GT/GS»GSsVS/3600+sHPSsRESsGT»VT/3600+5HPTHRET 20FORMAT (/3X"HEAT"3XA4(4X"TUBE"Y7X"TUBE"/ +3X"LOAD" 7X"TeDeAX"WALL"AX" 1D 6 X"K"TX""DENSITY"/ +#2X"BTU/HR "3C(6X"IN")2X"BTU/HR FT F LB/FT*t3*"/ +1PE10:35s0P3F8¢4sF9:25F11+1) + LB/HR FT BTU/HR FT F LB/FT*3'/ +* FUEL:"F6¢05F8¢05FTe05F835sF10.25F11.25F12.1/ T QUT SP. HEAT VISCOS'Y + CONDUCTIV'Y DENSITY"/9X"“PSI"SX"F"6X"F"4X"BTU/LB F » “ u7 HEATX2 CONTINUED 585 +" SALT'"F6 OoFS 0:F7 OJFS 35F10+2,F11.2,F12.1) - 590 595 24FORMATC(//™ NUMBER"4X2("TUBE"AX)"EQUIV "6 X"VOLUMES" 7X""BUNDLE"/ 600 +"@F TUBES LENGTH SPACING DIAM'R FUEL SALT TUBE"2X"WEIGHT"/ 605 412X"FT "2(5X“IN"2X)3(2X“FT*3")4X“LB"/F7-0:F8-l:2F9.4:3F6.1:F8 0) " 610 615 26FGRMAT(//4X"LMTD WALL DT“IOX"FILM DT CIEFFICIENT"/ 620 +SX"F"TX"F"16X"F"4X"BTU/HR FTt2 F"/2F841,3X" FUEL:", 625 4F8+41,F11.0/20X"SALT3"sF8¢15F11.0) 630 : ' L , : ' 635 28F@RMAT(//"FLOW RATIG"11X"FLOWS"4X"VELOCITIES PUMPING 640 4 REYNPLDS"/3X"GT/GS*"11X"LB/HR FTt2 FT/SEC"6X"HP" 645 +5X“NUMBERS"/F8+4,4X"” FUEL:"1PE11+4,0PF8:1,F11.0,F10.0/ 650 +!3X"SALT'"1PEllo4:0PF8 1,F11.0,F10.0/77) ' 655 GO T@ 1 660 21STOP 665 SUBRGUTINE SLAM3 COMM@N CLAM:CURT:SI:S2:SS:S4:SS:T!:T23T3:T4:TS 670 S1=CLAM3 S2=S3=CURT3 S4=64.3 S5=1.3 RETURN 675 SUBRGUTINE TLAM;3 COMMON CLAM,CURT»51,52553554,55,T1,T2,T35T4,T5 680 T1=CLAM3 T2=T3=CURT3 T4=64.3 T5=1.3 RETURN - 685 SUBROUT INE STURB3COMMON CLAM:CURT:SI:S2aS3:S4:SS:T!aT2:T3:T4:T5 - 690 S1=+0323 S2=0e3 S3=+83 S4=.2563 55=.23 RETURN 695 SUBRGUTINE TTURB3COMMON CLAM:CURT:SIoS2aSS:SA:SS:Tl:T2:T3oT4:T5 700 T1=.0233 T2=0.3 73=-Bi T4=.1843 TS=.23 RETURN 705 $DATA : LENGTH ABGUT 5800 CHARS. L8 APPENDIX C SAMPLE COMPUTER PROGRAM INPUT AND OUTPUT - This Appendix contains information on the‘preparationVOf input for - the computer program described in Appendix B. A suggested input form, com- pleted, and the corresponding paper tapeiinformation are shown, followed by a sample printout from a cdmputer run. B | Table C-1 shows a suggested input form for HEATXE,with-data entered for two sample cases. Note that the given units are ndt completely con~ sistent but are specified for convenience. Conversibn to a'éonsiStent set is performed internally by the program. : For each item specified in the column headed "DAT(I)", the correspond- ing "I" must be given. Also, the pairsrof input'numbers specified must agree with the corresponding number at the top of the form. Note that for the first case a complete set of input (the first 19 items) must be given. The initial case number need not be specified, in which case the program will start with "one", incrémenting by unity for each sucéeeding'case. For all cases after the first, only those items differing from the immediately preceding case need'bé changed. Note that if item 20, "Case Number", is specified, the normal sequence of consecutive case nunmbers is interrupted, continuing with the new value. A normal termination of the computer run is obtained by specifying "NIN", the pairs of input numbers, to be zero or negative. If "NIN" is omitted, inadvertently or otherwise, an abnormal termination will occur, with an error message that may be disregarded. | Table C-2 is a printout of a paper tape prepared from the specificé— tions of Table C-1. The line numbers shown are not essehtial; the exist- ing program ends at line T05, so that any greater line number will suffice for starting the tape. It is suggested that an initial line number of roughly 800 or greater be used for input to allow for possible program eXpansion. The input is free-form, i.e., the numbers fiay be typed in any con- venient form (note the mixture of exponential, fixed-point, and integer forms) with as many or as few numbers per line as convenient. It may be v 49 Pairs of Input Numbers _ 19 5 0 " Quantity Units | I DAT(I) 1 DAT(I) DAT(1) Beat Load Btu/hr 1 | 1.2 | | Shell Side: - Pressure Drop Psi 2 100 Inlet Temperature | OF 3 1500 Outlet Temperature. | °F | ¥ | 1050 Fluid Specific Heat | Btu/1b °F 5 .32k " viscosity Ib/hr £t 6 23.5 | " Conductivity | Btu/br £t °F | 7 .58 " Density o/te° 1 8 | 208 Tube Side: Pressure Drop Psi .9 100 Inlet -'I‘emperature Op 10 950 Outlet Temperature | °F 11 | 1200 Fluld Specific Heat | Btu/1b °F - | 12 . 12 437 " Viscosity Ib/hr £t | 13 1.95 13 12.6 " Conductivity | Btu/hr £t OF | 1 " .266 1h 2,66 " Demsity w/ee> |15 | ng 15| 13 Tubes: - 0. D. In s .3125 Wall Thickness In , _117'.- | 023 " Conductivity |Btu/br ££°F | 18.] 1.5 " Density /e’ g | sm | Case Number .. el ; 20 | 19 © Teble C-1. Input Farm for EEATX2, Shoving Semple Input for Two Cases. >0 800 19 . 801 1.25E9 ' 802 2 100 3 1300 4 1050 S +324 6 23.5 7 «58 8 208 803 9 100 10 950 11 1200 12 «36 13 195 14 266 15 119 BO4 16 «3125 17 023 18 11.5 19 531 805 5 - 806 12 437 13 126 14 2.66 15 132 807 20 19 _ - 808 0 Teble C-2, Printout of Paper Tepe Prepasred from Data of Té,blé C-1. - uy ol seen by comparing Tables C-1 and C-2 that the partlcular grouping used puts similar items on one line. The results of a computer run; uSing the input tape of Table C-2, are shown in Table C-3. The program spaces the printouts to give two cases per page, CASE 1 HEAT TUBE TUBE LBAD QeDeo WALL BTU/HR IN IN 1.252E+09 «3125 «0230 P DROP T IN T 2UT PS1 F F 52 TUBE TUBE TUBE IeDe K DENSITY IN BTUWHR FT F LE/FTt3 2665 1150 531.0 SP. HEAT VISCOS'Y CONDUCTIV'Y BTWLB F LB/HR FT BTU/HR FT F FUEL: 100, 1300. 1050. 2324 23.50 58 SALT: 100. 950. 1200. «360 1.95 27 NUMBER TUBE TUBE EQUIV. VBLUMES BUNDLE OF TUBES LENGTH SPACING DIAM'R FUEL SALT TUBE WEIGHT FT IN 4944. 31.5- +4106 LMTD WALL DT F F 100.0 177 FUEL?: - SALT: FLEW RATIO FLOWS GT/GS LB/HR FTt2 11179 FUEL: 6+4973E+06 SALT: 7.2632E+06 CASE 19 REAT TUBE TUBE LeAD BeDeo WALL BTU/HR IN IN 1252E+09 «3125 « 0230 P DROP T IN T OUT PS1 F F IN FTt+3 FT*3 FT*3 LB «2823 T4.9 603 2246 34757, FILM DT C@EFFICIENT F BTU/HR FTt2 F 47.0 2091. 35.2 3271. VEL@CITIES PUMPING REYN@LDS FT/SEC HP NUMBERS 8.7 S40. 6504. 17.0 E50. 82720, TUBE TUBE TUBE I.D. K DENSITY IN BTU/HR FT F LB/FTt3 «2665 1150 531.0 SPe HEAT VISC@S'Y CONDUCTIV'Y BTU/LB F LB/HR FT BTU/HR FT F FUEL: 100. 1300. 1050. 0324 23.50 « 58 SALT: 100. 950. 1200. « 437 12.60 2566 NUMBER TUBE TUBE EOUIV. VOLUMES BUNDLE OF TUBES LENGTH SPACING DI FT IN 4444. 28.1 <4132 LMTD WALL DT F F "100.0 22.1 FUEL: SALT: FLEW RATI® FLOWS GT/GS LB/HR FTt2 « 9456 FUEL: 7.0404E+06 SALT: 6«65TS5E+06 Table C-3. Computer Printout of Results for Input Data of Table C-1, AM'R FUEL SALT TUBE WEIGHT IN FTt+3 FT*+3 FTt3 LB «2899 617 48.4 18B.2 28871, FILM DT C@EFFICIENT F BTU/HR FTt2 F 55.2 e2isg. 227 6324, VEL@CITIES PUMPING REYNOLDS FT/SEC HP NUMBERS 9.4 540. 7237 14.0 631e. 11734. \ DENSITY . LB/FTt3 208.0 119.0 DENSITY LB/FT*3 208.0 132.0 ah A Wy - 98-99- - 100-101. *\_'N'G';:B\oocqc\\n::umi—' s?zbbuaxpgwg;gowmoamozmmm 1L4-16. 17. 18. 19. 20. 21. 22. 25-32. 33, 55 36. 57. 38. 59. Lo. 41. ha, b3, 88. 90, 91-92 95. . 9k, 95-%. - 97. 102-106. . * - U in g 2R 53 ' EXTERNAL DISTRIBUTION David Elias, AEC, Washington - R. Jones, AEC, Washington Kermit Laughon, AEC-OSR 5 T. W. McIntosh, AEC, Washlngton ‘M. Shaw, AEC, Washington . W. L. Smalley, AEC-CRO Division of Technical Information Extension (DTIE)V Laboratory and University Division, ORO ORNL-TM-2952 INTERNAL DISTRIBUTION L. Anderson L4, R. N. Lyon F. Bauman 45. H. G. MacPherson E. Beall L6. R. E. MacPherson Bender 47. H. E. McCoy E. Bettis 48. H. C. McCurdy S. Bettis 49, H. A. Mclain G. Bohlmann 50. L. E. McNeese J. Borkowski 51L. J. R. McWherter .I. Bowers 52. A, J. Miller B. Briggs 5. R. L. Moore W. Collins 54, - E. L. Nicholson W. Cooke 55. A. M. Perry B. Cottrell 5. R. C. Robertson L. Crowley 57-66. M. W. Rosenthal L. Culler - 67. J. P. Sanders R. DiStefano 68. A. W. Savolainen J. Ditto 69-T0. Dunlap Scott P. Eatherly : 71, M. J. Skinner R. Engel T72. 1. Spiewak E. Ferguson 75. D. A. Sundberg P. Fraas 74. R, E. Thoma D. Fuller 7. D. B. Trauger R. Grimes - 76. A. M. Weinberg 'G. Grindell "T77. J. R. Weir ' 0. Harms | - 78. M. E. Whatley N. Haubenreich ' 9. G. D. Whitman E. Helms | 80. L. V. Wilson W. Hoffman 81-82. Central Research Library R. Kasten , 83. Document Reference Section J. Keyes, Jr. 84-86. Laboratory Records E. LaVerne 87. Laboratory Records (IRD-RC) I. Lundin ' - - Director, Division of Reactor_Llcensing, AEC, Washington Director, Division of Reactor Standards, AEC, Washington Executive Secretary, Advisory Committee on Reactor Safeguards