TSFAPCH LIBRARY P’ " GENTRALR = : | = CEI;OCUMENT COLLECTION 4 2 2 RN = (& 3 445k 0349657 1 ORNL-1716 N SP;;?:} t‘mfl i o N DOoT - 3— ot | ARG RESEARCH AND DEVELOPMENT REPOST | €& “\I Vi !".!' ©, J., 'f" 1 ?ifi i : bt -.'_4.'....'.‘I 4 | A » ki AP . iy -I". l'.l J I Y 3 e gyt g - €5 Wi’?f O™ o = o : S i . S22 hw:z. ANTY TURBULENT HEAT TRANSMRM‘! ! * A Lak S E "; i e ey IS MOLTEN FLUORIDE SALT MIXTURE TO bl :'-.{ by SODIUM-POTASSIUM ALLOY IN A e | SR DOUBLE-TUBE HEAT EXCHANGER E: ju D. F. Salmon o o i 2 =\ £z S E £ | % o e Q Mmoo CENTRAL RESEARCH LIBRARY DOCUMENT COLLECTION LIBRARY LOAN COPY DO NOT TRANSFER TO ANOTHER PERSON If you wish someone else to see this document, send in name with document and the library will arrange a ioan. OAK RIDGE NATIONAL LABORATORY OPERATED BY CARBIDE AND CARBON CHEMICALS COMPANY A DIVISION OF UNION CARBIDE AND CARBON CORPORATION (143 POST OFFICE BOX P OAK RIDGE, TENNESSEE ORNL 1716 Th document ons ts of 3] pages Copy’d( of 265 copres Se es A Contract No W 7405-eng 26 ANP DIVISION TURBULENT HEAT TRANSFER FROM A MOLTEN FLUORIDE SALT MIXTURE TO SODIUM POTASSIUM ALLOY IN A DOUBLE TUBE HEAT EXCHANGER D F Salmon DATE ISSUED NOV 3 1954 OAK RIDGE NATIONAL LABORATORY Operated by CARBIDE AND CARBON CHEMICALS COMPANY A Division of Union Carbide and Carbon Carporation Post Office Box P Oak Ridge Tennessee LR m 3 445b D349L57 4 NN BN — F=E000-MTMTTOOEAC>P>PIMOP=ELECLMODETOOQODNO>PTITMTIOMNNOO-DTO Adamson Affel Bailey (consultant) Baldock Barton Bettis Btl{ington Blankenship Blizard Bredig Bruce Callihan Cardwell Center Charpie Clewett Chitford Cottrell Cochran Cowen Culler Emlat (K 25) Ergen Fraas Grimes Grindell Hamilton Hoffman Hoffman Hollaender S Householder T Howe W Johnson H Jorden W Keilholtz P Keim T Kelley Kertesz M King A Lane E Larson S Livingston N Lyon D Manly EMOQAVATrUOOEMIP>PMEOA> TN TEOX g INTERNAL DISTRIBUTION 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 8190 91 92 96 97 98 99 100 B L J Z J P J COM-Pr«eTMmM-M-NN=E>r@OTOMPITTITO-MX> = NNUooNzZzTNOPFPIPOrARIVIOCLOEETITM 0O m ANP ORNL 1716 Special McDonald Meem Miller Morgan Murphy Murray (Y 12) Nessle Patriarca Poppendiek Reyling Salmon Savage Savolainen Shipley sman Skinner Smith Smith (consultant) Snell Stair (consultant) Storrs Susano Swartout Taylor Trice Van Artsdalen VonderlLage Warde Weinberg White Whitman Wigner (consultant) Williams Wilson Winters Library Biology Library Laboratory Records Dept Laboratory Records ORNL RC Health Physics Library Metallurgy Library Reactor Experimental Engineering Library entrgLBesearch Library 104 105 106 107 108 109 120 121 122 123 131 132 133 138 139 140 141 148 149 150 151 152 153 154 155 156-160 161 162 163 165 166 170 171 172 173 174 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 202 203 204 210 211 222 223 232 233 234 235 236 237 238 EXTERNAL DISTRIBUTION Air Force Engineering Office Oak Ridge Air Force Plant Representative Burbank Air Force Plant Representative Seattle Air Force Plant Representative Wood Ridge ANP Project Office Fort Worth Argonne National Laboratery (1 copy to Kermit Anderson) Armed Forces Special Weapons Project Sandia Armed Forces Spectal Weapons Project Washington (Gertrude Camp) Atomic Energy Commission Washington (Lt Col M J Nielsen) Battelle Memorial Institute Brookhaven National Laboratory Bureau of Aeronautics (Grant) Bureau of Ships Carbide and Carbon Chemicals Company (Y 12 Plant) Chicago Patent Group Chief of Naval Research Commonwealth Edison Company Convair San Diego (C H Helms) Curtiss Wright Corporation Wright Aeronautical Division (K Campbell) Department of the Navy — Op 362 Detroit Edison Company duPont Company Augusta 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Laboratory Berkeley University of California Radiation Laboratory Livermore Walter Kidde Nuclear Laboratories |ne Westinghouse Electric Corporation Technical Information Service Oak Ridge Division of Research and Medicine AEC ORO CONTENTS Introduction Description of Equipment Test Procedure Method of Calculation Correlation of Data Test Results Discussion of Results Conclusions Nomenclature Appendix 1 Equation for Intermediate Axial Stream Temperature with Logarithmic Distribution Appendix 2 Derivation of Equations for Wilson Line Analysis Appendix 3 Physical Properties of the Fluoride Salt NaF ZrF , UF, (50 46 4 mole %) and of Sodium Potassium Eutectic Alloy Appendix 4 Sample Calculation of Data Point 4 o A A 10 12 13 16 18 19 22 TURBULENT HEAT TRANSFER FROM A MOLTEN FLUORIDE SALT MIXTURE TO SODIUM POTASSIUM ALLOY IN A DOUBLE TUBE HEAT EXCHANGER D F Salmon INTRODUCTION Circulating fuel reactor systems for high per formance high temperature power plants place exacting requirements on the fluids which must serve as heat transfer media It 1s necessary that the fluids have good heat transfer properties be stable chemically at an elevated temperature have a reasonably low melting point be compatible with container materials and require only a min mum in pumping power Aside from the chemical problem involved in finding materials with which the proper amount of nuclear fuel may be com bined there are the research and the experimenta tion required to determine whether the above mentioned specifications are met Mixtures of fluoride salts were found to show promise for the circulating fuel application This report 1s concerned with an experiment to measure the heat transfer characteristics of the fluoride salt mixture NaF ZrF , UF , (50 46 4 mole %) The primary purpose of the experiment was to make a correlation of film heat transfer coeffi cients and a secondary purpose was to determine the effect on heat transfer of deposits resulting from corrosion or mass transfer of container ma terials DESCRIPTION OF EQUIPMENT A schematic diagram of the various components of the test apparatus 1s shown in Fig 1 The only pump available for the fluoride salt circuit was a type 316 starnless steel sump pump capable of delivering 10 gpm at 40 ft of head and 3600 rpm This pump was designed for high temperature application and for liquids which could not be sealed against directly at the shaft in the ordinary manner It had a water cooled rotary face seal for maintaining an inert gas blanket on the fluid being pumped An automatic level control system was provided for maintaining the liquid level in the pump within prescribed limits The heat transfer coefficients were measured in a double tube heat exchanger The fluoride salt was cooled in the center tube by a countercurrent flow in the annulus of sodium potassium alloy (hereafter referred to as NaK) The center tube of the heat exchanger made of nickel was 0 269 in in inside diameter with a length to diameter ratio of 40 The outer tube was 3‘4 in schedule 40 type 316 stainless steel pipe which was rigidly connected to the center tube at one end and bellows joined at the other end to allow for dif ferential expansion Heating of the fluoride salt was accomplished in a length of 1 in schedule 40 Inconel pipe by electrical tube furnace elements assembled on the pipe and covered with preformed insulation The NaK stream was cooled by natural convection of air in a section of finned pipe which was ducted and provided with a damper for control The NaK was circulated by a conventiondl electromagnetic pump The fluoride salt and the NoK flaw rates were measured by water calibrated venturi tubes the calibrations were corrected to reflect the discharge coefficients and the dif ferences 1n densities of the respective fluids An electromagnetic flowmeter was also available for determining the NaK fiow rate Inlet and outlet temperatures of the fluoride salt and the NaK were measured by fixed Inconel sheathed Chromel Alumel probes on the center lines of the piping An adjustable probe that was provided in the annulus of the heat exchanger could be brought in touch-contact with the outer surface of the center tube wall for temperature measurement These probes were calibrated to ]/2°F against a National Bureau of Standards [~ | certified platinum—platinum-rhodium thermocouple in a calibrating furnace. Thermocouple readings were taken on a Leeds and Northrup K-2 potenti- SURGE TANK — FLUORIDE SYSTEM ——=—LIQUID METAL SYSTEM HEAT EXCHANGER-, —e— CENTRIFUGAL PUMP HEATER SECTION FLOWMETER VENTURI Figt 1 VENTLURI FLOWMETER ometer, and an ice-bath cold junction was used. Figures 2, 3, and 4 are photographs of the test equipment, UMCLASSIFIED DWG 18344 ELECTROMAGNETIC FLOWMETER LEC COOLER FEFH iHH} F T — = — A H- | | 1 1 | — ELECTROMAGNETIC g PUMP Schematic Diagram of Bifluid Loop. Fig. 2. Instrument and Power Panel. = HEAT EXCHANGER T FLUDRIDE SALT HEATING SECTION NS VENTLURI FLOWMETER SUMP TANK AND FLRNACE 8 UNCLASSIFIED | PHOTO & 5881 MoK FLOWMETER ELECTROMAGNETIC ¥ - L i ’rd-"-r:fl-hlh—.-:_l.__— | e - ¢ | Nek COOLER BYPASS FILTER CIRCUIT | B H Fig. 4. NaK Loop. TEST PROCEDURE The melting point of the fluoride salt was approxi mately 960°F ! and consequently 1t was neces sary at all times to maintain the walls of the fluoride salt system above this value In fact the walls were kept at from 50 to 100°F above the melting point as a precaution against freezing For all runs the electrical power to the fluoride ]Physrcal Property Charts for Some Reactor Fuels Coolants and Miscellanecus Material (3rd Edition) ORNL CF 53 3-261 (March 20 1953) salt heaters was controlled to maintain a constant inlet temperature to the heat exchanger The fluoride salt pump speed was set to give a desired flow rate and this flow was maintained for a series of different NaK flow rates The damper to the NaK cooling section was adjusted in each case to hasten attainment of steady state condi tions before data were recorded Data were taken during each run at each NaK flow rate a total of 80 data points was taken METHOD OF CAL CULATION A heat balance on the fluoride salt and NaK streams in the heat exchanger was made initally to serve as a check on the validity of the data and to provide the basis for calculation of the heat flux g/A_ The value of g used for determining the heat flux was an average of that obtained by applying the first two of Eqs 1 to the fluoride salt and NaK streams (1) wF C‘F AtF Sy It wN CN AL‘N U, Ao AILM where the subscripts F and N refer to the fluoride salt and the NaK respectively The insulation heat loss from the heat exchanger was neglected since 1t was in actuality less than 1% The over all heat transfer coefficient was calculated from the third of Eqs 1 q/Ao (2) u, = ~ LM The adjustable probe located 16 diameters down stream from the fluoride inlet provided the outer surface temperature of the center tube from the outer surface temperature the inside surface tem perature was determined by using the conduction equation | % n q, D) 3 t - oy 3 wF wN 2flkwL A loganthmic axial distribution of temperature was assumed for calculating the stream tempera ture opposite the measured wall temperature Der ivations of the equations for obtaining these temperatures are presented in Appendix 1 The following equations were then used to arrive at a film heat transfer coefficient 9a (4) by = Altpg 4y = twr] and 7 v ) by = Altun = thio 4y An individual heat transfer coefficient may be distingui shed from the film coefficients given above in that 1t 1s obtained by separation of the over all coefficient defined in Eq 2 Some such separation process s always required when the difficult problem of measuring surface temperature is not attempted In this case the valuable graphical analysis of the over all heat transfer coefficient attributed to Wilson by McAdams? is useful The analysis 1s based on the premise that a plot of ]/Uo vs 1/0% 8 will produce a straight line if one of the fluid velocities s held constant and the other 1s varied over a specific range of values Wilson s method was applied to the data of this experiment as shown in Fig 5 where 1/U_ 1s plotted against 1/v,,° 8 The run with the greatest number of values for NaK velocity was used to 2y H McAdams Heat Transmission 2d ed McGraw Hill New York 1942 p 273 establish the slope of the lines The lines were extrapolated to 1/v,,9 8 = 0 which was equivalent to letting the NaK velocity approach infinity in which case the NaK film resistance /b, ap- proached zero By assuming the value of »_ to be constant along each of the Wilson lines an individual co efficient for NaK was separated form the over all coefficient by using the following equation (derived in Appendix 2) An individual heat transfer coefficient for the ] fluoride salt was then separated from the extrapo (7) by = lated over all coefficient at ]/UN0 8 by using the _]___ 122 — 0 0000788 equation (derived in Appendix 2) U, F 122 (6) by = — 0 0000788 C SSFE 0 G 23303 9 o 8 e / /0/ /0‘(0 // 7 / 6 . ///a < // / -|$ /t A// 5 / ] / - A DATA POINTS 3 4 5 /‘ /.—A‘ A DATA POINTS 24 25 26 27 28 4 A ® DATA POINTS 2 6 7 8 // O DATA POINTS 9 {0 11 12 13 // e 3 %o 01 0z 03 04 05 06 07 os 09 010 - Fig 5 Wilson Line Plot CORRELATION OF DATA Dimensional analysis of the physical properties together with the hydrodynamic and geometric factors affecting heat transfer between a turbulently flowing fluild and a bounding surface such as a tube gives a product function of the Nusselt Reynolds and Prandt| moduli The function s usually written as (8) Nu = CRe™Pr? The relationships of these parameters for ordinary fluids such as water gases or oils as differ entiated from liquid metals have been empirically determined from the data of many experimental investigations the exponent » 1s 0 8 However for the constant C and the exponent p there 1s variation in the evidence the values depend on whether the fluid 1s being heated or cooled on the magnitude of the fluild viscosity and on whether the evaluation 1s based on the bulk temperature of the stream or on an average of this temperature and the surface temperature McAdams recommends® for fluids of high wvis cosity that 1s presumably higher than twice that of water the Colburn equation The generally accepted value for 1 1 (9) Nu = 0023 Refo BPrf 3 or that of Sieder and Tate 1 014 ) (10) Nu=0027{— Re0 8p; 3 Fuw For these equations the Reynolds modulus should be in excess of 10000 The viscosity correction term (pL/yw)o 14 compensates for the variation 1n the temperature difference between the bulk temperature of the stream and that of the wall In the transition range of Reynolds modult from approximately 2 100 to 10 000 called by McAdams the dip region 4 there ts a dependency on the fength to diameter (L/D) ratio of the heat exchange surface the amount being afunction of the Reynolds modulus Eckert® states that the equation of Hausen 3ibid p 168 YUbid p 167 = R G Eckert Introduction to the Transfer of Heat and Mass p 115 McGrow Hill New York 1950 u 014 2é (1) Nu =0116 (— (Re ® - 125) P 4| (oy? Pr 1+ [— L will satisfactorily reproduce values in the Reynolds modulus range from 2300 to 6000 Equation 11 1s also useful for the entrance region of tubes where the velocity profile has not developed fully al though the Reynolds modulus based on mean stream velocity 1s sufficiently high for full develop ment The theoretical approach to turbulent heat trans fer in a tube has advanced to the stage where experimental values can be predicted with very good agreement von Karman s postulation of three zones tn the flow field namely the laminar sub ayer the buffer layer and the turbulent core was largely responsible for the advance Although the theoretical approach was not used in this work reference will be made to an extension of von Karman s theory by Boelter Martinelli and Jonassen (as described by Eckert®) and by Martinell1 7 The extension concerns the temperature rotio (t - t)/(tw - tc) which was determined by them and plotted as a function of Reynolds and Prandtl modult The result gives the amount of deviation expected when center line temperature rather than bulk temperature 1s used to evaluate physical properties in correlating experimental heat transfer data The correlations discussed above for ordinary fluids do not hold for liquid metals which have low viscosity and high thermal conductivity and thus very low Prandtl moduli Thermal conductivity 1s important even in the turbulent core of the stream where for ordinary fluids 1t 1s assumed in the equations that all the heat is transferred by mixing action For heat transfer to liquid metals 1n a tube Martinelli® derived an equation which was later greatly simplified by Lyon ? but there is as Sibid p 125 7R C Martinelh Heat Transfer to Molten Metals Trans Am Soc Mech Engrs 69 955 (1947) 81bid p 947 959 R N Lyon Forced Convection Heat Transfer Theory and Experiments with Ligquid Metals ORNL 361 (Aug 19 1949) ye%% abundance of data to substantiate therr wor There 1s no widely accepted procedure for calcu lating heat transfer to turbulently flowing fluids in annult whether they are ordinary fluids or liquid metals The usual practice 1s to apply the tube equations with an equivalent diameter sub stituted and to add a correction term consisting of the ratio of annulus diameters to some power One equation for liquid metals 1n annult corrob orated in particular with NaK by Werner King and Tidball (described in the work of Claiborne 19) IOH C Ci iborne A Review of the Literature on Heat Transfer 1n Annuli and Noncircular Ducts for Ordinary Fluids and L quid Metals ORNL CF 52 8 166 1s the following (12) Nu,, =1[49 + 00175(Re x Pr)° 8] The bracketed quantity 1s equal to 07 of Lyon s expression’ for Nusselt s modulus in a tube and the diameter ratio correction 1s recommended by Monrad and Pelton who experimented with ordtnary fluids tn annular spaces The work of Monrad and Pelton 1s described by Claiborne'® and also by McAdams ! ”W H McAdams Heat Transmission 2d ed McG aw HIl New York 1942 p 201 TEST RESULTS A total of 80 data points was taken during the test but only 19 of the points were used in the analysis for this report The remaining data were not used because of fouling that occurred on the fluoride salt side of the heat exchanger as a result of mass transfer of iron from the stainless steel pump parts When the heat exchanger was sectioned a layer was found which built up gradually from the hot end to a thickness of approximately 0 030 in at the cold end Spectrographic analysis showed the layer to be pure iron The basis for selecting the data points that were analyzed 1s indicated in Fig 6 where the fluoride salt system pressure drop Is plotted as a function of volume flow rate The points are compared with a theoretically calculated curve of pressure drop vs volume flow rate The chosen points fall on the curve representing an unfouled condition while the rejected points lie considerably above this curve The sequence of the measurements can be traced Instances can be seen where pressure drop increased sharply without increase in flow and 1n other cases where pressure drop remained constant while flow increased The data points used in the analysis and the pertinent calculated quantities are tabulated In Table 1 Physical properties of the fluoride salt and the NaK are plotted as functions of temperature in Appendix 3 A sample calculation of data point 4 1s presented in Appendix 4 The fluoride salt flow rate was varied from 1 to 5 gpm and the system pressure drops for these flows were respectively 5to 55 pst The NaK flow rate was varied from 17 to 9 25 gpm the NaK system pressure drop was not measured Reynolds numbers for the ranges of flow rates given were 4 400 to 21 000 for the fluoride salt and 21 000 to 100 000 for the NaK Limits of the over all heat transfer coefficient based on the outside area of the center tube were 1140 and 2550 Btu/hr ft2 F Fluoride salt film coefficients from 2000 to 8200 Btu/hr 12 F were calculated Heat fluxes at the outer surface of the center tube from 196 000 to 484 000 Btu/hr 12 were obtained Minimum and maximum fluid velocities in the heat exchanger were 8 to 30 fps for the fluoride salt and 1to 65 fps for the NaK Fluoride salt temperature at the heat exchanger inlet was varied from 1200 to 1400°F and the corresponding outlet NaK temper ature was varied from 1050 to 1250°F The range of the axial temperature differences through the heat exchanger was 10 to 42°F for the fluoride and 37 to 300°F for the NaK The logarithmic mean temperature difference varied from 172 to 305°F 60 50 40 30 AP (psi1} 20 4 DWG 23304 FLOW RATE (gpm) Fig 6 Fluoride Salt System Pressure Drop vs Flow Rate for Each Run 68.] _ 64 g8-65 63/< ie;? 66 57 5 a N 51\ /5 3\ \n / 52\\‘9 0/ /56 O / 53 ——9 ~ 8-55 | g~g o , Ne2 58 59 60 ’ 74 / 46 47 /74 75 / 4 49> 0&473 50 \70/ 487169 72 7 Yy 40/®,45 4t 42 43~ " -44 7 UNFOULED 37 38 / 39 34 35 . 36:&/ / 77 , _ g ~76 79 78/ / 30 4 29 3132 — / >~ THEORETICAL 33 / 27 / 20 24 I\ 25 26 22 —F\ 23 28 e 19 21 2. ' / 7 14 67 8— A 18\ /7 1516 170} ’ g /// sS4 /,.)(9 10 11 12 13 13q 0 20 30 40 50 60 TABLE 1 MEASURED AND CALCULATED RESULTS OF HEAT TRANSFER EXPERIMENTS MEASURED OR DATA POINTS CALCULATED QUANTITY (1 2) 3) {4) (5} © 7} (8 {9 (10) a1} (12) (13) [ (13 (24) (25) (26) n (28) , 12205 (13433 | 13230 (13237 |13215 (13171 (13288 [ 13308 [ 13157 | 13328 |1333.4 (13337 [1333.4 [ 13342 [ 14291 | 14193 {14230 [14208 [ 14053 N1 11545 (11402 | 11819 [ 11798 [ 11645 [1102.4 [ 11183 | 1126 0 | tos7 4 [ 10582 | 10571 | 10532 10546 10552 | 1267.4 | 12327 | 12284 | 12229 | 12007 N 11519 (11851 | 11950 [1201.4 | 12035 (11150 [ 19429 {11519 | 1083.4 [ 10539 | 10536 | 10498 |[10535 | 10561 | 12533 {12187 | 12176 [12141 | 1214 5 At 101 268 148 146 156 |272 298 28.3 a7y |43 a5 423 Mne 424 25.3 269 270 284 276 Ary 000 |829 1087 |19 |s48 |571 482 385 814 598 499 430 37.4 370 1508 | 966 71.4 542 466 we 4580 | 4060 {8110 | 8450 |8450 |3810 |3810 | 3310 2300 2300 (2300 {2300 (2300 | 2300 {4050 |4325 4325 |4290 | 4340 wy 2250 |1170 | nso 1160 {1700 2235 | 2560 | 3060 1320 | 1940 | 2405 | 2780 }2120 | 3120 | 635 1196 1700 [ 2360 | 2950 e 14320 |33700 | 37200 | 38240 | 40850 (32150 | 35200 | 33 420 | 27 000 | 29,400 |29 600 | 30150 | 29900 | 30200 | 31780 | 36040 |36200 (37750 |37 100 N 16720 | 24000 | 31800 {32190 {35750 {31640 (30600 (29200 | 26600 | 29050 |29760 | 29620 |28950 1 28620 23750 | 28620 | 30040 |31 700 | 34 100 153520 | 28850 | 34500 |35220 (38300 {31895 | 32900 | 31310 | 26800 | 29225 [29680 |290885 | 29425 | 29 400 {27765 | 32,330 33120 |34 725 |35 600 A 1724|2302 1841 (1886 |18946 (2300 (2206 [2099 (2794 |2840 (2802 2809 |276.4 |2769 21R6 |2199 2161 12103 2144 U 1138 {1582 (2362 | 2357 [2553 | 1750 1882 1882 1212|1300 1338 | 1342 1342 1340 1600 1858|1931 2080 | 2096 Fi0 4) 12183 | 13334 (13180 (13188 {13159 | 13067 | 13170 | 13196 [ 13011 [ 13167 13168 [13168 [13178 [ 13165 [ 14203 | 14103 [14128 {14099 |1394 6 N(D 4 10902 (11115 | 11456 | 11423 11343 {10804 | 10992 [ 11108 | 10262 | 10348 |10372 | 10326 |10406 | 10398 12154 |1200.4 {11971 [12020 |1i826 WF 11682 1155 (12312 | 12366 [12437 | 11485 | 11775 | 11848 | 11116 | 10847 [10848 {10812 {10845 | 10870 |1282.4 | 12527 [1252.4 {12506 | 12519 b 4780 (3785 |&150 {4620 8190 |3110 | 3840 | 3590 2182 | 1950 1977 | 1961 1950 1980 |[3108 |[3185 (3182 |3360 | 3855 by 3230 (4950 |8830 [7520 [7160 !vi700 | 9500 | 9610 5910 119320 122840 | 21970 (28800 | 22800 |9240 |22,280 [20400 |36200 |14 100 bew1 ) 5740 [ 5740 [5740 [3055 | 3055 | 3055 2025 |2025 [2025 2025 [2025 |2025 [3672 (3472 [3e72 3672 3672 TR 770 | 7500 (10100 (10880 (19230 (19230 | 7040 [11570 {15400 | 16120 |16720 | 15880 |4700 | 8580 | 9430 14 600 15/400 N g 812 625 1030 {117 1380 |525 615 601 372 326 N 328 326 332 478 486 486 516 601 N 803 123 2195 (1845 (1780 |2910 [2360 2364 |1480 |483 571 548 79 570 2283 (5515 |505 8950 |3495 Newr ) 9 55 9 55 955 [518 516 518 339 339 339 339 339 339 5 64 564 5 64 564 5 64 N ywi 1914 {1873 (251 261 478 47 4 760 |288 384 402 402 3965 (1163 |212 2335 {381 38,15 R o 9040 110260 |19 970 | 20800 {20620 | 9100 | 9300 | 938O 5450 | 5640 | 5640 | 5640 |5640 | 5640 12200 {12800 |12880 |12700 |12 470 R g 8610 (9080 (18170 {19080 |19 180 | 7880 {8000 | 8090 4435 [ 4400 (4400 | 4390 | 4400 | 4400 10680 (10820 ;10980 [10750 |10 780 Ry 72700 138750 |39100 (38420 |56,300 |72100 | 82400 | 101300 |41 600 61800 | 75900 |87 700 | 98400 | 98 400 | 21580 | 40600 |57700 |80 100 | 100 200 Pr 675 513 535 535 543 |5355 5 43 535 564 [536 536 536 536 536 393 407 402 408 426 L 7 09 579 587 58 585 ]657 63 620 69 686 686 689 4 86 4 86 4.50 480 472 481 4.93 Py 000811 /000596 | 0 00596 | 0 005% [0 0059 | 0 00611 | 0 00611 [ 0 00596 | 00063 | 0 00629 | 0 00629 | 0 00629 | 0 00629 | 0 00629 | 0 00579 | 0 00579 |0 00579 |0 00579 | 0 OS8O Nmb idi i whi hd k h f h Fi v & R me rome d | 1 fd pi 13 DISCUSSION OF RESULTS The fluoride salt results are compared with Eq 9 in Fig 7 and with Eqs 10 and 11 1n Fig 8 A least squares analysis of the data in Fig 7 de termines a line to within 4% of Eq 9 while the averaging line compared with Eqs 10 and 11 s approximately 20% low |t appears then thatevalu ating the physical constants at an average of the bulk temperature and the wall temperature produces a better comparison of the results for the fluoride salt with correlating equations for ordinary fluids The scatter of the fluoride salt data 1s no doubt a reflection of the erratic nature of the heat bal Although the axial temperature differences measured were small and would result in large percentage errors for a small discrepancy in ab- solute value they would tend to be consistent The electromagnetic flowmeter readings for the NaK would likewise be consistent even if tn error The fluoride salt flow rate on the other hand al though measured with an accurately calibrated ances venturi was quite likely the cause of the scatter ing The pressure measuring technique on this venturi involved closely controlling liquid levels in the transmitters by means of floats and auto matically operated solenoid gas valves The length to diameter ratio of the center tube warrants some consideration here For short tubes where the velocity profile and boundary layer have not developed fully the heat transfer coefficients will be greater than those for established flow Investigations cited by Brown and Marco'? indicate the himiting (L/D) ratio for this condition to be 40 Hoffman'3 shows entrance length that 1s number of tube diameters where the film coefficient 1s 1 1 times the established value plotted as a function 20 | Brown and 5 M Mareo Introduction to Heat Transfer 2d ed p 110 MecG aw Hill New York 1951 By w Hoffman Turbulent Forced Convection Heat Transfer in Circular Tubes Contarming Molten Sodium Hydroxide ORNL 1370 (Oct 3 1952) o DWG 23305 2X10 O RESULTS FROM USE OF MEASURED WALL TEMPERATURE A RESULTS FROM USE OF WILSON LINE ANALYSIS EQUATION (9) 10% / o i 7 P o “ //z‘ a 5 z // i Vet Q/fl/g 4// Q e & /// / [ ; y4i //@ 10 10° 2 5 104 2 5 103 R g Fig 7 Comparnison of Fluoride Salt Results with the Colburn Equation 10 w 2 08 2X10 © RESULTS FROM USE OF MEASURED WALL TEMPERATURE A RESULTS FROM USE OF WILSON LINE ANALYSIS 10° V. EQUATION (11) /~———EQUATION (10) v | WITH = 40 i o A // O o / ;:/ 1, / L BN = s 2 / / : A o - /s 2 A |7 2 7 o© 7// // A D/ 2 A, VI 10 3 4 10 2 5 10 2 5 10° Fig 8 Comparison of Fluoride Salt Results with the Sieder and Tate Equation and with the Hausen Equation of Reynolds modulus times Prandtl modulus for molten sodium hydroxide Since the fluoride salt has a comparable Prandtl modulus the plot should be applicable and for the range of data of this expertment entrance lengths up to 50 are ind: cated Therefore 1t would be expected that the fluoride salt results would be slightly high and 1t 1s possible that such a condition 1s masked by the fouling that occurred Another point to be discussed 1s that in all the correlating equations a bulk temperature was used for evaluating the results while center line or axis temperatures were measured in the equipment The work of Boelter et al 7 when applied to salts indicates the ratio (z, -~ t)/(tw - tc) for the fluoride salt results to be 0 92 and the ratio for the NaK to be approximately 0 58 For the fluoride salt data therefore the discrepancy in volved In using an axis temperature rather than a bulk temperature 1s small and certainly within the accuracy of the experiment but a large amount of uncertainty arises for the NaK data This uncertainty 1s borne out In the comparison of the NaK results with Eq 12 in Fig 9 The relation ship between axis and bulk temperature however has hmited meaning for the NaK stream since 1t was flowing in an annular space Failure of the measured NaK heat transfer co efficients to coincide with the theoretical equa tions does not necessarily reflect on the accuracy of the fluoride salt measurements but it indicates the difficulty involved and the greater precision required in making liquid metal heat transfer corre lations 11 NCLASSIFIED DWG 23307 EQUATICN (12) Ly FOR 5" 25 O RESULTS FROM USE OF MEASURED WALL TEMPERATURE A RESULTS FROM USE OF WILSON LINE ANALYSIS Fig 9 Comparison of the NaK Results with the Werner King and Tidbaill Equation CONCLUSIONS The fluoride salt can be considered to be an ordinary fluid with respect to heat transfer and the equations in the literature can be used to design heat exchange equipment or to predict its per formance A similar conclusion was made by other workers at ORNL for the nonuranium bearing fluoride salt mixture NaF KF LiF (115420465 mole %) '* This would not include cases where the fluid had self generating heat sources Use of iron bearing alloys such as type 316 144 W Hoffman Preliminary Results on Flinak Heat Transfer ORNL CF 53 8 106 (Aug 18 1953) 12 stainless steel together with material not con taining tron 1n high temperature fluoride salt circu lating systems will result in mass transfer of the iron to cold surfaces if there 1s turbulent flow and if there extst large temperature differences Fric tional resistance to flow will be greatly increased and heat transfer performance of equipment will be likewise impaired The Wilson Line approach can be used to de termine heat transfer coefficients of fluoride salts at elevated temperatures 1n a double tube heat exchanger where sodium potassium alloy 1s used as the cooling or heating fluid NOMENCLATURE Constant Outer area of heat exchanger center tube ft2 Inner area of heat exchanger center tube ft2 Transverse flow area of heat exchanger annuius ft2 Constant Specific heat of the fluoride salt Btu/lb °F Specific heat of the NaK Btu/Ib F Constant Product of specific heat and mass flow rate for the fluoride salt Btu/hr °F Product of specific heat and mass flow rate for the NaK Btu/hr °F Tube or pipe diameter in general ft Inner diameter of center tube ft Outer diameter of center tube inner diameter of annulus ft QOuter diameter of annulus ft Equivalent diameter of the annulus or hydraulic diameter (D] ~ DO) ft Film heat transfer coefficient for the fluoride salt Btu/hr ft2 F Film heat transfer coefficient for the NaK Btu/hr ft? °F Thermal conductivity of center tube wall material Btu/hr ft °F Thermal conductivity of the fluoride salt Btu/hr ft °F Thermal conductivity of the NaK Btu/hr ft °F Length of heat exchanger center tube ft Differential length of center tube ft Constant equtvalent to (U nD ), Btu/hr ft F Constant Constant Rate of heat transfer from the fluoride salt stream Btu/hr Rate of heat transfer to the NaK Btu/hr Average rate of heat transfer between the fluoride salt and NaK streams Btu/hr Differential rate of heat transfer Btu/hr Bulk temperature of stream °F Bulk temperature of fluoride °F Bulk temperature of NaK F Axis or center line temperature of stream °F Temperature of tube wall surface °F Inlet fluoride axis temperature to heat exchanger F 13 14 F2 N1 N2 L F(0 4) EN(o 4) At F At At At A‘LM Qutlet fluoride axis temperature from heat exchanger °F QOutlet NaK axis temperature from heat exchanger °F Inlet NaK axis temperature to heat exchanger °F Fluoride axis temperature at 0 4L °F NaK axis temperature at 0 4. °F Center tube surface temperature on fluoride salt side at 0 4L °F Center tube surface temperature on NaK side ot 0 4. °F 'Fo 4) + th} oF 2 Fictive fluoride salt film temperature at 0 4L [ Differential fluoride salt bulk temperature °F Differential NaK bulk temperature F Over all heat transfer coefficient based on outer area of heat ex changer center tube Btu/hr ft2 °F Over all heat transfer coefficient at zero ordinate of Wilson plot Btu/hr ft2 F Mean flow velocity ft/hr Mean NaK velocity in annulus fps Mass flow rate of fluoride salt Ib/hr Mass flow rate of NaK |b/hr Temperature difference of fluoride salt and NaK at any cross section of heat exchanger °F Temperature drop of fluoride salt through the exchanger °F Temperature rise of NaK through the exchanger °F Temperature difference of fluoride salt and NaK at hot end of ex changer °F Temperature difference of fluoride salt and NaK at cold end of ex changer °F Logarithmic mean of At and At, F Constant (EI]— + Cl-> hr °F/Btu F N Constant 3 1416 Mass density evaluated at bulk temperature Ib/ft3 Mass density of fluoride salt evaluated at axis temperature 1b/ft3 Mass density of NaK evaluated at axis temperature |b/ft3 Absolute viscosity evaluated at bulk temperature Ib/hr ft Absolute viscosity of fluoride salt evaluated at axis temperature Ib/hr ft Absolute viscosity of NaK evaluated at axis temperature Ib/hr ft Absolute viscosity of fluoride salt evaluated at film temperature Ib/hr ft Nu Nu Nu Nu an Re Re Re Ff Re Pr PrD v HF PrD Vg Kry D v pNeN Absolute viscosity evaluated at tube surface temperature |b/hr ft Nusselt modulus (tube) Nusselt modulus for fluoride salt Nusselt modulus for NaK Nusselt modulus for an annular passage Reynolds modulus Reynolds modulus for fluoride salt Reynolds modulus for fluoride salt with viscosity evaluated at tpy Reynolds modulus for NaK Prandtl modulus Prandtl modulus for fluoride salt Prandtl modulus for fluoride salt with viscosity evaluated at try Prandtl modulus for NaK 15 16 APPENDIX 1 EQUATION FOR INTERMEDIATE AXIAL STREAM TEMPERATURE WITH LOGARITHMIC DISTRIBUTION To evaluate the temperature difference across the film at the point in the heat ex changer where the center wall temperature was measured it was necessary to determine the stream temperature at this position ® @ ., _L ! A, Aty l—— D‘_{ ok K > ~ — . | Aty _‘“_"N_ /-N// — ¢ } art gl —e |‘m— N By assuming a constant over all heat transfer coefficient with steady state operation and neglecting heat losses the basic equation for this configuration is (N dq = -wFCthF = -,uNcthN = UoerodLAt For the fluoride stream U aD dLA: O 0o 2 dt ., = -~ (2) F v er To integrate Eq 2 At must be written as a function of L This is done in the usual derivation of the logarithmic mean temperature difference found in the literature there- fore (3) At = Arje”PML The constants have been grouped and simplified as follows = C and WNEN = CN “F°F T “F ] ] B = — — — CF CN M = UaaD o Substituting Eq 3 in Eq 2 gives MAt, @ dp = - oML g F Integrating and considering the boundary condition when L. = 0 and tp =tg, Eq 4 becomes At _ (5) tp = tgy - E(l ~ o FML) In like manner for the NaK stream At, ) (6) ty = I —fi(l ~ o7 AL Equations 5 and 6 can be written for the position where the wall temperatures were measured at 0 4L and also changed to involve only the measured temperature quantities By noting that ] - N BC. = 1 - Mn and BC, = M At tn n and by using Eq 5 04 0 e S N 5 T, and by using Eq 6 At fitf ' A At \® 4 (8) N &) = TN —-——K;[l - } N 1 A 17 18 APPENDIX 2 DERIVATION OF EQUATIONS FOR WILSON LINE ANALYSIS In a liquid to liquid heat exchanger where neither fluid changes phase if one of the fluid velocities 1s held constant and the other 1s varied over a range of settings 1n turbu lent flow the film coefficient of the fluid at constant velocity can be determined by a graphical method called the Wilson Line or Wilson plot When the mean temperature of the constant velocity flusd does not vary appreciably the film coefficient will be essentially constant The film coefficient of the other fluid where there are not large changes of physical properties with temperature 1s a function solely of the velocity The graphical method was used 1n this experiment to obtain coefficients of the fluoride salt and thus separate the over all heat transfer coefficient to obtain a NaK film coeff cient |f the series resistance concept 1s used the over all coefficient 1s related to the film coefficients as follows 1 o ? 1 Uo bFD 1 2"aw bN (1) Equation 1 neglects the resistance of any foreign deposits on the heat exchanger walls but such deposits would enter the equation 1n a term similar to that for the wall res:s tance that 1s the middle term in the right side of the expression The equation relating the NaK coefficient (Eq 12 in the text) reduces to (2) by = a + bUNOB ForD_ =0329mn D =02691n andk =34 8 Btu/hr ft °F Eq 1 above becomes 1222 = - + 00000788 + 0 F a+buN (3) 1 Uo 8 Sincethe NaK velocity 1s the only significant variable a plot of l/Uo vs 1/a + buNo 8) should produce a straight line For such a plot the constants a and b must be known They could be taken from Eq 12 of the text instead 1/U_ was plotted against 'I/vN0 8, as 1s usually done with ordinary fluids The data of the experiment proved to be fairly well correlated by straight lines Inspection of Eq 3 above shows that when the term involving ”No 8 approaches zero or when the Wilson Line 1s extrapolated to the zero ordinate 1t 1s posstble to write for all the intercepts 1222 (4) + 00000788 ] Uoo F From Eq 4 it 1s possible to solve for the fluoride salt film coefficient that s 1222 (5) by = 1 — ~ 00000788 ) oo Since, the fluoride salt film coefficient 1s essentially constant along any of the lines 1t is possible to separate the NaK film coefficient from any of the over all coefficients Substitution in Eq 1 above gives 1 1 b = = (6) N ] 1222 1 — — —— - 00000788 — Uo bF Uo U ] oo APPENDIX 3 PHYSICAL PROPERTIES OF THE FLUORIDE SALT NaoF ZrF, UF, (50-46-4 mole %) AND OF SODIUM POTASSIUM EUTECTIC ALLOY The physical properties of the fluoride salt were taken from the third edition charts of the ANP Physical Properties Group' and are represented as a function of temperature in Fig 10 The charts are revised pertodically as new data become available The NaK properties given 1n Fig 11 were taken from the second edition of the Liquid Metals Handbook 1% 5 N Lyon (ed ) Liquid Metals Handbook NAVEXOS P 733 (Rev ) (June 1952) 19 20 VISCOSITY (Ib/h £ DENSITY {1b/ft%) e 4 DWG 23308 50 mp=960 F AN Cp=031£003(Btu/lb °F) 40 (1022 F-1562 F) HEAT OF FUSION=50 cal/cm3 [ VISCOSITY 30 20 \\‘\ 10 0 / 20 0\\ k CONDUCTIVITY / e 10 210 0 ———] p DENSITY o 200 \ 190 {80 900 1000 1100 1200 1300 1400 1500 1600 TEMPERATURE ( F) Fig 10 Physical Properties of the Fluoride Salt vs Temperature F) THERMAL CONDUCTIVITY {Btu/hr ft HEAT CAPACITY (Btu/1b-°F) DENSITY (1b/ft3) UNCLASSIFIED DWG 23309 14 13 12 0 270 11 {0 09 08 07 0 260 06 05 04 0 250 170 55 0 165 54 0 53 0 160 52 O 51 0 15 5 500 49 0 150 48 0 47 0 14 5 460 450 140 200 300 400 500 600 700 800 900 1000 1400 1200 TEMPERATURE (°F) Fig 11 Physical Properties of NaK (56 wt% Na-44 wt% K) vs Temperature VISCOSITY (lb/hr ft) THERMAL CONDUCTIVITY Btu/hr—it2( F/ft) 21 APPENDIX 4 SAMPLE CALCULATION OF DATA POINT 4 Experimental Data tpy = 1323 7°F tpy = 1309 1°F tyy = 1179 8°F ty, = 1067 9°F wp = 8450 Ib/hr wy = 1160 Ib/hr t,n = 1201 4°F Heat Balance 9p = wpCpltpy = tp)) (8450)(0 31)(14 6) = 38 240 Btu/hr In = wnenltny = tno) = (1160)(0 248)(111 9) = 32 190 Btu/hr (Heat loss less than 1% and therefore neglected) gp —ay 6050 — = 16% 95 38 240 g = 35220 Btu/hr Over all Heat Transfer Coefficient qav U = —— o AoAtLM (tpy —tn1) = {tpy —tn2) 1439 - 241 2 Aty = - 188 6°F LM In—— 2412 F2 N2 35 220 U =——— - 2357 Btu/hr ft2 °F ° =0 0792(188 6) W Wall Temperatures 1201 4 (measured) whN D, Tgy In th = th + 27k L w 0 329 35220 In 02 =12014 + ————— = 1236 6°F 27(34 8)(0 922) 22 Stream Temperatures At, (At2 )04 t =tpy ———m—|1 = {— F(0 4) Fl AtN At 1 1 - AtF 1323 7 1439 [1 - 1229] = 1318 8°F (1-766) - AtN At,— ‘AtF Aty \® 4 EN(o 4) = INy ‘——At"—l “\ % N 1 1 AtF 1179 8 — (4 947 66) = 1142 3°F Film Coefficients b qav F = Az[‘F(o 4) " t, ]l 35 220 , = —————+—— = 6620 Btu/hr ft< °F 0 0647(82 2) b qav N ——————— Alt, N~ tN(o 4)) 35 220 —— = 7520 Btu/hr ft2 °F 00792059 1) v Wilson Line 1 , — = —— = 0 000425 hr ft< °F/Btu U, 2357 wy 1160(144) vy = = =2 15 ft/sec PnAL, (48 2)(0 448)(3600) Lol osa v 08 184 From Fig 5 at = 0 for this line 1s 0 000292 o0 UNO 8 1222 g = ——————————= 5740 Btu/hr ft? °F — 0 0000788 0o 23 1 - = 7500 Btu/hr f12 °F bN 11222 — 00000788 U o F Dimensionless Moduli At tp, = 1278°F cp = 031 Btu/lb °F Ry = 252 Ib/hr ft kp =134 Btu/hr ft °F beD, 662000 269) Nu, = e N7 CF TR T T134(12) 4w 4(8450)(12) Re ., = _ - 19 080 fl'p‘.Fsz (25 2)(0 269) CEiE; 0 31(25 2) ’ / 3 Prp, = T =583 (Prp)° = 1801 1 - 4 Nup(Prp) ° =62 At ¢ = 1319°F F(0 4) cg = 031 Btu/lb °F pp =23 1 Ib/hr ft kp = 134 Btu/hr # °F At t,p = 1237°F 27 5 tb/hr ft = It wF b D FP: 6620(0 269 Nu, = 8600289 ko 134(12) - 4w 4(8450)(12) 20 800 °F TupD. | (23 1)(0269) “FEF 031023 1) Pro = = - 535 F kr 134 24 ] (F’rF)é =175 At 1y ¢ = 1142°F cy = 0248 Btu/Ib °F py = 477 Ib/it? py = 04 Ib/he ft ky = 16 65 Btu/hr ft °F bnDe 7520(0 495) Nuy = = ~ 1845 ky 16 65(12) PNP YN 47 7(0 495)(2 15)(3600) ReN = = = 38 420 EN (12)(0 4) CNEN 0248(0 4 ky 16 65 Rey x Pry =229 25