ORNL-TM-4079 FORCED-CONVECTION HEAT-TRANSFER MEASUREMENTS WITH A MOLTEN FLUORIDE SALT MIXTURE FLOWING IN A SMOOTH TUBE J. W. Cooke B. Cox 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. ” i oY ) Contract No. W-T405-eng-26 Reactor Division ORNL-TM-4079 FORCED-CONVECTION HEAT-TRANSFER MEASUREMENTS WITH A MOLTEN FLUORIDE SATT MIXTURE FLOWING IN A SMOOTH TUBE J..W. Cooke B. Cox r— i - NOTICE——ou 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, not any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, com- pleteness or usefulness of any information, apparatus, would not infringe privately owned rights, MARCH 1973 OAK RIDGE NATIONAL IABORATORY Oak Ridge, Tennessee 37830 operated by UNION CARBIDE CORPORATION for the . U. S. ATOMIC ENERGY COMMISSIO product or process disclosed, or represents that its use | PISTRIBUTION OF THIS GOCUMENT IS GNLIM " "o P ) iii CONTENTS Abstract . Introduction . . . .« . v v v v 4 0 v d e e e e e e e e e e e e Description of the Apparatus . . . . . + + ¢« ¢ v « ¢ ¢ ¢ 4 e 4 . W Operating Procedures . . . . o & v o« & & o o o o o s o o o o o o Calculations . Results . . . . Discussion . . . . « « . . . o . o ., ConcCluSionNsS « « o ¢ ¢ ¢ ¢ o ¢ 4 4 s e 4 4 e 4 e e e e e e e e e Acknowledgments . . . i . . 0 4 4t e i i e e e e e e e e e e e References . « + « v o« « « & & N ... e s e e e s e e s Appendix A — Additional Details of the Experimental System . . . . Appendix B — Experimental Data . . « ¢ ¢« v ¢ ¢ ¢ ¢ ¢« ¢ v o o 4 o . Appendix C —-Computef Program . .« ¢« « ¢ ¢ v v 6 e 4 e e e e e e s Appendix D — Chemical Analyses and Physical Properties of the Salt .11 15 16 24 27 27 27 29 37 b3 25 Y o} N i) FORCED-CONVECTION HEAT-TRANSFER MEASUREMENTS WITH A MOLTEN FLUORIDE SALT MIXTURE FLOWING IN A SMOOTH TUBE J. W. Cooke B. Cox ABSTRACT Heat-transfer coefficients were determined experimentally for a proposed MSBR fuel salt (LiF-BeF,-ThF,-UF,;67.5-20.0-12.0-0.5 mole %) flowing by forced convection through a 0.18-in.-ID hori- zontal, circular tube for the following range of variables: Reynolds modulus 400 — 30,600 Prandtl modulus L — 14 Average fluid temperature (°F) 1050 — 1550 Heat flux (Btu/hr.ft?) 22,000 — 560, 000 Within these ranges, the heat- transfer coefficient was found to vary from 320 up to 6900 Btu/hr-£t®.°F (Nusselt modulus of 6.5 to 138). Correlations of the experimental data resulted in the equations: Ny, = 1-89 [N, Vo (D/L)]° P g, ‘with an average absolute deviation of 6.6% for Npo < 1000; A 2/ 3 i/ 3 0.14 Ng, = 0-107 (No = —135) Ny~ (u/w) , with an average absolute deviation of 4.1% for 3500 < N, < 12,000; and ' _ o~ O.8_1/ 3 O.14 NNu B 0.0234 NRe N;r ‘(“/”s) 2 with an average absolute deviation of 6.2% for N__ > 12,000. Re - Keywords: Heat transfer, fused'salts,‘forced convection, heat exchangers, fluid flow, correlations. INTRODUCTION The de51gn of molten salt reactors requlres detailed information about the tranSport properties of the proposed fuel coolant and'blanket mlxtures. Although the molten salts generally_behave as normal fluids with respect to heat transfer,l'2 the possibility of unexpected effects, such as nonwetting of metallic surfaces or the formation of low-conductance surface films, indicates that heat-transfer measurements for specific re- actor salts are needed.® This report describes heat-transfer experiments with a proposed reactor fuel of mixed fluoride salts (LiF-BeFpThF,-UF,; 67.5-20.0-12.0-0.5 mole %). The technique employs forced convection of the liquid salts through a smooth thin-walled Hastelloy N tube. Resist- ance heating supplies the tube with a uniform heat flux. This method is particularly well suited to the molten salt system because the electrical ,resiStapce of the molten salt is very large”compared with that of the metal tube. Furthermore, the resistance of Hastelloy N remains nearly constant over the entire temperature range of the measurements, which simplifies the achievement of an axially uniform heat flux. In additionm, a conétant heat capacity of the molten salt in the observed temperature range makes possible several convenient assumptions in the calculation of local fluid bulk temperatures. DESCRIPTION OF THE APPARATUS - The apparatus for studying heat transfer with the molten'salt system is shown schematically in Fig. 1 and in the photograph, Fig. 2. Molten salt flows by means of gas pressure through a small diameter, electrically heated test section. The flofi of molten salt alternates in direction as pressure from an inert gas supply is added to either of two storage ves- sels located at each end of the test channel. Each 6-gal salt reservoir is suspended from a weigh cell whose recorded signal indicates the flow rate. The flow of salt reverses automatically by the action of solenoid valves that control the flow of inert gas to the reservoirs. The rate of flow of the salt may.be varied from 0.25 to 1.7 gal/min, emptying a reservoir in from 3 to 20 minutes. ) | The weigh cell circuit shown in Fig. 3 illustrates the electrical and mechanical systems that control the flow of gas and thereby the flow ‘of molten salt. A second suspension system maintains tension on the test section, to prevent it from sagging, by means of counter weights connected by‘flexible cables. The test section consists of a smooth Hastelloy N _tube, 24.5 in. long, 0.25-in. outside diameter, and 0.035~in.-wa114 | REVERSE FLOW CONNECTING TUBINGI ) « ORNL-DWG 68-12942 ARGON SUPPLY P WEIGHT CELLS-TO “1 CYCLE CONTROL LOW VOLTAGE TRANSFORMER F"-"_L—._]" ‘ ST L oem R WATER COOLERS /-msnmocoum.ts : (24) ONE INCH CENTERS pemmmaed \ MIXING CHAMBER a— SALT TANK I TEST SECTION SALT TANK —e —— | . REGULATOR Xj . TO ‘ BUILDING VENT . PRESSURE I GAG_E/'@- - YEe—ELECTRIC VALVE —~ ELECTRIC MEATERS Fig. 1. Schematic diagram for determining the heat-transfer characteristics of molten salt by forced convection. PHOTO 76387 | Fig. 2. Photograph of the apparatus viewed from the same aspect ‘ . | as that of Fig. 1. ( - N o WEIGH CELL TANK . TANK i} ” "N " ORNL-DWG 72— 11510 -~ =~ VIoAR RHEOSTAT MECHANICAL DRIVES ~=~, HONEYWELL I em'——v F-————- RECORDER CONTROL e} e T Spayrd A - i 1 | I | SOLENOID VALVE o SOLENOID VALVE GAS Fig. 3. Weigh cell circuit for molten salt heat-transfer system. thickness and is resistance heated with a 60 Hz ac power supply. A detail of the mixing chambers located at each end of the test section is shown in Fig. A-1l, Appendix A. The electrodes connecting the test section with the power circuit serve also as end plates of the disk-and-donut mixing chambers. The power circuit to the test section is shown in Fig. &4, The electrical power to the test section is supplied by a hh0/25 v, 25 kva transformer and is measured with a General Electric watt transducer, also ‘shown in Fig. 4. The test section is insulated with a 3-in.-thick 1ayer of vermiculite powder containedrin’afsheet metal tray. The salt reservoirs and connecting tubes are heated by auxiliary clamsheil and Calrod heaters placed in positions indicated in Fig. 1. A typicaljheater circuit for an auxiliary heater is depicted in Fig. 5. h , | The inlet and outlet salt temperatures are measured by four, 4hQ-mil- diam, Chromel-Alumel sheathed thermocouples inserted into two wells in each mixing chamber (Fig. A-1). The temperature distribution along the test section is measured by a series of 24 Chromel-Alumel thermocouples (0.005-in.~diam wire) spot welded at 1-in. intervals to the outside tube wall. The scheme for attaching these thermocouples is shown in Fig. A-2. Details of a salt reservoir can be seen in Fig. A-3. The interior of these tanks as well as the test section and the mixing chambers are stress relieved and hydrogen fired before they are assembled. A data acquisition system provides for the automatic monitoring of the temperatures; record is made by a papef printout-and a paper tape punch. In this system a multichannel Vidar data recorder reads emf signals from each thermocouple, from the weigh cells, and from the power circuit in a sequential switching arrangement known as a "crossbar scanner." The manufacturer claims an accuracy of better than +0.5°F for the Vidar system. The data recording equipment is shown schematically in Fig. 6 and in a photograph in Fig. 7. The weigh cell and wattmeter calibration curves and a list of per- tinent experimental equipment may berfound in Appendix A as Fig. A-l, Fig. A-5, and Table A-1, respectively. C. 1||-—_-| " " | ORNL-OWG 72-145H £0-5A ' \D J PANELBOARD POTENTIAL = FRAME GROUND HC POWER TRANSFORMER TRANSFORMER L) — F—__T LT 173 - ’f ! ' SIGNAL CURRENT ° 150V | WATTMETERI ' 70 VIDAR | TRANSFORMER ] o I | - _l 1+ ) WATTMETER 1 ngsgg:ggg“ RANGE SWITCH PANEL BOARD BUILDING - GROUND _ FRAME GROUND Fig. 4. Test-section power circuit for molten salt heat-transfer experiment. o} ORNL-DWG 72-11542 POWER CIRCUIT 15 VAC — e, NEUTRAL HOT EVI=VOLTMETER ' Eil=AMMETER K= RELAY VARIAC Eil 0-150V s 0—10A - " — —- INSTRUMENT L If =] POWER - | TEMPERATURE RELAY | CONTROLLER | _® HEATER Fig. 5. Typical heat__er circuit for molten salt heat- transfer experiments. L] ) " ) a0 TE REF. JUNCTION COMPENSATOR ORNL-DWG 72-11543 Fig. 6. Thermocouple circuit for molten salt heat-transfer system. DIGITAL 7 PRINTER A CUNNINGHAM o VIDAR > SCANNER »| DIGITAL . ‘ _ { VOLTMETER \ Y . [ 1 L. TAPE SEQUENTIAL PUNCH TIMER of data recording equipment. 0T - b ® e " 11 OPERATING PROCEDURES In preparation for the addition of the molten salt mixtures, the system including the test section is heated to the desired temperature level above the melting point of the salt mixture. Approximately 165 1b of the molten salt is then introduced into one of the reservoirs by the force of argon gas pressure. Salt is forced back and forth through the test section as the operation of the apparatus is tested - for leaks, blockages, thermocouple and data recording functioning, etc. After the initial checkout procedure, the system is put on a standby mode by vent- ing the gas pressure to the atmosphere and allowing the salt to siphon to * equal levels in both reservoirs. The standby mode is used to protect the test-section thermocouples by minimizing the heating of the test section. Before each run, temperatures in the test section are raised to about 1000°F over a period of 45 minutes and the salt flow is reestablished. A fixed flow rate is established and power to the test-section heater is in- creased to the desired heat flux. When the temperatures indicate steady- state conditions, all parameters — power input, flow rate, and tempera- tures — are continuously recorded. The flow of salt is reversed when one 'reservoir is nearly empty, and the heat flux is momentarily reduced to about half the operating value to prevent a temperature excursion in the test section at the time of zero flow. The upper range of flow rates is limited by the time requiréd to empty one of the reservoirs. Whenever the temperature exceeds the desired level, the system is allowed to cool by reducing the power to the test section and other appropriate heaters. Periodic calibrations of radial heat losses were made by measuring the power. required to maintain an empty test section in an isothermal condition as a function of temperature level. The information furnished by thisd calibration is used in each run, when an isothermal check of the test-section thermocouples is obtained at the desired temperature level This procedure resulted in several salt leaks when a number of power failures occurred during the standby condition. Melting of the confined salt was invariably accompanied by rupture of the thin-walled tubing due to the expansion of the salt upon partial melting. A better standby pro- cedure would be to drain the salt into one reservoir, allowing unrestrained expansion of the salt during melting if an unexpected freeze should occur. 12 with the hot salt flowing afid‘only enough heat added‘to the test section to equal the radial heat loss. In Fig. 8, typical test-section thermo- couple readings from an isothermal run show a scatter band of +4°F about the average outside wall temperature. The sheathed thermocouples in the ‘mixing chambers read;slightly higher during isothermal runs and are be- lieved to be more accurate. Their readings, therefore, provide the basis for standardization and the tube wall readings are corrected to this standard. " | ‘ Extensive tests were condficted to insure the reliability of the 'apparatus and experimental procedures. The first test-section tube pro- duced erratic axial temperature patterns which did not improve with more thermal insulation of the test section. Subsequently, the anomalous axial temperature profiles were traced to the test section, in which a hole had burned through the wall and had been repaired by welding. IExcessive weld material protruding into the tube was thought to have disturbed the tem-- perature and velocity profiles. Replacement of the test section eliminated the difficulty. , ' - Other possible sources of error were investigated during the search - for the cause of the temperature irregularities. Electrical conduction through the molten salt would result in additional heating of the salt, but the ratio of the resistivity of the salt to that of the test section is greater than 2500, indicating very little heat generated in the salt in this manner Additional calculations of the radial temperature distri- bution®* confirmed that not more than O. 2% of the power was expended by electrical conduction in the salt. Temperature variations due to free convection are believed to be larger than those attributable to internal heating; but according to the criterion of Shannon and DePew,® free convection in the horizontal test- section p081t10n is insignificant compared with forced convection in the range of Reynolds numbers described in this work. As an additional check of nmatural-convection effects, the reactor fuel salt experiments were repeated with the test section anchored in a vertical position while other equipment arrangements'and operational pro- cedures remained unchanged. The object of the change was to compare the effects of free convection in the vertical and horizontal positions. A ORNL DWG 69-11028 8 , tube outside wall temperature (°F) B %) ET t v 1300 3 0 5 10 15 20 2c x, distance from inlet (1n.)_ Fig. 8. Tube wall thermocouple readings during isothermal salt flow. 14 crack developed in one of the piping connections to the test section after 8 runs and repairs were not attempted. However, the results of - the vertical runs did not show any difference.in the effect of free con- vection as related to the orientatlon of the test sectlon The data are presented later in the report and 1n‘Appendlx B. _ : The possibility of heat conductlon losses to the electrodes at the ends of the test section prompted calculatlons to be made based on the conservative assumptions of max imum héat'flux and a minimum Reynolds' numbér The results of these calculatlons show that the net heat con- duction in the axial direction is less than 0.1% of the total heat gen- erated in the test section at a dlstance of 0. 25 1n - from the entrance. The electrical resistivity of the,Hastelloy N test-section tube varies less than 1% in the temperéttre‘range-of;lbOO to 1500°F and the heat capacity of the salt varies less than 5% ovér;fhersame temperature raenge. The variation of the radial heat loss along 1éhgth of tube is less than 10% and the'heat loss itself is less than 5%. A constant axial voltage drop measured aldng the test section verified the uniformify of the heat flux generated in the test-section fialf,and-provided a check of ~the wall thickness and tube radius variation‘as-a?ffinction of its length.' Experiments conducted with a well-known heat-transfer salt (HTS)” provided a final test in the new test section of the experimentél pro- cedure. Earlier experiments® showed that HTS data are well correlated by standard heat-transfer'equations. The experiments with HTS in the present system demonstrated that the outside wall temperatures remained parallel to the mean salt temperature over half of the tést;éection length, indicating fully developed flow and a constant heat-~transfer coefficient. In 11 runs with HIS, the experimentally determined values of the heat- transfer coefficient were compared with those predicted by standard cor- relations. Ten of the values of the heat-transfer coefficient were | within’l3% of that predicted by the Sieder-Tate correlation® and the other value was within 25%. Before the system wfis.charged with reactor salts, the HTS was removed by extensively flushing with water and drying in heated vacuum for 10 days. *HTS: KNOs-NaNO,-NaNOs (44-49-7 mole ). o ) 15 CALCULATIONS The local coefficient of forced-convective heat transfer is defined by the equation b e 1) X (tg = t5) where h = coefficient of heat transfer, Btu/hr:ft®-°F; h , at position x along tube; heat-transfer rate to fluid, Btu/hr; A = heat-transfer (inner) surface area, ft°; Lo} " t =rtemperature, °F; tp, fluid mixed mean at any poSition; ts, inner surface of the tube at any position x; t,, outer surface of the tube at any position x. Beyond the thermal and hydrodynamic entrance regibns; hX reaches an asymp- totic value. For a constant heat flux, (q/A)x, this limiting value will occur when (tS —-tm) reaches a constant value. X The inside tube wall temperature is related to the measured outside tube wall temperature by the equation g +q (r )? tw'_ ts - - 2 - 2 m(=)--|- (: :) 2 Tk (_rw) - (rs) r 2 2 Tk 'k = thermal conductivity of fluid, Btu/hr.ft-°F; k , thermal conductivity of tube; L = test-section length, ft; test-section tube radius, ft; r outer surface; gs inner surface; ry, this is the solution to the one-dimensional steady-state heat conduction equation with a source term and a heat-loSs; qL; at the outside wall.’ The only variable on the right-hand side of Eq. (2) is the thermal con- ductivity of the metal wall, Kk , which remains nearly constant. over small temperature rises along the tube. Thus, when the temperature profiles tw and tm are parallel, the fluid flow in the tube 1s essentlally fully developed. 16 For most of the measurements, the heat gained by the fluid in traversing the test section was calculated by the equation q = ch(tm’o - tm,i) » | (3) in which ‘ CP = specific heat of fluid at constant pressure, Btu/lb-°F, w = mass flow rate, 1b/hr, . and subscripts o = outlet ~For the later messurements (Runs 210 through 220), the heat gained by the fluid was determihed‘from the eiectrical heat generation in the‘test section corrected for the calibrated heat loss. By calculating the heat input in this manner, the influence of the uncertainties in measuring the fluid mixed-mean inlet and outlet temperatures can be reduced. The computer program used for reducing the experimental data is given ~in Appendix C. RESULTS Heat-transfer coefficients were determined experimentally in 7O runs covering the laminar, transition, and turbulent flow regimes. Ten rfins with HTS to test the eéuipment are included with data shown in Appendix B. The physical properties and chemical analyses of the molten salt are listed in Appendix D, Tables D-1 and D-2, respectively. The duration ef:a rfin usuelly permitted time for three thermocouple seens to demonstrate thermal steady state. Figure 9 shows typical outside wall temperatures end'mean fluid temperatures. A straight line is drawn between the mean inlet and mean outlet fluid temperatures by assuming con- stant phys1cal pr0perties of the molten salt and uniform heat transfer over the inner surface of the test-seetlon wall. These assumptions are supported by the constant heat capacity of the molten salt in the observed temperature range and the ‘constant resistance of the Hastelloy N test section mentioned earller e s st b i F)] [} 17 ORNL-DWG 7211517 ® ® ® e @ ¢ * ’ 1300 +* ® ol o o @ ° @ TUBE OUTER WALL . & FLUID @ 1200 e @ @ . . . ”00 / - T ' : RUN 133, Vg, = 597 & 1000 ' W 1600 2 & ¢ O 0 ® o ot o w e 0 ¢ 8 0o ¢ & g & & o ) a o . = w - . 1500 n .___ RUN 157, Ngq = 28,104 1400 4 1200 | o o ® @ ° ® @ @ 100 " ’ RUN 186,Aj,= 4277 1000 : 0 5 10 - 15 20 25 X, DISTANCE FROM INLET (in.) Fig. 9. Axial temperature profiles for molten salt flowing in a smooth tube at laminar (Nge = 597), turbulent (Npe = 28,104), and transition (N = 4277) flow. ' 18 Three regions of N are shown in Fig. 9 — the laminar, transition, and turbulent at NRe-= 597, 4277, and 28,10k, respectively. The co- efficient of heat transfer hx assumes its limiting value rapidly for turbulent flow; but in laminar and transition flows, a significant entrance region is evident. This entrance region is seen more clearly when h_is plotted versus the distance along the test section x as in Fig. 10 for the transition flow run. After the thermal and hydrodynamic boundary layers become fully developed, h.x decreases to a limiting value. The test section is not long enough for hx to reach the limiting value in laminar flow. Therefore, integrated values of hx over the entire tube length, coupled with the parameter D/L, are used in developing the lam- inar flow correlations; whereas, the limiting constant h values are used for the transition and turbulent heat-transfer correiations. Standard heat-transfer correlations for the three flow regimes are given in the following discussion of Egs. (4) through (8). Heat-transfer data from the 70 runs are then presented in the dimensionless forms of standard correlations for comparison using the data listed in Appendix B and the physical properties in Table D-1. 1. For laminar, forced flow in the absence of natural convection, the equations of Sieder and Tate® and Martinelli and Boelter® are, respectively: N = 1.86 [N, N (D/L)1 2 (p/u )0t (4) and Ny, = 1.62 [N N, (D/1)}° . (5) 2. For transition region flow beyond the entrance region, a modified form of Hausen equatior® is: 2/ 3 i/ 3 ' Ny, = 0.116 (NRe - 125) Ny, (u/us)°°14 . (6) 3. For turbulent flow, the equations recommended in Ref. 9 and attributed to McAdams and to Sieder and Tate are respectively: N 2 NO.B NO-4 Mg = 0:023 Npe N | (7) _ 0.8 _1/ 3 0.14 NNu = 0.027 Nfie N;r (“/“s) 1800 X h_, Local Heat Transfer Coefficient (Btu/hr.rt2.°y) 1700 1600 1500 1400 1300 [} o 5 10 15 20 x, distance from inlet (in.) ‘ Fig. 10. Axial variation of the heat-transfer coefficient (N‘Re = 4277). 25 6T 20 where = il Nusselt modulus, hD/k, dimensionless, :fia = Prandtl modulus, Céu/k, dimensionless, 5 Reynolds modulus, pVD/u, dimensionless, and = mean velocity of fluid, ft/hr, inside diameter of tube, ft, = fluid density evaluated at fluid mixed-mean temperature, 1b/ft>, r o U <« n = fluid viscosity evaluated at fluid mixed-mean temperature, 1o /hr-ft; ng, evaluated at temperature of the inner surface of the tube. : , Equations (%), (6), and (8) are compared with the eiperimental data in Fig. 11. The experifiental results are in good agreement in the laminar region but are slightly below the equations representing the transition and turbulent regions. For example, in the range 3500 < NRe <_30,000, the data lie about 13% below Egs. (6) and (8). The heat-transfer data could not be correlated in the transition range 2000 < Nfie < 4000 because of entrance effects that persisted over the length of the test section. The laminar date do not fit Eq. (5) as well as Eq. (4), as shown by comparing Figs. 12 and 11. Similarly, Eq. (7)'provides'no significant improvement in the correlation of the data for Np > 10,000 over that of Eq. (8) [compare Figs. 13 and 11]. . | The data plotted in Figs. ll'through 13 suggeét‘that the experimental data for laminar and turfiuient flow can be fitted to functions’of the form: n . Ordirate = K N , | | (9) where K and n are dimensionless constants having different values for laminar and turbulent flows and the "ordinate™ is the ordinate used in Fig. 11. Least-squares fits of the data to the form of Eq. (9) were carried out assuming a constant value (1/3) for the Prandtl modulus exponent. These fits werertriéd with and without a viscosify ratio cor- rection term. We found that when thevviscosity ratio correction term was included, the values for the Reynolds modulus exponent, n, came closer to the commonly accepted values of 1/3 for laminar fiow and 0.8 for turbulent flow. The resulting equations fitting the experimental " p n i n 014 HEAT- TRANSFER FUNCTION 21 ORNL DWG 72-11514R A Vertical O Horizontal _ 08 13 0.14 Npo =0.027 N O Wp, > (pfued™™ [SIEDER-TATE ] n : 1 : g & /vNu=o.us(NR:’3-125mp,’3 (/i) >/ 2| = [HAUSEN] £ a 2 ! 1 Nyu=1.86 [Ngy Np (D/L)] Pipfug®'? [SIEDER-TATE] 10 102 2 5 103 2 5 10* 2 5 108 Nge» REYNOLDS MODULUS Fig. 11. Comparisons of the molten salt data for Egs. (L), (6), and (8). | ' - | 2 - ORNL-DWG 72-11515 z o — O 2 - W e 5 W | T W = 12,000. Because the data in the transition region did not follow the form of Eq. (9), the equation for the experlmental data in this range of Ny was obtained by adjusting the coefficient 1n Eq (6), giving the following relation: . | _ /3 _ O.la Ny = 0-107 (N;e_ 135) Nop (u/us) ’ (12) with an average absolute deviation of 4.1% for 3500 < N, < 12,000. Re The heat-transfer measurements made with the test section oriented in a vertical position to test for the possible effects of free convection are in good agreement with the standard correlations, except for four higher points (see Figs. 11 and 13). These higher points were obtained with downflow in contradiction to the predicted enhancement of heat trans- fer with upflow. Thus, a systematic thermocouple error in one of the mixing chambers is the most probable cause of the higher results with downflow. | DISCUSSION The results indicate that the proposed reactor fuel salt behaves as a normal fluid in the range 0.5 < N?r < 100 with regard to heat transfer. It should be noted that uncertainties in the physical properties of the salts reflect as great an effect on the correlations as does the un- certainty in the heat-transfer coefficient. Our data lie below the standard correlations in the turbulent and transition regions but not in the laminar region. If the deviations in our data were caused by low-conductance surface films or entrained gas, one would expect the effect to be apparent in all three regions. An un- certainty in the viscosity of the salt might explain the discrepancies in ) ny L. 25 the turbulent and the transition regions since the heat-transfer function in the laminar region i1s almost independent of the viscosity. 1In addition, the lower values in the transition regime could be the result of the failure of the thermal boundary layer to fully develop over the length of the test section. ' The problem of boundary-layer development is most pronounced in the range of Reynolds number 2000 < NRe < 4000, where entrance effects persisted for the entire length of the test section. The same effect could be produced up to No_ = 5000 at higher wall heat fluxes. Figure 14 illustrates the apparent effect of heat flux on the entrance region length. At N = 3762 and a wall heat flux of 2.55 X 10° Btu/hr.ft®, there is no region of constant heat-transfer coefficient. In contrast, temperature profiles at a similar Reynolds number, Nfie = 3565 and the lower wall heat flux of 0.74 X 10° Btu/hr-ft® show a constant heat-transfer coefficient over most of the test-section length. Since the viscosity of the fluid decreases with increasing temperature, heat transfer from the tube wall may be exerting a stabilizing effect on the laminar boundary 1ayer,9'1° thus delaying transition. Future experiments with the fuel salt should include system modi- fications so that the entrance region effects in transition flow can be better evaluated. Possible modifications would be the insertion of an ‘unheated calming section prior to heat addition to permit establishment of the hydrodynamic boundary layer before changing the temperature pro- file., This would separate the two effects that now occur simultaneously. Another possibility would be to increase the length of the test section while maintaining a constant heat flux élong theAléngth. A sufficiently long tube might allow fully developed flow pattefns-to be‘reached before the test-section exit. 26 - ORNL-DWG 72-11519 1500 @ oo L o’ ¢ ° * | ¢e o | ® 0 1400 | — ® - e TUBE OUTER WALL ¢ ® FLUID _ ® 1300 5 E . w ® 5 1200 1 2 ‘%’ Nge = 3762, g/A=2.55X10° Btu/hr . it2 i / / 1100 1200 ° o e X e 00000004000 ® 1100 |- a1 N 2 Npe = 3565, g/A =0.74 X10° Btu/hr - ft 1000 | | ‘ 0 5 10 15 20 25 X, DISTANCE FROM INLET (in.) Fig. 14. Comparison of axial temperature profiles of the molten salt at similar NRe with heat flux varied by a factor of 3.5. . 27 CONCLUSIONS We have found molten fluoride salt mixtures to behave, for the most part, as normal fluids with respect to forced-convection heating in a smooth tube. Although the present results average ~13% below the standard literature heat-transfer correlations, one must realize that some un- certainties exist in the physical properties of the salt and that the standard correlations themselves are based on heat-transfer data using fluids such as air, steam, water, petroleum, etc., which exhibit a +20% scatter band around the standard curves. No evidence of the existence or influence of low-conductance surface films, such as corrosion products, gases, or oxides, was found in the present studies. In the Reynolds modulus range from 2000 to 5000, we did find the heat-transfer coefficient to vary along the length of the tube in a manner which appeared related to a delay in the transition to tur- bulent flow. We believe this delay inrtransition is abetted by the stabilizing influence of heating a fluid whose viscosity has a large negative temperature coefficient. We intend to make further studies of this phenomenon. ACKNOWLEDGMENTS The design, construction, end operation of these experiments were made possible by the able assistance of J. J. Keyes, Jr{, H. W. Hoffman, R. L. Miller, J. W. Krewson, W. A. Bird, and L. G. Alexander. REFERENCES 1. H. W. Hoffman, Turbulent Forced-Convection Heat Transfer in Circular Tubes Containing Molten Sodium Hydroxide, USAEC Report ORNL-1370, Oak Ridge National Laboratory, October 1952; see also Proceedings of the 1953 Heat Transfer and Fluid Mechanics Institute, p. 83, Stanford University Press, Stanford, California, 1953. 2. H. W. Hoffman and S. I. Cohen, Fused Salt Heat Transfer — Part III: Forced~Convection Heat Transfer in Circular Tubes Containing the Salt Mixture NaNOg-NaNOz-KNO;, USAEC Report ORNL-2433, Osk Ridge National Laboratory, March 1960. 10. 11. 12. 13. 28 H. W. Hoffman and J. Lones, Fused Salt Heat Transfer — Part II: Forced-Convection Heat Transfer in Circular Tubes Containing NaK-KF-LiF Eutectic, USAEC Report ORNL-1777, Oak Ridge National Laboratory, February 1955. H. F. Poppendiek and L. D. Palmer, Application of Temperature Solu- tions for Forced-Convection Systems with Volume Heat Sources to General Convection Problems, USAEC Report ORNL-1933, Oak Ridge National Laboratory, September 1955. R. L. Shannon and C. A. DePew, Forced Laminar Flow Convectlon in a Horizontal Tube with Variable Viscosity and Free-Convection Effects, ASME Technical Paper 68-WA/HT-20. E. N. Sieder and G. E. Tate, Heat Transfer and Pressure Drops of Liquids in Tubes, Ind. Eng. Chem. 28(12): 1429-1435 (1936). P. F. Massier, A Forced-Convection and Nuclear-Boiling Heat-Transfer Test Apparatus, JPL-TR-32-47, Jet Propulsion Laboratory, March 3, 1961. E. R. G. Eckert, A. J. Diaguila, and A. N. Curren, Experiments on Mixed-Free-and-Forced-Convective Heat Transfer Connected with Tur- bulent Flow Through a Short Tube, NACA TN-297k, National Advisory Committee for Aeronautics, July 1953. W. M. Rohsenow and H. Y. Choi, Heat, Mass, and Momentum Transfer, Prentice-Hall, Englewood Cliffs, New Jersey, 1961l. H. Schlichting, Boundary Layer Theory, Uth ed., McGraw-Hill, New York, 1960. A. R. Wazzan, The Stability of Incompressible Flat Plate Laminar Boundary Layer in Water with Temperature Dependent Viscosity, pp. 184-202 in Proceedings of the Sixth Southeastern Seminar on Thermal Sciences, Raleigh, North Carolina, April 13-1k, 1970 S. Cantor, ed., Physical Properties of Molten-Salt Reactor Fuel, Coolant, and Flush Salts, USAEC Report ORNL-TM-2316, Oak Ridge Natlonal Laboratory, August 1968. J. W. Cooke, Thermophysical Propertles, pp. 89-93 in MSRE Semiann. Progr. Rept Aug. 31, 1969, USAEC Report ORNL-4449, Oak Ridge Natlonal Laboratory. ' o (3] a " AT) 29 APPENDIX A ADDITIONAL DETATLS OF THE EXPERIMENTAL SYSTEM D) * Y4 x 0,035 in. TUBES, WALL TURNED TO | Y% x 0.042in. - TUBE T [ % /"/I/,/I/,(/."/’JP— 3 ey . & T T e ‘4 t,'.‘ 4y, o ORNL-DWG 72-11522 LAVITE WEDGE TO HOLD THERMOCOUPLES AGAINST WALL - 0.040 in. CHROMEL-ALUMEL STAINLESS STEEL SHEATH THERMOCOUPLE {in. SCH. 40 PIPE: A e e ] \] Ak 0.010in. — L S A A AL A AT A kb I iheiinl = N Y A S el e o it el il el i Lol il el Lol il Lo & I-——‘/4in. /\-’_/\/\/ o 8 HOLES 542 in.DIAM EQUALLY SPACED ON ELECTRODE—ay 13/c in. DIAM CIRCLE 3% in. DIAM HOLE ) \ \ ) ! TEST SECTION T T T T T ’ A ? ri 4 3 e T N\ %) &4 | ] ? ! 1 1 | A i Y ANNNNN Ygin. RADIUS LSS /2 SECTION A-A 27%in. Fig. A-1. Mixing chamber weldment. L4 ¢ 32 ORNL-DWG 72-11524 |_.— CERAMIC FIBER 4~ INSULATION SLEEVE 36 GA.C. A. BARE WIRE SPOT WELDED TO THE TEST SECTION TEST SECTION : ! Fig. A-2. Scheme for the attachment of a test-section thermocouple. ¥ " 33 ORNL-DWG 72-11523 N (\ ¥ % 0.042 in. DIP LEG TUBE P 44x0.035 n. THERMOCOUPLE WELL TUBE | Y42 0.035in. VENT TUBE -, 10in. ‘8¥%in. 1% %0.0421n. FILL TUBE 1 | tin. A R \& /1 4 ] L |/ / ] - W 1 L 4 1 A 91 1 / ] /1 / 1 ] 7 / / 5 33 in. [ 1 1 ] ] / % / ¢ / ] / L / / / ] ¥ / tin, 1 fa—————— 8 54 in. DIAM . Fig . A.- 3 * 0.322in, WALL SCHED 40 PIPE CAP De'tail of a Salt reservoir. | CHART READING (%) \ - ORNL-DWG 72- 41521 100 110 % | - —1 100 -0 ,o%’o : / ® 7 | / 7 * | _ ‘ 70 - o " TANK B L .~ / o 80 . L"TANK A 2 T ~- 50 o”;"’,,t”f’ 60 / 7 o INCREASING WEIGHT 1 /L’ e DECREASING WEIGHT B e ‘ | | 50 * 40 20 | - 0 10 20 30 40 50 60 70 80 90 100 "o STANDARD WEIGHT (pounds) Fig. A-4. Weigh cell calibration curve. 1€ 35 ¥ ORNL -DWG 72-4520 POWER ( watts) 2\ < 3 < o / 0 20 40 60 80 100 SIGNAL ( millivolts) Fig. A5, Wattmeter calibration curve. " 36 PERTINENT EXPERIMENTAL, EQUIPMENT Equipment Load Cells BLH electronics Type T3Pl and T3P2B StriE Recorder Honeywell Model BY153X2VV-(WT) -(IV)Al (modified) Current Transformer Nothelfer windings Labs, Incorporated Model 14388 Digital Voltmeter Vidar ' Model 521 System Coupler Vidar Model 650-12 Scanner Cunningham Scannex Control Model 000113G Tape Digital Printer Franklin Electronics, Inc. Tape Punch Process Tally Corporation Model 1665 Tape Drive Model P150 Tape Reader Model 1848 Wattmeter General Electric Type 4701 Watt Transducer Thermocouple Reference- Junction Compensator Universal Compensator Model RJ4801-CS Thermocouples Chromel-Alumel - Capacity or Range 500 1b (150% overload) 3 mv/v input L-2 Special 25 kva (prim. & sec.) 48 v prim. 4 x 250 amp sec $10 mv to +1000 v in 6 decade stages 2.5 — 10.0 in 2.5 steps Accuracy +0.02% full scale (see Fig. A-L) +0.25% full scale +0.01% of full scale (least count 1.0 pv) (see Fig. A-5) +0.75% 37 APPENDIX B EXPERIMENTAI, DATA Table B-l. Experimental Data for Heat-Transfer Studies Using the Salt LiF-BeF,-ThF,-UF,; 67.5-20.0-12.0-0.5 mole % Run Tin T-out oT : v q/ A Heat a h = 7 " N’b No. (°F) (°F) (°F) (1b/br) (Btu/hr.ft® Balance (Btug e Pr Nu st . x 10~%) hr*£t2 . °F) 107 1388.3 1436.0 Wr.7 2532.0 4.07 1.05 4882 15,993 6.3 106.1 56.000 115 1362.7 14%15.8 53.1 1387.2 2.48 1.12 2831 8,345 6.6 61.5 31,902 117 1383.7 1k38.4 Sh.T 1807.2 3.33 1.01 3617 11,419 6.3 78.6 41.497 119 1379.1 1436.6 57.5 1185.0 2.30 1.05 2302 7,495 6.3 50.0 26.270 121 14118.0 14744 s6.4 2191.2 k.16 1.0k ' 4590 14,917 5.8 99.8 54.082 122 1456.2 1507.9 51.7 2968.2 5.17 1.04 6192 21,647 5.5 134.6 74415 123 1488.2 1537.8 k9.6 3206.4 5.36 1.00 6462 25,119 5.1 140.4 79.762 127 1097.9 1156.4 58.5 1636.8 3.23 1.05 1936 - 5,005 13.1 h2.1 16.713 129 1082.7 1163.3 80.6 250.8 0.68 1.01 396 738 13.5 8.6 3.359 130 1081.5 1177.1 95.6 279.6 0.90 1.00 4a7 839 13.3 9.2 3,563 131 1089.8 1159.9 70.1 227.h4 0.54 1.02 Lo7 673 13.5 8.8 3.488 132 1090.6 1160.2 69.6 256.2 . 0.60 0.97 381 760 13.4 8.3 3.265 133 1029.6 1118.7 89.1 221.4 0.66 0.93 357 550 15.9 T.7 2.821 134 1036.3 1134.8 98.5 155.4 0.52 0.93 358 b5 15.3 7.8 2.94}4 143 1062.8 1117.7 54.9 1785.0 3.30 1.04 1940 L,oho 1kh.5 ko2 16.148 14y 1075.4 1135.7 60.3 1900.8 3.87 1.0h4 2200 5,523 13.8 47.8 18.563 145 1048.2 1103.4 55.2 2007.6 3.73 1.04 2129 5,304 15.0 46.3 17.459 146 106L4.0 1115.9 51.9 2199.6 3.85 1.04 2513 6,026 14.6 Ssk.7 20.984 147 1076.9 1131.0 S4.1 2307.6 4.20 1.04 2727 6,573 1k.0 59.2 23.072 148 1093.5 1148.3 54.8 2506.8 4.63 1.03 3068 7,583 13.2 66,7 26.549 1k9 1460.4 1482.9 22.5 1166.4 0.89 0.94 2230 8,393 5.6 48.5 27.007 150 1460.6 1u489.5 28.9 1700.4 1.66 1.03 3434 12,260 5.5 Th.7 L41.7H3 151 1469.4 1488.4 19.0 2093.4 1.3 1.01 3977 15,282 5.5 86.4 48.472 152 1477.0 1501.8 24.8 2458.2 2.05 1.00 4573 18,300 5.4 99.5 56.022 153 1486.7 1513.4 ° 26.7 2784.6 2.51 1.09 5426 21,235 5.6 117.9 65 .520 6¢ Table B-1 (Continued) -T T 6T W o, (M (B (B (/) /Q/A s e (o N, §_ ¥ T No. °F °F °F 1b/hr Btu/hr*ft Balance - (Btu N N, N x 107%) hr-ftl'°F) "Re Pr Nu St 154 1496.1 1523.3 27.2 3057.0 2.80 1.0k 5740 23,719 5.1 124.8 T1.557 155 1466.3 1484.7 18.4 3205.2 1.99 1.02 5551 23,21k 5.5 120.7 67.668 156 1475.0 1488.2 13.2. 3262.2 1.45 0.99 5229 23,861 5.5 113.7 63.927 157 1479.7 1502.7 23.0 3505.8 2.72 1.07 6627 26,192 S.h4 144,21 81.181 158 1466.3 1483.8 17.5 1282.2 0.76 0.89 2236 9,284 5.5 48.6 27.265 159 1466.7 1492.6 25.9 1401.6 1.22 0.99 2708 10,171 5.5 58.9 32.943 160 1471.3 14k92.2 20.9 1512.0 1.06 0.93 274 11,107 5.5 59.6 33.394 161 14724 1hok .k 22.0 1615.2 1.20 0.99 3033 - 11,853 5.5 66.0 36.980 162 1463.7 1522.0 58.3 - 1254.6 2.46 1.0k 2675 9, 46k 5.2 58.2 32.754 163 1470.0 1527.5 57.5 1425.6 2.76 1.05 3071 10,884 5.2 66.7 37.571 164 1480.0 1535.8 55.8 1513.8 2.85 1.07 3334 11,770 5.1 72.5 41.151 165 1486.9 1539.2 52.3 2105.4 3.71 1.02 4385 16,497 5.1 95.3 54.119 166 1501.6 1546.2 4.6 2803.2 4.21 1.06 5852 22,512 5.0 127.2 72.942 167 1513.9 1561.7 4y7.8 34m.0 5.60 1.02 6892 28,499 4,9 149.8 86.348 170 1064.6 1080.1 15.5 1797.0 - 0.94 0.97 1737 4,528 15,9 37.7 14.620 171 1066.3 1082.2 15.9 2346.0 1.26 1.01 2340 5,938 15.7 50.9 19.818 172 1069.8 108k4.0 1k.2 2722.8 1.31 1.05 2905 6,939 15.6 63.2 24,811 173 1049.0 1081.2 32.2 202.2 0.22- 0.96 320 493 16.3 7.0 2.671 186 - 1061.6 1076.2 14.6 1597.8 0.79 0.9 1445 3,986 16.0 31.4 12.161 191 1062.0 1078.5 16.5 1318.2 0.7h 0.94 1041 3,322 15.9 22.6 8.713 192 1064.6 1080.3 15.7 1460.4 0.77 0.99 1337 03,690 15.7 29.0 11.274 193 1235.2 1262.7 27.5 1106.4 1.03 1.01 1591 4,731 9.3 34.6 16.075 195 1247.0 1270.6 23.7 2333.4 1.86 1.0k 3560 10,200 9.1 7.4 36.392 198 1255.8 1296.0 40.2 3001.8 4,07 1.04 4645 13,693 8.7 101.0 47.638 21.2 2.30 1.09 4752 14,944 8.6 103.3 49.533 199 1273.2 12944 3219.6 Ot Table B-1 (Continued) ?gn Tin) Tou; 8T w q/A Heat . h - . (°F °F (°F) (1b/nr) (Btu/hr £t® Balance (Btu N N N N X 1 -5 ) hr- ftl oF ) HRE Pr Nu gt 200 1279.6 1303.7 2.1 3392.4 2.76 1.07 5050 16,088.0 8.4 109.8 53.017 201¢ 1237.8 1263.8 26.0 1351.2 1.18° 1.07 2ko6 5,892.4 9.1k 52.3 24.7 202% - 1250.7 1272.6 21.9 1717.8 1.27 1.01 2762 7,660.9 8.94 60.0 28.6 203° 1252.2 1276.2 24,0 2050.2 1.66 1.16 4029 9,200.0 8.89 87.6 L41.9 204° 1258.& 1282.h 2h.0 2299.2 1.86 0.99 3625 10,435.5 8.79 78.8 37.7 205° 1229.9 1255.0 25.0 1395.0 1.18 1.01 2119 5,910.9 9.41 461 21.5 206° 1231.7 1255.4 23.7 1704.0 1.36 1.10 3004 7,238.9 9.39 65.3 30.7 207 1243.6 1268.1 24k.5 2036.4 1.68 0.97 3122 8,947.4 9.08 67.9 32.1 208° 124k7.2 1270.6 23.4k - 2338.8 1.84 1.12 4337 10,359.7 9.00 ok.2 4h.9 210 1132.u, 1156.1 - 70.1 2110 1.69 1.01 2416 6,512 12.5 = 52.5 22.15 211 1168.4 1215.% = 150.8 ~ 2105 3.38 1.01 3049 1, 696 '10.8 66.3 28.96 212 . 1203.4 1226.7 59.9 2102 1.69 1.03 2823 8, ,230 10.2 61.4 27.89 213 1138.1 1168.7 30.6 2654 2.76 1.04 3477 8 566 12.2 5.6 32.07 214 1097.9 1149.6 51.7 2807 4.92 1.01 3573 8,297 13.3 T7.7 31.27 215 1248.1 1256.1 8.0 2887 0.79 0.97 4335 12,374 9.2 gh.2 44,98 216 1258.3 1276.2 18.0 . 2914 177 1.03. ‘bhoo . 12,957 8.8 97.6 46.89 217 1280.6 1310.6 30.1 2791 - 2.85 1.05 4616 13,454 8.2 100.3 L49.10 218 1288.1 13K1.7 53.6 2753 5.03 1.03 4915 14,035 T.7 106.9 52.56 219 1293.8 1383.2 89.4 1593 5.04 1.03 2999 8,620 7.3 65.2 32.12 220~ 1118.5 1155.7 136.1 1140 1.51 1.02 1082 3,554 12.8 23.5 9.60 N aHea.t balance = (sensible heat gained by fluid + heat loss)/(electrical heat generation). e = B (T, 072 (ufu )™ ®Pest section oriented vertically. Table B-2. Experimental Data for Heat-Transfer Studies Using the Salt Hitec (KNO,-NaNOy-NaNOs; UL4-49-T mole %) © G m o) et et (ot R, &, K ° ° °F r u/hr-ft ance u | N . x 10_5) hr 'fi!' °F) NRe qur NNu St 87 537.6 677.3 139.7 157.2 0.85 0.99 283,5 2,314 9.3 17.0 7.34 88 540.8 591.3 50.5 1375.2 2.69 1.05 2499.4 15,450 11.3 150.0 64.3 89 567.5 621.0 53.4 2071.8 4.30 0.98 3516.6 25,640 10.2 211.0 93.1 96 574.8 624.3 k9.5 2195.h4 h.21 1.08 k450.9 27,578 10.1 267.1 119.7 97 601.4 650.7 49.3 1589.4 3.04 1.00 3045.6 21,76 9.3 182.7 84h.2 98 608.4 658.5 50.1 1097.4 2.13 1.06 2473.8 15,349 9.1 148.4 69.3 99 618.5 672.5 54.0 630.6 1.32 1.03 1386.4 9,165 8.7 83.2 39.2 101 608.8 702.4 93.6 592.8 2.15 1.10 1332.4 9,065 8.3 79.9 37.6 102 633.1 657.2 2hk.1 640.2 0.60 0.99 1656.8 9,142 8.9° 99.k u7.7 103 618.8 634.8 16.1 1551.6 0.97 1.05 4151.9 20,848 9.4 249.,1 117.6 104 582.2 669.1 86.9 1603.8 5.41 0.99 3096.6 22,357 9.1 = 185.8 8k.1 2N 8Heat balance = (senéible heat gained by fluid + heat loss)/(electrical heat generation). b= _ ¥ /% V-3 ~0.14 gy = Mgy )™ 2 (/)04 43 APPENDIX C COMPUTER PROGRAM COMPILER OPTIONS = NAMEs MATN,OPT=02,LINECNT x6),SOURCEsLBCOICINOLIST »DECK , LOAD s MA® 4NOEDT ToNCT Do NOXPE & C I AM A MNOLTEN SALT HEAT TRANSFER PROGRAM 5 ISN 0092 REGAL L oMPROT oKL 9 K2 9 K3 ¢ Kb o ALINC s MU ¢ NI AV G ANG o K1 NOW 1G ISN 0€03 DIMENSICN TC{30D ¢XLI3C) o TI(3O) 4 TB{3Y) oM 30}, INE200),0U(2CC),0¢200) 12 ISN 0CO& DIMENSION NUNDL3G) 13 1SN 0CO0S INTEGER FTLLCTC 15 ISN €006 6 03 10 Jsl,13 : 30 iSN ocC? TL=5%(J=1)¢) 40 ISN 0008 1usSey 50 1SN 0009 READ To(INUL) DUCT) oInlL, IW) 60 ISN cO10 ? FORMATES(LI,F5,2,2X)) . 70 ISN 6011 19 CCNTINGE ‘ 7% ISN 0Cl2 0 20 t=l,1y 76 ISN 0013 , ‘ I1=INCE}+1 77 ISN 0014 . IFIDUCTI).GE.NNEY LI d=0ULT) T7AL ISN CO16 20 CINTINLE 7742 ISN 0C17 1 (D(45).L7,900.) GC TO 27 . 778 ISN 0019 G631 To 22 T7C ISN 0C20 21 0(46)==D{4¢) 770 ISN dc21 22 CINTIMNLE TTE ISN. 0022 D 30 1=1,50 78A ISN 0C23 : LI =0y ‘788 ISN 0024 30 CONTINUE 78C C TEMP FIT FOLLOWS FNR 150 F REF JUNCTION YF TG 1900 DEGREES F 79 tgn_gggg_m_ B D7 4201 =1 446 N ) 794 1SN 0026 If (DCI).LT.1.959) 6C TO 400 ‘ 798 ISN 0028 IF (DOC(I)eGELL 99, AND.DI{T1).LT.5,30) GO TO 401 79C ISN 0C30 TF (D(I)eGE.5.01.AND.D{I).LT.12.Cl) GC TO 402 790 ISN CC32 . IF (D(I)sGE.10.01 ANDDUTI)LT12.01l) GO TO 403 T9E ISN G034 IF {D(I)eGEL13.01.ANDC{I)oLT.17,01) GO TO 404 ‘ T9F ISN 0038 : IF (0(1)eGELLTa01sAND DI LT .22.99) 6O TO 405 796 ISN G038 IF (D(IYeGEL22.99 AND.DEI) LT 27.99) GO TO 435 ToM ISN 0040 ~ TF (0(1)e6GFe29.99 AND,O([).LT.33,60) GO TO 407 791 ISN €042 ' . TF (DUI}4GEe33,0,AND.DII).LT.35.0) GO TO 4C8 794 1SN 0CA4 : IF (D(I)eGER.36.0.ANDO{E) LT 37.7} GO TO 409 T79% ISN GOAS . IF (D(1)«6GE.39.0) GC TO 410 T9L ISN 0048 - a0C D(I) s %50,+(236.~150.1/1.,99¢(D([)-0.} 79L1 1SN 0€49 - GO TQ 420 T9M ISN €050 41 DEI) 22264037 e=2363/(5,01-1,92)0(D{1)-1.99) TON ISN 0051 o IF DUT)eGEL258 dANDD{T1)oLE.290.) D(I)=Dl I)~0.6 TON1 1SN 0053 . IF (D(1) eGEL280s o AND D(I)olEadLlée} DLI)=DL)=0,5 T9N2 ISN 0C5S% GO TO 420 790 CISN XC56 . 402 DI =371.¢1592.=3714)1/(10.G1=5,01)%{C(1)-5,01) 79¢ 1SN 0057 ~ 1IF {(DUI),GEL532.00) O{I)=D(1)=).%0 79P1 ISN 0059 O(1)aD(1)+1.0 79P2 ISN 3060 IF (D{I).LE.42%.) CUI)=D(1)-0.20 7903 1SN 0062 _ GO TO 420° 799 ISN G083 403 DI1)=562,+({721.-592.3/{13.01=10.21)«(C(I)-1C,01) T9R ISN 0064 . GO TD 420 79S 1SN 0C65 404 DlI)=722.40890.=72141/(17.01=13.21)%(C(1)=-13.01) 79T 1SN 0066 G0 TD 420 . S : 79u ISN ©O67 4CS DIT) =861 ,+(1142,-91,)/(22.99-17. oxntcctln-xv.axs T9v ISN aCe8 : GO TO 420 79w ISN 0069 4)& DUI)=1143,+ (1444 ,-1143.)/(30,00~-22. 99;tcot:'-za.cc) -C.10 79% ISN GOTO IF (D(T1).GE.1396.) D(I}=sCtI)e.3 79x%1 ISN nCT2 IF(D(1)eLEal234.) CUII=N(1) 4,20 79X2 ISN 0CT4 6D TO 420 79Y ISN 6075 407 DUIY 2l 446, + (1576 ,.-1644,)7(33,00-23.99)%(D(1)=~29.99) 792 ISN 0CTe¢ IF (DCIF.LELLIS284) D(I)=D(]I)-0,.5 1921 2 ISN CQ78 IsN 0079 1SN 0080 ISN 0C82 ISN 0C83 ISN 2084 1% 0085 ISN 0086 IS8 ocaa ISN 0089 ISN 0090 1SN 0091 ISN 0092 TSN 0C93 ISN 0C94 ISN 0095 ISN 0096 ISN 0097 ISN 0099 ISN 0100 ISN 0101 ISN 0102 1SN 0103 1SN 0104 . ISN G105 ISN 0106 1SN 0107 ISN 0108 ISN 0109 ISN 0110 ISN 0111 ISN 0112 ISN 0113 ISN 0114 ISN 0115 ISN 0116 ISN 0117 ISN Olle ISMN 0119 ISN 0120 __ ISN 0121 - ISN o122 ISN 0123 ISN 0135 JISN 0098 25 51 52 58 GO TG 420 DULI=L5T6a9{1710,=157641/136,00-33.00)%(DIE)-233.0D) IF (D(1).GE.1635,2AND.D(T}.LE.1673.) DUI)=Dl 1)20.4 G0 TO 420 DE1)=1700.+(1848.-1710.1/(39.00-36.00)#(0( 1)~ 36.00!*.10 G0 TO 420 . 0(1181548.0(19‘1.-1848-)!(41.00-39.60)OID(ll-39.00) -¢10 IF (D(1).RE.1892,) DII]'D(I"O S CONTINUE PRINT 23 FORMAT (1H1) D0 25 1I=1,20 JsD(5C) e, 2 PRINT 26,4 FORMATI{LHGy *NEXT IS RUN *,14) CONTI MUE D{41)=DU(41) 0(42)=DU{42) FIC=0Ul&l)¢0,2 = . _ . _ CYC=DU(42) #0.2 UWAVGEAVGIC ol o2 44750,23:7500 CALL TKER{C 46 UNAVG) PRINT 51 FIRMAT (lHl-4X09HSUBSCSIPT'68'6HU CAT2,9X +6HC CATA) 0058 _I=1,50 e e PRINT 5241 DU1I},C(T) FCRMAT(TX g [3¢8X oF8u298XyFBL2) CONTI MUE C COMASTANTS FOLLCW., THE THERMAL K*S #RE TENMP CEPENDENY Rl=,180/2. . 01=0,180/12, . R2=,250/2. RI=6,00/2. R4=3,0%68 KL IS GIVEN ON CARD 845 K2=0,06 © K3=9,00 "7C END 66 Ké=l4, 32 N=2 L=24.5% SPH1 =0.324 DAA=0.5 D!GtO.S OF CCNSTANTS XLE1}=.750 DX=l.00" ‘D0 60 [=2424 Ms]=-] XL{l)=XL(M)¢DX CONTINMNUE TAO=(D{27)+D(28)} /2. TAI=(D{29) +D{30)) /2. T881=(D(31)eD(32)) /2, T8BO=(0(33)+D{34)) /2. . IF(TAD.GY, TAL)GO TC 61 . TA=TAl 61 G) TQ 62 TA=TAO ot ISN 0136 62 lFuaeo.ct.msn 60 19 63 ISN 0137 . TAR=TABI ISN 0139 G? TO 64 . ISN 0140 63 138=TBAO ISN 9141 64 CONTINUE ISN 0182 IF (TA-TBB)66+688 ISN 0143 . 66 TIN=TA 1SN 0144 TIUT=TBE ISN 0145 GO TO 70 ISN 0146 58 TINsTRS ISN 0147 TOUTaTA ISN 0148 70 CONTINUE ISN 0149 IF (TA-TBB) 73,71,71 1SN 0150 7100 72 1=1,24 ISN 0151 M225-1 - 1SN 0152 TO(1)=C(M) ISN 0153 12 CONTINUE ISN 0154 GO TO 80 ISN 0155 ... 1203 75 I=1,24 - ISN 0156 T0(1)=c(1} ISN 0187 7% CONTINLE 1SN 0158 8C CONTINLE o C CARE MUST BE TAKEN WITH REGARD TO SIGN CCAVENTION FOR FOLLOWING Q AND DT 1SN 0159 QWM2400,783,6*D (4T)$200.%3,412/0149). ISN_0]60 MOOT=D(48)%60, ISN 0161 DT=UWAVG ~ D{46) ISN 0162 QLCAL®={(0,275TE-3)#CT*OT ¢ 0.1100 DT ~ 0,1724E-1) ISN 0163 QLF=QLCAL/ (2,93, 142R2%L/144,) ISN 0164 QUF ==QLE ISN 0165 oct-xu.nsu?.n.nz.ocwual-mzslnoxn(o(%i-mzaluoxai ISN 0188 OT=AVG (Dy] 9244, 750,23.750) = D{46) ISN 0167 Qms-z.ta.utu.-o.s»Ilz.t(-onl(chcnsnzuxzouos(Mlkanxab ISN 0l88 QLEST=QEL + QINS ISN 0169 QF-Mnottspmtnout-nul ISN 0170 QDPs= L 702,93, 14*R18L) #L 44, ISN 0171 QBAL-(QF-QLCAU /7QWm 1SN 0172 . o HLWEYC —— ISN 0173 X1=X1=-42%0 ISN 0174 X2=FTC+CTC~] ISN 0175 . K2wXK2=4250 ISN 0176 110 PRINT 111 IS 0177 111 FIRMAT l1H1.09x.mx.ux.auxm.lox.lua.ux.zms.ux.zun,nx.zuro - - __8 112X p2HNU,» 11X ¢ 24R E¢ 12X ¢ 2HPR) ISN 0178 DO Li5 I=1,24 ISN 0179 XaXLAI) ISN 0180 _ - ATT=T0{l) - 25. ISN 0181 112 KL=TK(ATT) ISN 0182 T I=TCAII=(0F = CLCAL) /(2.,%3,14%L/712.9K1 )% o 8 . {R2¢R2/(R2#R2-R1 *R1 } *ALOG(R2/R1)~0.500) ' 8 +QLF*R2/12 . /K1 *ALOG(R2/R1) ISN 0183 ATT={TI(T)+TC(I)}/2, ISN 0184 KLNOW= TK(ATT) : ISN 0185 UK =ABS (KINOW-K1) ISN 0186 IF (UK. GE.D.1) GO TC 112 ISN 0184 X00=X/ (2,#R1) ISN.- 0189 TECI)=TIN ¢ QDCP#3 ,14%2,#R1#X/MOCT/SPHL/ 14, 1SN 0190 HUD) =QEDP/ZLTI(IN-TELI)}) ISN 0191 CALL PRCP(REND ¢PRNC,MU,RHO,TB( 1) ,R1, CCNDySPHL,MDOT) 345 350 355 360 365 3190 400 410 420 430 440 430 460 470 “75 480 430 500 510 520 530 540 550 560 570 575 576 5717 578 580 585 590 610 &50 660 710 720 730 740 810 azn 821 430 840 841 845 350 as1 852 862 863 o6& 865 870 880 890 895 By Ly ISN 0192 1SN 0193 . ISN 0194 ISN 0195 ISN 0196 ISN 0197 ISN 0198 TSN 0199 ISN 0200 ISN 0201 ISN 0202 ISN 0203 ISN 0204 [SN 0205 ISN 0206 ISN 0207 ISN 0208 ISN 0209 IsNo210.__ _ ISN 0211 ISN 0212 ISN 0213 ISN 0214 ISN 0215 114 11§ .. 439 451 452 | 453 - 434 90 IsNoae ISN o217 ISN 0218 1SN 0219 1SN D220 1SN 0221 ISN 0222 ISN 0223 15N 0228 . . " ISN 228 ISN 0226 1SN 0227 ISN 0228 ISN. 0229 ISN 0230 ISy 0231 ISN 0232 . IS 0233 ISN 0234 ISN 0235 ISN 0236 ISN 0237 ISN 0238 .. ISN 0239 ISN 0240 ISN 0241 ISN 0242 ISN 0243 ISN 0244 __ . ISN 0245 ISN 0246 ISN 0247 91 93 94 96 NUNO (I )=H{1)%2,.%R]1 /12, /CCND PRINT 114 4X yXODoHOIY»TBII)oTI(1h,TOUT)oNUNO( 1), REND,PRNN FORMAT (1HO49F13.4) CONTYINLE HAVG=AVG {H +FTC +CTC o X1 4 X2} PRINT 450,HAVG FIRMAT(1HD 4 "AVG H BTU/HRSQFTDEGF = '-910 2} WAVGSAVG {TIWFTC,CTCoX1 X2} PRINT 451 ,%AVG FQRMAT (1HO s *AVG INNER HALL TEMP DEGF = "F30-3l BAVGSAVGITBFTC +CTCe X1 4X2} PRINT 452,BAVG FORMAT (LHO ,'AVG RULK TEMP DEGF = *,F10.3) T OAVGSAVG{TOFTC 4CTCo X1 oX2) PRINT 453 ,CAVG FORMATI1HO o*AVG OUTER WALL TEMP DEGF s ' ,FL10.3) NUAVG=AVG I NUNO oF TC (CTC oX1 4 X2) PRINT 454 ,ANUAVG FORMAT_(1HC*AYG NUSSELY NC. = *,F10.%) CALL PROP (RENO ¢ PRNC o MU sRHO 4 BAVG yR1 ¢ CCAD, SPP!!HDOT' VRAT=MU 82 TA=0,02328/RHO PRINT 90,QuMm FORMAT (1HL + *WATTMETER BTU/HR = * ;T35,F10.3) PRINT 93 Q8 e e FORMAT (1HO ¢ "HEAT TC SALT BTU/HR = *,T35,F10.3) PRINT 93,QLCAL FORMAY [1HO *CAL HEAT LOSS N’UIHR = 1,735,F10.3) PRENT 94 ,QLESY FDRHAT(IHO.'EST HEAT LOSS BTU/HR = ¢,T35,F10.3) GaN ___ FARMAT(THO,FTEST SECTICN NO. = ‘9735- 1oy . GaMDOT 7{3.14%R]1*R] ) *144, .97 23 100 101 472 473 4T4 471 471 478 PRINT §7.G FORMAT [LHO »°G LB/HRFT2 = *,T33,E12, 5' VEL=MDUOT/RHO/(3.14*R14R1/144,.)/3600, PRINT. 98,VEL _ FORMAT (1HO ¢ TEST VEI.G:IYY FT/SEC = ",735,F10.3) PRINT 99,RHO FIRMAT (1HO,*BULK SAI.T DENSITY LB/FTI = *,T35,F10.2) _PRINT 100,My FORMAT (1HC,"BULX SALT VISCOSITY LB/HRFT = *,T35,F10.3) PRINT 101,CCND FORMAT (1HO,%BULK. SALT CCND BYUZHRFTLEGF = *, T35,F10.2) PRINT 472,1TIN FORMAT(1HO*INLET TEMP DEGF = *,T35,F10.3) PRINT 473, Y0UT FORMAT (1HO »"OUTLEY TEHP DEGF = 94T7335,F10.3) _JCHGsTCUT=-TIN. . PRINT 474, TCHG FORMAT(LHO »*TOUT = TIN DEGF = %,T35,F10,3) PRINT 471,PDOT FORMAT (1HO 9 *MASS FLOW FATE LE/HR = ¢,7135,F10,3} PRINT &4TT.FENQ - FIRMAT {JHC,*AULK REYNCLDS NO: = '.T!S.FRO-ZD PRINT 478,PRNO FIRMAT (1HC,'BULK PRANCTL ND. = '.TSS,FIO.!I PRINT 4T0,C0DP 897 900 910 920 930 935 940 950 955 960 eT0 9718 980 $9C 995 100G 1005 1010 1015 1017 1018 1019 10204 10208 102081 102082 gh ISN 0248 470 FORMAT (1HO,*NET HEAT FLUMA BTU/HRSOFT = *,T23,El12.5) TSN 049 PRINT &76,08AL ISN 0250 476 FORMAT (1HO»*HEAT BALANCE = *,T35,F1).3) ISN 0251 DEFH=MDOT®SPHL S (TOUT=TIN)/(2.%3.16*R1 4L/ 164 . S{WAVG=-BAVS) ) ISN 0252 PRINT 47%,CEFH ISN 0253 475 FIRMAT(LHL 4*H BY DEF BTU/HRSQFTDEGF = *,T35,F10.,2) ISN 0254 NNO=DEFH®2 ,*R1/12. /CCNC 1SN 255 PRINT 4751 ,hNO ISN 0256 4751 FORMAT (1HC,*NUSSELT NC, = *,T35,F10.2} C FROM MERE ON THE NND USED WitL BE THE INTEGRATED VALUE ISN 0257 NNO=NUAVG ISN 0258 GRNO= 01 *$23RETAS3 2, 2¢RHO* #2% (HAVG=BAVG) /{MU/26C0, )42 ISN 0259 _ PRINT 981,GRNO 1SN 0260 ST FORMAT (LHO o SGRASHOF NOe = 9,T35,F10.4) ISN 0261 GINO=3,14/4, *RENO*PRAO2 . *R1/ (X2-X1) ISN 0262 PRINT 4752 ,GINO ISN 0263 4752 FORMAT (1HO,'GRAETZ NO.(F=B) = *,T35,F10.4) ISN 0264 BTRM=0,0722%{GRNO*PRAD2 . *R1/{X2-X1) ) 440,75 ISN 0265 PRINT 4753 ,8TRM ISN 0286 4753 FORMAT (1HO,*BUGYANCY TERM FOR VERT,LAM = *,T35,F10.4) ISN 0267 STF=NNO/(PANO®#0.33) /{ FUSS0 14) ISN 0268 DSF=NNO/PRAOS®0 . 4 ISN_0269 _ OBH=COND/(2.%R1/12,) %C .023%{ RENO*%0 .8 )&({ PRND*%0,.4) ISN 0270 PRINT 4B81,CBH . ISN 0271 481 FORMAT (1HO o *MC_ADAMS H_BTU/HRSCFTCEGF = 9,T35,F10.2) ISN 0272 STTH=CCOND7 (2,#R1/12.)1%0.02T*(REND*#0, 8) * (PRNO*#0,32) 8 (MU0,.14) - ISN 0273 HTRH=COND/ (2, #R1/12, 140, 116 (RENO##. 667 ~ 125.) #PRNO*#,33 - _ 8 MER],14) ISN 0274 STHCOND/(Z.#R1/12.) %1 .86% (RENC#PRNO#2, #R1/(X2-X1) }#40.33 ISN- 0275 [F (TA-TBS)} 200,210,210 ISN 0276 200 DLH=COND /D1#1. T54(GING. = BIRN) 430, ,33_. ISN 027T GO TO 220 ISN 0278 210 ocn-couorol¢1.1s—tcznn + BTRM)#%0,33 ISN 0279 22 CONTINUE 1SN 02%0 STHeSTHR (MLERO18) ISN 0231 COLH=0, 023‘(01*Gl**O.BIDI‘CCNBOOO 66745PH1 40,33 ISN 9282 === CLMH=]l .e5%COND/DL#{GINCEMU)*20,33 ISN 0283 FGRNO=GRNO*MU**2 _ ISN 0284 CFR=NNO/{PRNO**0,33 ) ¢ (MU*#0,33) ISN 0288 FILM=( WAVG +BAYG)} /2. T C DIM GROUPS AND PROPS THAT FOLLCW ARE NO LCNGER AT BULK TEMP IsN 0236 CALL PROP{REND,;PRNC¢MJ yRHOFILP+R1 yCCADy SPHL,MDOT) ISN 0267 . COLH=CCLH®NMU*%0,33 /MU*90,8 1SN 0288 FGRNO*EGRNC/MUae2 1SN 0289 IF (TA-TBB) 230,240,240 ISN 0290 230 CLMH=CLMH/MU#%0,33%(1. = 0.015#(FGRNO)*+0,33) ISN 0291 GO TO 250 ISN 0292 240 CLMHaCLMH/WU*G.33%(1, ¢ 0.015%(FGRNC)1%$0.33) ISN 0293 25C CONTINUE ISN 0294 CF=CF/MUssC,23 ISN 0295 CRENO=RENC 1SN 0296 PRINT 4811 ,COLH ISN 0297 4811 FIRMAT (1HC,'COLBURN TURB M BTU/HRSQFTDEGF = %,T35,F10. z: ISN 0298 CALL PROP(RENN¢+PRNCy MU JRHO yWAVG oR1 + CCNDy SPH1,MOOT) ISN 0299 STTHaSTTH/ (MU**0,1 4} ISN 0200 HTRH=H TRHZ (MU$#*0.14) ISN 0201 STHaSTH/ (MLE$D, 14) ISN 0202 PRINT 482,STTH: 1235 1240 1245 1250 1260 1270 1290 1291 1292 12924 12928 1293 1294 129% 1296 1297 1298 1299 1300 1301 1310 1320 1330 1340 1350 1355 1357 1358 1360 1360A. . 13608 1360C 13600 - 1360CE 1361 1361A 1361A00 1361A0 1361A1 13618 136181 1361C 13610 1136101 136102 136103 136104 136105 1361D6 136107 136108 1361¢£ 1361F 1362 13628 1362C 1363 1364 o ISN 0303 482 FIRMAT(1HO,%S-T TURBULENT H PTU/HRSCFTDEGF = *,T35,F10.2) ISN 0304 PRINT 4821 JHTRH- ISN 0305 4821 FORMAT (1HO,*HAUSEN TR H ATU/HRSOFTDEGF = *¢T35,F10.2) ISN 0306 PRINT 483,STH ISN 0207 483 FORMAT (1HO,°S~T LAMINAR H BTU/HRSQFTLEGF = *,T35,F10.2) ISN 0208 PRINT 484,4DLH ISN 03209 484 FORMAT(1HO,*MART VER,LA¥ H BTU/HRSQFTCEGF = *,T35,F10.2) isN 030 PRINT 4840 LW ISN 0311 4840 FORMAT (1MO,'COL VERT,LAN H BTU/HRSQFTDEGF = *,T35,F10.2) ISN 0312 PRINT 484)1 (DAF ISN 0313 4841 FORMAT (1HCe'MC ADAMS FACTCR = 9,T33,F10.3) ISN 0314 PRINT AB42,CF ISN_ 0318 48642 FORMAT (1HQo*COLBURN FACTOR s % ,¥35,F10.3) TSN 0316 PRINT 4843 ,CREND ISN o7 4843 FORMAT (1HU9*CLBAN RENC = *4T35,F10.2) ISN 0318 STFaSTE® (ML®#),14) ISN 0319 PRINT 488,STF ISN 0320 485 FIRWAT (1HO4*S-T FACTOR = ¢,T35,F10.3) JSN_03, e BT e e 1SN 0222 PRINT 486 ETL ISN 0323 486 FORMAT (1HO o*EFF TUBE LENGTH IN = *,T35,F10.3) ISN 0324 VRAT={ VRAT /MU} 20,14 ISN 0325 PRINT 487, VRAT ISN 0326 AB7 FORMAT (1MO,°VIS RATIO TC O.14 = *,T35,F10.4) ISN. 0227 _ __ _ _OFACT=STYERVRAY . . . 1SN 0328 PRINT 488,CFACT - ISN 0229 488 FORMAT (1HO,*MART FACTCR = *,T35,F17.2) o C A LOOK AT A SNCOTH CURVE THRU THE DATA POINTS NAY BE EDUCATIONAL ISN 0330 CALL YLSITCIFTCHCTC2) ISN 0331 G0 T0 6 —_ISNOM2 - END ___ . .. ADCONS FOR EXTERNAL REFERENCES 1365 1366 1366A 1367 1368 1369A 13698 134981 136982 .1369C1 1369C2 -1369C3 1369C4H 1369CS - 1369C6 1370A ‘13708 1370C 1372 © 1373 T 1374 . 1378 - 1376 1377 . 1378 1379 1380 1390 © 1391 1400 1401 0¢ CCMPILER CPTIONS =~ NANE= MAIN,CPT=02,LINECNT =6) ySOURCE,EBCOIC,NOLISTs0ECK LOAD 4 MAP,NOEDL T,NOI B¢ NOXREF ¢ THIS FUNCTICN CCMMITS 3RD CRDER CRTHOGCNAL SINS BY AVERAGING VALUES Al0 C BEGINNING WITH NO. M AT X1 AND ENOING wiITH I CCNSECUTIVE VALUES AT X2 A1l ISN 0002 FUNCTICN AVG(Y,M,[ X1,X2) A20 ISN 0003 DIMENSION Y(50) 4X(50),A(4),P(50,4),5P2(50,4) A30 ISN 0004 REAL NPyLS A3S ISN 0005 A{l)s0 , _ A40 1SN 0006 Al21=0 AS0 1SN 0CO7 Al3)=0 A60 ISN 0008 Al4)=0 A70 1SN 0009 _ P(1s1) =1, AT2 ISN 0010 Pll,2)=1, AT3 IsN ool _ Plis=. . ‘ , o ‘ AT4 1SN 0012 Pllo4d)=l, ATS - ISN_ 0013 NP=l-1 490 ISN 0014 DO 490 L=2,1 , ASS ISN 0C15 XtL) =L=1 AST ISN OCl6 o PLyl)= 1. A100 ISN CCL7 . PULs2)mle=2.*X(LI/NP _ _ Al11C ISN 0018 PILe3) =l o=E 0 X (L) /NP X (LI *IX L) =1, ) FNPZINP-1,) A120 ISN 0019 © PAL ) =1 o=12#X (L) INPH30 . #X (L) #(XIL) =14 ) /NP/INP=1.) A130 . ‘ 8 —20.#X (L) #(XIL) =14 )*IX(L)=24)/NP/INP=1.} /INP-2.) A131 ISN 0020 49C CONTINUE = A13% ISN 0021 SP2(1+1) =NP+1, . Al40 ISN 0022 __ __SP2(142)=(nPel,) ‘lNPtZ 21 /13:*NP) Al50 IS8 0023 SP2(1+3) =(AP+L. ) #(NP42 ) $(NP+3.)7 (5. ¢KP)/(NP-1,) A160 ISN 0C24 © SP2(1e4)={AP+L.I#INP#2,) #(NP+3. D (NP+4.) /(T NP /INP=1,)/(NP=2,) ALTO ISR 0025 DN S50 Jsl 44 4200 ISN 0026 . DD 500 K=l,] 1 A210 ISN 0027 AN =ALI) $Y(KOM=] JRP (K, ) . 4220 IS!!_O_QZ_B_-_____SOO .. CONTIMNUE . . . S A230 SN 0029 ALIV=A IV 7SPUT,0) A240 ISN ooao 550 CONTINUE A250 ISN 0031 PRINT 6C0 4270 ISN 0032 600 FORMAT (1H1,10HORIGINAL o13HLEAST SCUARES,LOM PCEV) A280 1SN €033 © T DB T00 J=ll ‘ A290 ISN 0034 CLSEACLI*PIINLIRAL2)0P ()2 2AL2D2F{J I 4ALL)*P LI, 4) ' A3L0 ISN 0035 ' PDE Va (LS~Y(J¢ ¥=1) ) #100./ Y (JeM=1} A305 ISN 0036 PRINT 650,Y{J+M=1),LSPOEV A310 ISN 0C37 650 FORMATY (FB.245XFB8e245XsF842) A320 ISN 0038 700 CINTINLE A330 ISN 0039 X3=X2-xX1 A340 ISN 0040 750 AINT=A(1)%X3 ¢ A(2)% (X3-X3#82/NP} + A350 | 8 AL2)%(X3 =3, 9X30%2/NP+6 . /NP/(NP=L. J (X 365373, -X3%%2 A351 8 72.)) . A352 5 Al4) (X3 =6 ,#XI¥®2/NP+30 ./ NP/ (NP-1o bR{X 384 3/3 =X 3042 A353 a 720)=20 /AP (NP=14)/ (NP=2,) $(X3€£4/4,=X3334X 3£X3)) A354 ISN 004l AVG=AINT/X3 A390 ISN C042 . RETURN A440 ISN 0043 END A450 TS ISN 1SN ISN ISN ISN ¢ _COMPILER CPTIONS = NAMEa 0002 0003 c004 0005 0006 0coY T 0008 0009 FUNCTICN TE{TEMPF} TEMPC={TEMPF=32.,1%5,/9, . IF (TEMPC~440.110,10,20 10 3c 40 50 7C 75 8c 55" TK=0.128+(,155~.128) /200 . *(TEMPC~2074 ) GO TO 80 IF “(TE ¥PC=500.130430 440 TK=0,160+(.1T4=,160) /6C, @{TENPC 440, ) 63 10 80 IF (TEMPC=-¢8C. 150,50 ,6C TKa0.174+(.193=.174) /100 . $(TEMPC=507.) 62 _T0 80 TIF CTEMPC=140.)70,70,75 TK=0,2084{.230-.208) /6C. *(TENPC-680.} G0 TO 80 TK=0,2304( ,248-.230) /160, '(TE"PC-TkO.l TK=TK*5T7,.82 _RETURN END HAlNoCPTIOZcLINECNT-GO¢SOURCE|EBCDiC-NOLISToDECKoLOADoHAP-NDFDlToHOlD'NOXREF “CTHTS FUNCTION DETERMINES THERMAL K FOR IMNCR-8 kKl0 K20 X30 K&0 K50 K60 K70 ‘K80 K90 K100 K110 K120 K130 K140 K150 K160 K170 K3a0C K301 2s CCMPILER OPTIONS = NAME= ISN 0002 ISN 0C03 ISN 0004 TSN 0005 ISN 0006 ISN 0007 1SN 0008 ISN $009 ISN 0010 ISN o011 1SN G012 ISN 0013 ISN 0014 ISN 0015 ISN 0016 ISM 0017 1SN 0018 ISN 0019 ISN 0020 1SN 0021 ISN_0022 ISN 0023 1SN 0024 ISN 0025 ISN 0026 ISN 0027 ISN 0028 1SN 0¢29 ISN 0030 ISN 0C31 ISN 0032 ISN 0033 1SN 0C34 1SN 003% ISN 0C38 ISN 0040 1SN 0061 ISN 0042 ISN 0C47 C CONSeCUTIVE VALUES AND REPLACES THIS ARRAY WITH AN NTH ORCER FIT SUBRDUTINE YLSUY Mo WN) DIMENSION Y501 oX(50)sA(4)4P(5044),SP2(50,4) REAL NP4LS Al{1)=0 "AL2) 20 A(3) =0 A(4) =0 Pil.1)=1, P{l.2)=l. Pll,311, T PlleRinl. NB =] -1 07 499 L=2,] X{Li=L~1 PlLsl)e 1. LPlLe2k =l o=2.8X (L) /NP 490 8 CONTINUE PlLe3) =l o =6 *X(LI/AP+S #X (LI (X (L) =10 }/NP/INP=]1,) PIL &)=L o =124 6X(LI /NP0 LEX(LI*(X{L) =LV /NP/(NP-1.) =20 XL 2UXILY-1 ¥ IX(LI=2.)/NP/INP=1}/INP-2,) SP2(1,1)=NP+l. SP2(142) sCAP+1 ) #(KP+2,) /(3 ,#NP) T SP2(Te3) 2 (NPRLL I R(NP42 ) E(NP+2 L)/ (5, %AP}/(NP=14) -.-300_ 550 €30 SP2{Is4)s{APeLl )2 LKP#2 ) F(NP+I )R {NP+4, ) /{T.ENPIFINP=1,)/7INP=2,) DN 550 J=l.4 - DO 500 Ks=l,1 AlJi-AIJIOVlKoM-lD*P(K.Jl CONTIAUE ACDY=A (S 7 8Se2¢1 0 CONTINUE PRINT 600 FIRMAY tlHl.lOHO&!GthAl +13HLEAST SCUARES,10H POEVY) DB 700 J=l,l IF (N LT.3) Al&)=0 IF(N.LT.2) A(3)=0 TF(N.LT L) A{2) =9 LS=A(1)*P(Jo1)+A{21 2P (U204 3)0F( 03 )2A (4 )P(J,s4) POEVSILS=-Y(JeP=1) )2100./7Y(J¢M=-1) PRINT 650,Y(J¢F=1),LS,PDEYV FORMAT (FB.2,5XFB.2,5X,FB.2) Y{J*M=-1)=L$ CINTINUE RE TURN END MAIN:OPT=N2 , L INECNT 260 ySOURCE» EBCOICNOLIST ¢ DECK s LOAD ¢MAPyNOEDL ¥ NCICoNOXREF T ™IS SURROUYTINE TAKES AN ARRAY Y WHCSE 1ST VALUE IS AT M WITH 1 TOTAL AlD ALl A20 A30 A3S 440 A50 A60 AT70 AT2 AT3 ATé ATS A90 ASS A97 A100 All0 A120 A130 A131 A135 A140 A150 A160 A1T0 4200 A210 A220 A230 A240 A250 A270 A280 A290 A294 A295 A296 A300 305 A31C A320 A230 350 A370 A7) €< _._._.____..f.QH.ElJ.EB_flP.I..IOUS. NAMEs MAIN,DPT=02,L EINECNT=60,SIZE=0000K o SOURCEyEBCDICoNOLEST ¢NODECK yLOAD ¢ MAP 4 NOEDIT ¢NOI1D¢NOXREF ..€ THIS SUBROUTINE USES THERMOPHYSICAL DATA FRCM CRNL=-TM=2316 AND URNL-4%49 . .. ... .. ISN 0002 SUBROUTINE PROPLREPRyVyRHO, TEMPF 4RsCOND+CPyW} P20 _ISN 0003 ____ _ __ TY={TEMPF-32,00/}.8 _ __ .. _____ e e e o ot e 2 22 e e et e e i ISN 0004 TuT+273.0 . “ISN 0005 = Y=Q.077¢EXP{6430,0/1) ___ __ . . . . — ISN 0006 . V=2 ,4]19%Y _ISN 0007 .. . RHO=R A AT R A SE=04a® ) o o e ie e e ————— e s ISN 0008 RHO=RHD®62,428 1SN 0009 LOND=0.69 ... .. e ——— ISN 0010 PR’CP‘VICOND : P140 — REn&, /N/3,14/(2,%R/12.3%HW P150 1SN 0012 RETURN : P19%9 SISN. 0013 END e e e e e e e e e e an et emremm e P2 » t ¥ 1S | | 55 - APPENDIX D CHEMICAL ANALYSES AND PHYSICAL PROPERTIES OF THE SALT e o7 Table D.l. Analyses of the Fluoride Salt Mixture (LiF-BeF-ThF, =UF,; 67.5-20.0-12.0-0.5 mole %) Before, During, and After Heat- Transfer Determinations Impurity Weight % - ' Before During® After Li T.1% 7.27 6.64 Be 2.57 2.53 2.46 Th ho.1 41.3 L43.5 U 1.87 1.84 - 1.72 F 45.4 T 45.4 Ni 20 ppm - - - - Cr <25 ppm - - Fe 78 ppm - — . S <10 ppm - - Na - 0.66 0.55 gAnalysis made Jjust prior to removal of the first test section. 58 Table D.2. Thermophysical Property Data for Molten Salt - Mixture LiF-BeFg-ThF,-UF, (67.5-20-12-0.5 Mole %) Uncertainty Ref. u (1b/ft-hr) = 0.187 exp [8000/T(°R)]1* 1054 12 k (Btu/hr-ft.°F) = 0.69° o s12% 13 o (1b/£t3) = 230.89 — 22.54 x 1072 t (°F)" + 3% 12 C, (Btu/1b*°F) = 0.324% - + g 12 Liquidus temperature = 895 °_Fa +10°F 12 ®Estimated values for the salt mixture LiF-BeF,-ThF,-UF, (68-20- 11.7~0.3 mole %). bMeasureq value for the subject salt mixture. _ * 9 » - O O0—~1 A £ N —~ o 11. 12-21. 22. 23-27. 28. 29. 30. 31. 32, 33. 34, 36. 37 38. Lo, hi. 4o, k3. by, 45, 146-55. 56, 57« 58, 59. 60. 61. 62. = 59 ORNL-TM-4079 INTERNAL DISTRIBUTION B. Aiexander. . I.. Anderson E. Beall Bender . S. Bettis . G. Bohlmann . J. Borkowski . Boyd . Briggs . Chapman . Claiborne, Jr. . Cooke . Cottrell ox (K-25) . Culler . DeVan . DiStefano . Ditto . Dworkin . Eatherly . Eissenberg . Engel . Ferguson . Ferris . Fraas . Frye . Gabbard . Gallaher . Gambill . Guymon . Haubenreich . Heimdahl . Hoffman . Huntley . Kasten Kedl Keyes, Jr. . Klepper . Krakoviak Kress ?Jkifiz?i?1fi1I1€2U123fi!fltfl2fl3fl'fi:§lfi!fl:g*UCchfljflib'ClUlE:Qlfiflwlfi 3 63. 6l . 65. 66. 67. 68. 69. 70. 1. 2. 73. Th, 5. 76, 7 78. 79. 80. 81. 82-83. 8h. 85. - 86. - 87. 88. 89. 90. 9l. 9. 93. ol . 5. 96. 97. 98. 99. 100-102. 103. 104-105. 106, Krewson . Lawson . Lundin . Lyon MacPherson . MacPherson McCoy . McCurdy . McElroy . Mclain . McNeese . McWherter Meyer . Miller L Milora R. Mixon L. Moore . M. Perry . Pidkowicz M W. Rosenthal W. K. Sartory Dunlap Scott J. H. Shaffer Myrtleen Sheldon J. D. Sheppard M. J. Skinner D. o < 0w HPEOQEHEHQZ HQ = tam-uiz:u:m-¢=cab'n= I. Spiewak D. A. Sunberg R. E. Thoma D. G. Thomas D. B. Trauger J. R. Weir G. D. Whitman .R. P. Wichner M. K. Wilkinson A. M. Weinberg Central Research Y-12 Document Reference Section Laboratory Records Laboratory Records — Record Copy 107. 108. 109-111. 112-113. 114-130. 131-132, 133. 13%-135. 136. 137. 138-139. 140. 60 EXTERNAL, DISTRIBUTION Branch Chief, Special Technology, RDT, USAEC, Washington, DC 20545 Director, Division of Reactor Development and Technology, USAEC, Washington, DC 20545 Dlrector, Division of Reactor Licensing, USAEC, Washington, DC 20545 Director, Division of Reactor Standards, USAEC Washington, DC 20545 Manager, Technical Information Center, USAEC (For ACRS Members) MSBR Progrem Manager, USAEC, Washington, DC' 20545 Research and Technical Support Division, USAEC ORO Technical Information Center, USAEC | D. F. Cope, RDT Site Office, ORNL A. R. DeGrazia, USAEC, Washington, DC 20545 Norton Haberman, USAEC, Washington, DC 20545 Kermit Laughton, RDT Site Office, ORNL o