e o fA_«EB RESEARCH ANIIIFIIIE!EI.IIPMENT REPORT ORNL-1508 @ i 3 yy45L 0349799 O ANP LIMITED DISTRIBUTION ENTRAL RESEARCH LIBRARY DOCUMENT COLLECTION DESIGN CALCULATIONS FOR A MINIATURE HIGH- TEMPERATURE IN-PILE CIRCULATING FUEL LOOP “ea M. T. Robinson and D, F. Weekes \ A1 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 loan. o e o - e N e - e =B B & Tl - s - - ‘5 oo B , - e - s o b W T ey % i i -y ”’ 1-",_ ; ¥ . & OAK RIDGE NATIONAL LABORATORY LY OPERATED BY | 2223 UNION CARBIDE NUCLEAR COMPANY \ :' -‘;? A Division of Union Carbide and Carbon Corporation &% e POST OFFICE BOX P - OAK RIDGE, TENNESSEE h‘ 5 pl'.l‘ e ¥ e : ,."_.g& A R ORNL-1808 This document consists of 31 pages. Copy’ 36 of 209 copies. Series A. Contract No, W-7405-eng-26 SOLID STATE DIVISION DESIGN CALCULATIONS FOR A MINIATURE HIGH- TEMPERATURE IN-PILE CIRCULATING FUEL LOOP M. T. Robinson and D, F. Weekes With An Appendix on Analog Simulation by E. R. Mann, F. P. Green, and R, S, Stone Reactor Controls Department DATE ISSUED SEP 19 1955 OAK RIDGE NATIONAL LABORATORY Operated by UNION CARBIDE NUCLEAR COMPANY A Division of Unioh Carbide and Carbon Corpeoration Pibst Office Box P Oak Ridge, Tennessee ¢ D - 9 s jRARIE STEMS gROY S ya?93 O ORNZBBBNRPREN ST EsIanrpp =3 .fi - CELPOEMVNEMAV-UEPONOCAOOCDPENEIIMOPOMATNOOMEDTONONDO FA T OomeopmMM e ToO D ITMIZEP-—"AMSETOMAMPP-MOUODITITDOLWOOOD-OOX SEGRANEEEBNES DRNO AW = . Center (K-25) . Cohen . Cottrell . Cowen . Crawfor Dismjile . Eml ‘_ Fel gl Y '''''' . Brundage 69. . Callihan 70-71. . Cardwell 72. Cathcart 73 . Chapman 75. . Charpie 76. Cleland 77. . Clewett 78. . Clifford 79. romer ) 84. . Crousalti A 85. . Cullegm 86. Cunnigih 87. OO ~MA M > MErMENIADNAZOCOIMMAEOOENDNCSPOPMAETETD D DN A CER P AONOZVN O P MMP MLKEAIATEIC AT R ORNL-1808 e R . Adamson ‘ . J. Gray . Affel . P. Green . Baldock R. Grimes Barton . 0. Harms . Baumann 52. C. S. Harrill . Berggren 53. E. Hoffman . Betterton, Jr. 54. A. Hollaender Bettis 55. . Holmes . Billington 56. . Householder inder 57. Howe . Blankenship 58. . Jetter . Blewitt 59. . Johnson . Blizard 60. Jones . Bopp 61. . Jordan . Borie 62. . Keilholtz . Boyd 63. Keim Boyle 64. . Kelley . Bredig 65. . Kernohan rooks (consultant) 66. ertesz . Browning 67. . King . Bruce 68. . Klaus Klein Lane Larson LaVerne . Lincoln Lind Livingston . Lyon . MacPherson (consultant) . Maienschein . Manly . Mann . Mann . McDonald . McQuilken . Miller . Miller . Morgan . Morgan . Murphy . Murray (Y-12) . Nessle . Oliver . Parkinson 96. 98. 99. 100. 101. 102. 103. 104, 105. 106. 107. 108. 109. 110. 11 112. 113. 114, 115. 116. 117. 118. . L. Sproull (consiiliant) . E. Stansbury \ . K. Stevens - . S. Stone 2 . |. Strough . J. Sturm . D. Susano . A, Swartout . H. Taylor . B. Trice . R. Van Artsdalen MEM-N=T0VOD0OMAPOITOMMIP>PIETIO M. Reyling 119. F. C. VonderL e F. Poppengiek 120. J. M. Warde ¥ T. Robinsf 121. C. C. Websiflf W. SavagelR 122. M. S. Wechgllfr W. Savolail 123. D. F. Weells C. Schweirfj 124. R. A. W¢g . Seitz {consqilihnt) 125. AL M. Y8 Kberg . D. Shipley 126. J. C. e . Sisman ) 127. G. DZi#hitman . J. Skinner A 128. E. f¥igner (consuitant) . P. Smith ! 129. G.gFWilliams . H. Snell ) 130. WA Willis . Wilson . JFE. Winters W C. Wittels ¥ D. Zerby Central Research Library # Health Physics Library F' Reactor Experimental Engineering Library . Laboratory Records Department . Laboratory Records, ORNL R.C. . ORNL Document Reference Library, Y-12 Branch ExTEAL iFRIBUTION 146. AFDREE) S 147. AFDRUM 148. AFSWA 149. Aircraffilb WADC (WCLS) 150. Argor gtional Laboratory 151. ATIg 152-154. Atqll¥ oy Commission, Washington 155. B - |C 156. GEE!le MBlorial Institute 157. tle ing — 158, Aer — Jer 1594 ief of Na Research 160- 1678 o|. GasserfBCSN) Convair — S CVAC - For . Director of L 3. Directorate o . Douglas . East Hartford 14 164-1 Piego rth ratories (WCL) apons Systems, ARDC g Office 171. Equipment Laljjiltory — WADC (WCLE) 175 GE — ANPD 176. Glenn L. Martin 177. lowa State College 178. Knolls Atomic Power Laboratory 179. 180. 181. 182-183. 184, 185. 186. 187. 188. 189. 190-192. 193-196. 197. 198. 199. 200-201. 202-204. 205. 206. 207. 208. 209. Lockheed ~ Burbank Lockland Area Office , Los Alamos Scientific Laboratory " Materials Lab (WCRTO) Mound Laboratory NACA -~ Cleveland NACA - Washington NDA North American ~ Aerophysics Patent Branch, Washington Power Plant Laboratory — WADC (WCLPU) Pratt & Whitney : Rand RDGN Sutherland SAM Technical Information Service, Oak Ridge Operations Office WADC - Library WAPD -~ Bettis Plant Wright Aero Assistant Secretary — Air Force, R&D Maintenance Engineering Services Division — AMC (MCMTA) Division of Research and Medicine, AEC, ORO CONTENTS Development of Loop Model ... 1 Basis of Heat Transfer Calculations .......ccooiiiiiiiiicieini i 3 Derivation of Heat Transfer EQUations ..o 4 Solution of Heat Transfer Equations ..o, 7 NUMEEICA] DB . oottt et s et e ea e sat s sae s smae b e b e b e e e e e s s b rna e pat e 8 Selection of Best Loop Model .........c.ooviiiiriniciii 8 Results of Design Calculations for the Mark VI Loop ... 10 Miscellaneous Calculations for the Mark Y Loop ... 11 Appendix A. Importance of Reynolds Number in Mass Transfer ..., 16 Appendix B. Analog Simulation in an In-Pile Loop—Liquid-Salt Fuel Study .......ccccoonviviminninn, 16 Appendix C, Time-Constant Modification through Positive Feedback ..o 25 DESIGN CALCULATIONS FOR A MINIATURE HIGH-TEMPERATURE IN-PILE CIRCULATING FUEL LOOP M. T. Robinson and D. F. Weekes DEVELOPMENT OF LOOP MODEL The calculations presented in this report have been carried out as part of the development of a small circulating fuel loop designed for a study of the effects of reactor radiation on the inter- action of fused fluoride fuels with container materials, and particularly with Inconel.! One of the principal purposes in making a small loop is to simplify construction and operation of the equipment to the extent that many loops can be run under a variety of conditions. Another con- sideration is that a small loop can be examined more easily after irradiation. Finally, a suf- ficiently small system can be inserted into any one of several vertical irradiation facilities in either the LITR or the MTR. This will allow high thermal- and fast-neutron fluxes to be used and will simplify experimental work by eliminating the need for elaborate beam-hole plugs. Two important considerations governed the choice of the basic design. Safety of both the reactor and the personnel dictated that no portion of the loop be left uncooled. This is especially important in the region of high thermal-neutron flux, since, in case of fuel stagnation, the temper- ature of the fuel will rise at a very great rate (650°C per second for fuel composition 30 in the MTR is a typical figure). Since the time neces- sary for taking appropriate corrective action is appreciable, a considerable amount of heat should be extracted from the high-flux regions of the loop to avoid melting of the container and release of fuel and fission products into the cooling air or into the reactor itself. It is impractical to use two cooling circuits so that there will be one for emergency use only, since such an emergency circuit cannot be operated sufficiently rapidly. The second consideration was simplicity, both of construction and of design calculation. 1Eor details of the mechanical design, development tests, etc., see reports by J. G. Morgan and W. R. Willis, Solid State Semiann. Prog. Rep. Feb. 28, 1954, ORNL- 1677, p 30; W. R. Willis et al., Solid State Semiann, Prog. Rep. Aug. 30, 1954, ORNL-1762, p 44 ff. As a result of these considerations, the basic design chosen was a coaxial heat exchanger, bent into a close-limbed U-shape. Fuel is pumped through the inner member in a loop closed by the pump, and cooling air is forced through the sur- rounding annulus. Studies have been made of several different ways of arranging the cooling-air circuit relative to the fuel circuit, as illustrated schematically in Fig, 1. Detailed calculations to be presented later show the marked superiority of the type 3 arrangement, when viewed as to the amount and pressure of air required to maintain the desired operating conditions. Studies have been made also of the effects that the diameter of the fuel tube and the length of the loop will have on the thermal behavior of the UNCLASSIFIED SSD-A-1052 ORNL-LR-DWG-3772 Uy Ty INNER LOOP SHOWS DIRECTION OF FUEL FLOW, OUTER LOOP SHOWS DIRECTION OF AIR FLOW Fig. 1. Models, Air Flow Patterns in Miniature Loop TABLE 1, SUMMARY OF LOOP MODELS Inside Diameter of Outside Diameter of Inside Diameter of a ) . Mark No. Fuel Tube Fuel Tube Air Tube Length Cooling-Ar (in.) (inJ) (in.) (cm) Type . IA 0.100 0.200 0.500 100 1 1B 0.150 0.250 0.500 100 1 NA 0.100 0.200 0.500 120 1 1B 0.200 0.300 0.600 120 1 ne 0.100 0.200 0.500 200 1 Iv 0.200 0.300 0.600 200 1 v 0.200 0.300 0.600 d 1 7 0.200 0.300 0.600 200 4 Vil 0.200 0.300 0.600 400 1 Vil 0.200 0.300 0.600 200 3 IX 0.200 0.300 0.600 200 2 %The length given is the value of the quantity S, defined in section on *'Solution of Heat Transfer Equations.’” The length of the U is about one-half this value. bSee Fig. 1. “Mark 11l was inserted to the bottom of the active lattice. d Mark V was unsymmetrical; entering the reactor, the length was 60 cm; leaving, it was 140 cm. system. The air-annulus spacing was not usually SSD-B-1064 ORNL-LR-DWG-3784 . I — — T varied but was kept as small as seemed . - MARK Y1 \ ] .. . T — ] consistent with ready fabrication. Only a little N —— MARK ¥ attention has been paid to positioning of the loop € S ———————— , ¥, ¥, AND : : 5 ——————— ARk TA ANbTg O L AND X relative to the thermal-neutron flux in a reactor, ¢ C—————— MARK 14 AND 1B since one such study showed that little experi- 3 MARK I . L o™ mental advantage accrued from a change in po- x .. . - . 3 3 1 — sition. Table 1 summarizes the dimensions and u /] AR—VERTFCAL MIDPLANE . . . z /Y o TR other pertinent data on the 11 configurations 2 - - - - 5 / | 0P OF AGTIVE examined in this report. The locations of the z / LATTICE . . 2 1 L \ various models with respect to the thermal- z e o z [ neutron flux distribution in position C-48 of the £ o Ll LITR h in Fi O 2¢ 40 60 80 100 120 140 160 180 200 220 =240 are shown In Flg. 2, DISTANCE f{cm) Fig. 2. Location of Miniature Loop Models in Position C-48 of LITR Compared with Thermal- Neutron Flux Distribution. BASIS OF HEAT TRANSFER CALCULATIONS The calculation scheme detailed in the following section is based primarily on the principle of the conservation of energy in a system which is in a steady (time-independent) thermal state., How- ever, a number of simplifying assumptions are required, both to allow derivation of appropriate differential equations and to permit their useful solution. In the derivation of the equations, two important assumptions are made. First, all heat is assumed to be removed into the cooling air. Transfer of heat by radiation from the outer wall of the fuel tube and by conduction to external parts of the system is specifically neglected. A correction could be made for radiative heat transfer, but this does not seem to be worthwhile in view of the approximate nature of the entire calculation. The second important assumption is that all heat flows radially out of the fuel tube; this assumption is at least reasonable, since the thermal resistance radially through the fuel-tube wall is certainly small compared with the axial thermal resistance. Furthermore, the radial temperature gradient is expected to be far greater than the axial one. These two assumptions result in a somewhat exaggerated calculation of the fuel temperature profile and an overestimation of the amount of cooling air required. In the course of solving the heat transfer equations, it is necessary to calculate the heat transfer coefficients which govern the flow of heat between fluid and container wall. For this calcu- lation the customary empirical correlations de- veloped by engineers for heat exchanger design?—4 have been employed. These relations apply only to cases where so-called established flow con- ditions prevail in the fluid. Away from the entrance to the cooling annulus, these conditions prevail in the cooling air, but the velocity distri- bution is changed because of the large rate of heat transfer.® This will result in somewhat greater turbulence in the air stream and, perhaps, in larger 2See, for example, W. H. McAdams, Heat Trans- mission, 2d ed., McGraw-Hill, New York, 1942. 3M. Jakob, Heat Transfer, Wiley, New York, 1949. 4). G. Knudsen ond D. L. Katz, **Fluid Dynamics and Heat Transfer,’’ Engr. Res, Inst. Bull. 37, Univ. of Mich,, Ann Arbor, 1954, Slbid., p 45 ff. The situation in the fuel is more complex, due to the presence of the large volume heat source. It seems likely that this will cause a substantial increase in turbu- lence in the fuel and will probably increase the heat transfer coefficients between the fuel and the tube wall. It has also been assumed that the physical properties of air and of fuel could be regarded as being independent of temperature. A detailed justification of this assumption is presented in connection with the solution of the equations. In any case, it is felt that the importance of this assumption is minor, especially in view of the large uncertainty (+25%) in the fission power generated in the fuel, heat transfer coefficients. To aid in interpreting the results of the calcu- lations which were made at ORNL, certain design criteria were adopted. Conditions which matched as closely as possible the behavior of an actual reactor would have been attractive; however, we thought it more important to design an experiment sufficiently flexible to allow a real analysis of the effects of several variables on the interaction of the fuel and the container. The important state variables are believed to be the flow velocity of the fuel, the intensity of the fission heat source, and the temperature range through which the fuel moves. These variables are not all independent. in particular, for a given fuel flow rate, the fission heat source largely determines the temper- ature range through which the fuel moves. The flow rate of the fuel is specified in terms of its Reynolds number, Ref (see Appendix A), the intensity of the fission heat source in terms of P,, the fission power generated per unit volume of fuel at the maximum thermal-neutron flux (in terms of the notation in the section entitled *‘Deri- vation of Heat Transfer Equations’’ P, = BP P max)s and the temperature range experienced by the fuel in terms of AT, the difference between the maximum and minimum values of the fuel temper- ature., We have attempted to design a loop which would have the values Ref Z 3000 , Py 2 1000 w/cc , AT, 2 100°C , and which meets the requirement that all fission specified conditions can indeed be met in a heat be removed in the loop proper so that no variety of ways, provided an ample supply of additional heating or cooling of the fuel would be cooling air is available. necessary in the pump. It was found that the DERIVATION OF HEAT TRANSFER EQUATIONS An element of a concentric tube heat exchanger external sink. The purpose is to find the steady- is shown in Fig. 3. Fission heat is generated in state temperature distribution in the system. the liquid fuel flowing in the central tube, is trans- ferred through the wall to the air flowing in the The symbols employed in the calculations are annular space r, < r < 74, and is removed to an defined below. Nomenclature Coordinates and Dimensions s = loop axial coordinate (the loop is defined by 0 § s S $) r = loop radial coordinate 7y = inside radius of inner (fuel) tube Ty = outside radius of inner (fuel) tube Ty = inside radius of outer (air) tube Physical Properties = Cpf = specific heat of fuel at constant pressure Cha = specific heat of air at constant pressure - kf = thermal conductivity of fuel k, = thermal conductivity of air kl = thermal conductivity of Inconel, averaged over T, 272 T, By = viscosity of fuel K, = viscosity of air Py = density of fuel p, = density of air Other Variables v, = linear velocity of fuel, averaged over g 2 . . . < < v, = linear velocity of air, averaged over T, =1 214 - 2 W, = fuel current, a7y . 2 _ 2 . W, = air current, 7r(r3 1)V, P, b] = heat transfer coefficient at r = " b, = heat transfer coefficient at r = ro - Tf = fuel temperature, averaged over r ,S_ T Other Variables {continued) T? fuel temperature at s = 0 1A T = air temperature, averaged over ) § r a 3 Tg = air temperature at s = ( T, = temperature of fuel tube at r = 7, T, = temperature of fue! tube at r = ) y = heat removed radially from fuel per unit time and unit of s ¢ = thermal-neutron flux 3 = fission power generated per unit thermal flux and per unit fuel density PO = fission power generated per unit volume of fuel at the maximum thermal-neutron flux Abbreviations =Yy T Y2t Y3 G, = 1/We, = 2/mr k;(Prf) (Ref) Ay = V/Wye,, = 2/m(ry + 79) k4 (Pra) (Rea) By = mrpB/W,c, = 20,Bp;/k; (Prf)(Re) yy = V27r by = Vmk(Nuf) Yo = (nry/r)/ 2k, Ya = V2mrphy = (r3 ~ r9)/mrok , (Nua) a; = (A = a,)/a, a3 = B/ a, = (GL3 + az)/a] Dimensionless Heat Transfer Numbers (Rea) = 2{(r, - 72)PaV o Pa Reynolds number of air (Ref) = 2r, pfvf/p.f Reynolds number of fuel (Pra) = poe,q/k, Prandtl number of air (Prf) = 'ufcpf/kf Prandtl number of fuel (Nua) = 2(ry — 1,) by/k, Nusselt number of air (Nuf) = 2r\h,y/k; Nusselt number of fuel (S¢f) = b1/pfcpf”f Stanton number of fuel In the steady state, in unit time, a mass of fuel taking with it a quantity of heat W, enters the fuel tube of the element at temper- W/Cpf[Tf + (dT /ds) ds] . ature ij bringing with it a quantity of heat W/c T relative to T, = 0. The same mass of The fission heat generated in the element is fuelp leaves at a temperature T, + (dT /ds) ds, ,qupfm-% ds. A quantity of heat y ds flows radially UNCLASSIFIED $50-A-1053 ORNL-LR-DWG-3773 Fig. 3. Element of a Cylindrical Heat Exchanger. out of the fuel tube into the annulus. Conservation of energy then requires de (]) flfffigfipf - waP/_ -y =’0 . A similar argument can be made for the cooling air in the annular element, which receives a quantity of heat y ds in the steady state in unit time, If the air flows in the same direction as the fuel, then aT, (2q) Y = Wiep, =0 . If the direction of air flow is opposite to that of the fuel, then dT a (26) y+Wac =0, ra 4 For the transfer of heat from the fuel to the tube wall at 7y and from the tube wall to air at Tos Newton’s law of cooling may be written in the form (3) y = err]b](Tf—Tl) = 2ar,b,(T, ~T,) . The usual relation governing radial conduction of heat in a cylinder may be written for the temper- ature drop through the wall of the fuel tube as 2mk (T ~ T,) 4 - ) Y In (r2/r|) If the abbreviations given above are introduced into Egs. 1 through 4, the following set of equations results: dT/ (5) o B¢ — oy aT, (6a) —— = a,y (parallel flow of fuel and air) , ds dT, (66) —— = ~a,y (counter flow of fuel and air) , ds (7) Tf - T, =y, (8) T'| - T, = YaY (9) T, - T, = y3y - The set of Eqs. 5 through 9, under appropriate boundary conditions, describes the dependence of the various temperatures on the physical properties of the fuel and of air, on the several state variables, and on the geometry of the system. The solution of these equations is difficult because of the dependence of the various coef- ficients on temperature. On the other hand, the. specific heats of ionic liquids (fused salts) are generally independent of temperature. Therefore it can be assumed that a, is constant, since conservation of mass requires that W, be constant, regardless of changes of temperature or of dimensions of the system. The quantity @, varies only as does the specific heat of air. This variation, about 6% from room temperature to 800°C, may safely be neglected because of other approximations made in the calculations, par- ticularly if Cpa 1S evaluated at the mean air temperature, The lack of sufficient data demands that k/ be taken as constant. Since the variation of p, with temperature is small (about 3% per 100°C), it, too, may be taken as constant. If, in addition, changes of the dimensions of the system with temperature are neglected — an assumption justified by the very small coefficient of expansion of Inconel — the quantities y, and y, may also be assumed to be constant. (An average value for the thermal conductivity of Inconel has already been used; see Nomenclature above,) Also, Y; may be con- sidered to be constant, if b, is evaluated at the mean air temperature. The variation of b, with temperature at constant mass flow is not large, NUMERICAL DATA Heat is transferred by forced convection in a cylindrical exchanger in accordance with empirical relations of the type (Nu) = [[(Pr), (Re)] obtained by dimensional analysis of experimental data, The systems with which we are concerned here are characterized by large ratios of length to diameter, and, as was stated earlier, the physical properties of the fluids are evaluated at suitable mean temperatures and then treated as constants, For the case of laminar flow, use has been made of the formula derived by Seider and Tate:? 2,1 1/3 (15) (Nu) = 1.86 [(Pr) (Re) T} (Re <2100) For fully turbulent flow, the expression proposed by Dittus and Boelter® has been used: (16) (Nu) = 0.023 (Pr)2/5 (Re)4/5 (Re >10,000) . In the intermediate region of incompletely de- veloped turbulence (2100 < Re < 10,000), the suggestions of Sieder and Tate’ have again been followed. The relation they recommend is presented in a graphical form which has been reproduced in various places.? Under the special assumption used here as to invariability of physical properties with temperature, this plot permits determination of (St} (Pr)2/3 for any (Re) and any length-to- diameter ratio. From this, (Nz) has been calcu- lated through the relation (17) (Nu) = (St) (Pr) (Re) . The physical-property data used in the analog calculations were obtained from various sources. The data for the physical properties of air are those derived from McAdams.'® The physical properties of fluoride fuel 44 were obtained from Poppendiek!! of the Laboratory. The thermal conductivity of Inconel is from the data of Haythorne.'2 The data are summarized below. The thermal-neutron flux used is that measured in position C-48 of the LITR.'3 (In earlier calcu- lations, values slightly different from those shown below were used for ¢/, oy and p;. The difference is only significant m the case of/ Cpf J) Air (200°C) B, = 0.00025 g/cm-sec Cpa = 1.05 joules/g-°C k, = 0.0004 w/em:°C Fuel 44 (815°C) He = 0.072 g/cmssec 1.00 ioule/g-OC k; = 0.0225 w/em-°C p; = 3.28 g/cm’ B = 54.0 x 10713 joule-cm?/g Incenel k, = 0,250 w/cm:°C 7E. N. Sieder ond G. E. Tote, Ind, Eng, Chem. 28, 1429 (1936). 8F. W. Dittus and L. M. K. Boelter, Univ. Calif. (Berkeley) Publs, Publs. Eng. 2, p 443 (1930). See, for example, ref. 3, Fig. 26-1, p 549. IOSee, for example, W. H. McAdams, Heat Trans- mission, 2d ed., McGraw-Hill, New York, 1942. My, F, Poppendiek, private communication te D, F,. Weekes. 12 A. Haythorne, Iron Age 162, 89 (1948). M. T, Robinson, Solid State Semiann, Prog. Rep. Feb. 28, 1954, ORNL-1677, p 27. See also Fig. 2 of this report. SELECTION OF Some typical results obtained for the Mark IA configuration are shown in Figs. 4 and 5. While none of the curves shown meet the desired boundary condition (Eq. 13), several conclusions can be drawn. If (Ref) is sufficiently high for some flow turbulence to be assured, AT/ will be very small, say 10°C or less. In order to get BEST LOOP MODEL valves of AT, near 100°C, it is necessary to use very small flow velocities, well within the laminar region. It is clear that insufficient fission heat is available, If the fuel tube is increased in size, a given value of (Ref) will be attained at lower linear velocity, allowing fuel to spend a greater time in the high-neutron-flux region of the loop. This change was made in the Mark 1B and Mark IIB models. In the latter case, the problem now was removal of the fission heat. Apparently, too little heat exchange capacity was available, This was remedied by increasing the length of the loop, forming the Mark IV configuration, A study was next made of the effects of the cooling-air pattern. Four loop models were used, one for each of the patterns shown in Fig., 1. The total quantity of air was held constant, giving lower values of (Rea) for the two cases with a divided cooling annulus. Other things being equal, the divided annulus would be preferred, since the air pressure drop for a given total air flow is much less than for the single-annulus models, Some results of the calculations are shown in Fig. 6. Due to an error in computing f3,, the curves do not correspond to irradiation in position C-48 of the LITR but to a flux of identical shape and doubled magnitude. The Mark VIII model appeared to be most suitable, since, in addition to the lower air pressure drop, it had the highest value of ATf. The final air temperature would A $SD-A-10T CRNL- LR-DWG-3794 860 840 820 ref 2 800 Rea = 10,000 FUEL COMPOSITION No.48 IN C-48 OF THE LITR T;, MIXED-MEAN TEMPERATURE OF FUEL (°Ch o 20 40 80 80 100 5, DISTANCE FROM INLET (ecm) Fig. 4. Effect of Fuel Flow Rate on Fuel Temperature Pattern in Mark 1A Miniature Loop. be lower for this model, also. On this basis, the Mark VIl configuration was adopted for the de- tailed study discussed in the next section, SSD-A-1069 RNL-LR-DWG-37 840 o DWG-3789 ¢80 @ n O . 10,000 @ o O = 20,000 Reg s 30 000 Pey . 40. Oop -~ @ Q Ref = 3000 T¢w MIXED-MEAN TEMPERATURE (°C) ~ o o FUEL COMPOSITION No.44 IN C-48 OF THE LITR 4 7 o0 20 40 60 80 100 5, DISTANCE FROM INLET {cm) Fig. 5. Effect of Air Flow Rate on Fuel Temper- ature Pattern in Mark 1A Miniature Loop. S5 D«A- ORNL-LR-0OWG-3793 500 T T T Rea =10,000 FOR MARK ¥I AND YII 880 F Reo = 20,000 FOR MARKIV AND IX . Ref » 3000 /; /| 860 o~ 7/ o N/ ) 5 s/ 7;, MIXED-MEAN TEMPERATURE OF FUEL {°C) & 760 0 25 50 75 100 125 150 175 200 s, DISTANCE FROM INLET (em) L\ Fig. 6. Effect of Cooling-Air Pattern on Miniature Loop. RESULTS OF DESIGN CALCULATIONS FOR THE MARK VIil LOOP The Mark VIII loop model is shown in Fig. 7. The v #Mulations are discussed in detail in Appendix B, The results are summarized by the plots of 9/ and of y vs s given in Figs. 20 to 27 (see Appendix B). The quantity 9/ may be defined as T, = T,9, The numerical data are given above in "“Number Data’’ and a plot of ¢ vs s is shown in Fig. 17 (see Appendix B). Several qualitative remarks can first be made. The positions of maximum and minimum fuel temperature are quite insensitive to the velocities of the two fluids. This allows placement of control thermocouples to be made with some precision. The value of AT/ decreases with increasing (Ref), but not indefinitely. The principal resistance to flow of heat is at the interface between air and fuel tube. At sufficiently high fuel velocities, further increases have only a small effect on the quantity of heat transferred from the fuel. From the results in Appendix B, those pairs of fluid Reynolds numbers must be selected which correspond to ‘‘realistic’ conditions, namely, 1. initial air temperature, Tg, near room temper- ature, 2. maximum fuel temperature near §15°C. From the data of Figs. 24 to 27, the values of y(O)oremelected, from which 79 — Tg is calculated by Eq. 10. The values of T - Tg are plotted vs (Rea) for several values of (Ref) in Fig. 8. The conditions above allow calculations of the “realistic’’ values of this quantity from (18) (19 - 19 The values of (T/ - To)m" were obtained from the curves of Figs. 20to 23. The resulting set of “realistic’’ conditions is indicated by the dashed line in Fig. 8. It is a simple matter to extend these calcuy- lations to a fuel wattage other than the one used here, as long as the shape of the thermal-neutron flux is not changed. In fact, if the fuel wattage, P o is replaced by a new value, nP,, the curves real — 785 - (T/ - T?)max . 10 of Appendix B still apply, but with the y and 0/ scales simply multiplied by a factor n. Extension to a five-times-greater fission wattage is made in Fig. 8 (this corresponds roughly to the use of fuel composition 44 in position A-38 of the MTR). The results of calculations for three different wattages are shown in Table 2. UNCLASSIFIED SSD-B-988 ORNL-LR-DWG-2252 FUEL OUTLET FUEL INLET §=0 AIR INLET = ~ = AIR INLET — 5:=5 —_ ) 1 1 4 it 1 -, 4 ] ] 43N A 7 ¢ T | 7 / 12 1 1 / 4 [y ¢ FUEL LOOP —4 1 4 [ r 1 / / ’ [ / i f AIR COOLING [/ ] g ANNULUS ¢ i 75 ) \Ks, AIR QUTLET \ Fig. 7. Mark VIl Model of Miniature Loop. SECRET SSD-B-1067 ORNL-LR-DWG-3787 10,000 8000 6000 5000 4000 3000 2000 THESE GURVES FCR 2700 w/ce 1500 LOGI OF REALISTIC Zor, o o 800 ™ 600 500 400 300 200 150 540 w/cc 100 10 152 3 45 7 10° 152 3 45 7 10° Rea Fig. 8. Estimation of Cooling-Air Requirements for Mark VIl Configuration of Miniature In-Pile Loop. TABLE 2, CALCULATED THERMAL BEHAYIOR OF THE MARK Yill MINIATURE LOOP Effect of Yolume Heat Source P e w/cc 540 1,540 2,700 (Ref) 3,000 3,000 3,000 (Rea) 16,500 70,000 167,000 Atr,, °c 49 134 245 Effect of Fuel Flow Rate (Py = 540 w/ce) (Ref) 1,500 3,000 6,000 10,000 (Rea) 19,000 16,500 15,500 15,500 AT,, °c 102 49 25 25 (Po = 2700 w/cc) (Ref) 1,500 3,000 6,000 10,000 (Rea) 368,000 167,000 118,000 118,000 AT, °C 510 245 125 125 MISCELLANEOUS CALCULATIONS FOR THE MARK VIil LOOP A decision to select one or another set of operating conditions for the miniature {oop depends in part on a number of things other than the heat transfer calculations discussed in this report. The necessary additional calculations are summa- rized in this section. Air Pressure Drop, Velocity, Volume, and Temperoture Rise, — The pressure drop in the air-cooling annulus was calculated by the con- ventional expression 2 2 , 2RT ,u-(Rea) P /s (9 p2-pd =t ity L ! 2 2 p 4(r, - r.) (ry —1,) 2 3772 where p, = pressure at air inlet, p, = pressure at air outlet, R = gas constant, S = length of loop, f = friction factor, and the other symbols are defined in ‘‘Derivation of Heat Transfer Equations.’”’ The friction factor was calculated from the relation of Koo:14:13 0.125 (20) f = 000140 + ——— . (Re)0.32 The outlet pressure, p 5 was assumed to be 1 atm. The resuits of the calculation for the Mark VIII loop are shown in Fig. 9. The volume of air required to attain various Reynolds numbers in the Mark Viil loop is shown in Fig. 10. The linear velocity of the air was calculated, assuming the pressyre to be the average of the inlet and outlet values, The results are shown in Fig. 11. The scale of Mach H4E . C. Koo, Thesis, MIT, 1932 (see ref. 2, p 119). lsThe relations proposed by Davis and others specifi- cally for annuli differ somewhat from the one used here. No appreciable error in the calculated Fressure drop results from this source (see ref. 4, p 134 tf). 1 numbers was calculated® by using the velocity of sound in air at 1 atm pressure at 200°C, 1500 ft/sec. it will be noted that the velocity of air is always subsonic in the Mark VIl loop. The rise in temperature of the cooling air may be calculated from Eq. 10. The maximum air tempera- ture is given by 21 T > > (21) zlmax) =Tf—2——a]y-§—. There are two values of this quantity, since the two branches of the cooling-air circuit experience different conditions. The calculated results for Y4 andbook of Chemistry and Physics, Chemical Rubber Publishing Co., Cleveland, Ohio, p 2257, 27th ed. UNCLASSIFIED SSD-A-1058 -LR- 3778 PRESSURE DRCP (psi) 6 8 10° 2 4 Rea 10 2 4 Fig. 9. Cooling-Air Pressure Drop for Mark VIl Configuration of Miniature In-Pile Loop. 12 UNCLASSIFIED SSD-A-¢t059 779 VOLUME (std. ¢fm) o 6 8 10° 2 4 6 810° Reag 4 10 2 4 Fig. 10. Air Volume Required for Mark VIl Miniature Loop. UNCLASSIFIED 550-A-1057 ORNL-LR-DWG-3777 2 T T 1 1 T 1 g 2408 * s - o E 6 z X g 2 - o 4 = > e < P Lol L1 6§ 810 2 4 & 810 Rea Fig. 11. Air Velocity for Mark VIl Configuration of Miniature Loop. the highggienir temperature for each of the cases of Table 2 are shown in Table 3. Fuel Pressure Drop, Velocity, and Volume, — The pressure drop in the fuel tube was calculated from the expression #fz(Ref)z L.s Ap = ——oeo—— @) 41""1'l P/ where L is the effective length of the loop; the other symbols have been defined before. The effective length was calculated by adding to the actual length (205 e¢m) an amount, 1507, to account for the bend at the tip of the loop. The friction factor was taken from McAdams.!? The results are shown in Fig. 12. The volume flow rate of fuel is shown in Fig. 13. The linear velocity is shown in Fig. 14. Thermal-Neutron Flux Depression. — The de- pression of the thermal-neutron flux has been 7w. H. McAdams, Heat Transmission, p 118, 2d ed., McGraw-Hill, New York, 1942. 18y . Lewis, A Semi-Empirical Method of Esti- mating Flux Depression, MTRL.-54-27, March 11, 1954. TABLE 3. CALCULATED MAXIMUM AIR TEMPERATURE IN MARK VIII LOOP Po = 540 w/cc Maximum Air Temperature (Ref) {Rea) Q) 1,500 19,000 450 3,000 16,500 500 6,000 15,500 540 10,000 15,500 550 Py = 2700 w/cc 1,500 368,000 30 3,000 167,000 200 6,000 118,000 290 10,000 118,000 300 {Ref) = 3000 Maximum Air Temperature PO (w/cc) (Rea) €C) 540 16,500 500 1,540 70,000 360 2,700 167,000 200 F estimated by using the trectment of Lewis,'® This is based on a correlation of some experi- mental data obtained by various workers at the MTR. A ‘“‘grayness’’ factor of 0.73 was found which is due to fuel alone. The Inconel walls of the fuel tube and of the cooling annulus contribute UNCLASSIFIED 550-B-1056 8-10 ORNL-LR-DWG-3776 100 LOOP + CONNECTING TUBES LOCP PROPER 10 aAp, (psi) 0.1 Refl Fig. 12. Fuel Pressure Drop in Mark VIl Loop. UNCLASSIFIED S50-B-108% ORNL-LR-DWG-3775 100 ¥, VOLUMETRIC FLOW (cc/sec) 10° 10° wt ref Fig. 13. Volumetric Flow of Fuel in Mark VIl Loop. 13 SSD-B-1068 UNCLASSIFIED DRNL-LR-DWG-3788 SS5D-8-1054 250 ORNL -LR-DWG-3774 100 | | . — 1 160 200 — 140 = 120 ¢ & w . : 5 100 3 E o 80 & S 2 PRESENT PUMP S o 3 - > O o > > — 60 ™ é 3 _ | © 100— -~ a0 PROPQOSED 30-cc PUMP — — 20 ANP LOOP 10-cc PUMP — / 0 1 50— / : VOLUME OF CONNECTING TUBES 10° 10 10° reaf VOLUME OF LOOP Fig. 14. Linear Velocity of Fuel in Mark VIII o | Loop. 0 5 10 15 DILUTION FACTOR another factor of 0.95. The over-ali grayness ig. 15. Dilution Factor in Mark Vill Loop. factor is estimated to be about 0.67; that is, Fig. 15. Dilution Factor in Mar oop two-thirds of the thermal flux is available to the Volume of loop proper, em3 41.6 sample, Volume of connecting tubes, cm3 14.4 ‘Dilution Factor,”” — A quantity known as the *!dilution factor’’ is of some interest in studying Volume of pump, cm® 76.2 in-pile corrosion. This quontity is defined as the Total 132.2 ratio of the maximum value of the fission power p generated in unit volume of fuel to the average 0 P 0.08 value, In a loop of the type being considered, s ’ this definition may be stated as J‘ y ds Po(nrfS + Vp) 0 (23) dilution factor = — Dilution factor 10.6 f y ds The effect of changing the pump volume is 0 indicated in Fig. 15, where V is the volume of the pump and of any Total Power, — The total fission power generated connecting tubes. The present situation in regard in the loop is calculated from Eq. 12, The results to the dilution factor is indicated as follows: are shown in Fig. 16. 14 TOTAL POWER (kw) 50 45 40 35 O o N o n o 15 $SD-B-1065 ORNL-LR-DWG-3785 /) / 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 PO' MAXIMUM SPECIFIC POWER GENERATION (kw/cc) Fig. 16. Total Power of Mark YiIl Loop. 15 v Appendix A IMPORTANCE OF REYNOLDS NUMBER IN MASS TRANSFER The frequent argument on the relative importance of linear velocity and Reynolds number in mass transfer between the container and fuel would seem to be settled by appeal to chemical engineering experience.'? It is found that excellent results are obtained in correlating mass transfer coef- ficients for fluids flowing in pipes by means of relations of the type 2r .k’ (24) = f(Scf), (Ref)] , / where &£’ is the mass transfer coefficient, D/ is the diffusion coefficient of the transferred species in the fuel phase, and (Scf) is the Schmidt number for the fuel: quee, for example, G. G. Brown, et al.,, Unit Oper- ations, p 517 #, Wiley, New York, 1950. ke (25) (Scf) = ——, PRy The similarity of Eq. 24 to the analogous heat transfer equation is evident, the Schmidt number replacing the Prandtl number, and the nameless group on the left side replacing the Nusselt number., Even more striking is the fact that for many cases the Dittus-Boelter equation (16) applies to mass transfer with the same coefficients and exponents as those used in heat transfer. It is quite clear, therefore, that the Reynolds number is fully as significant in mass transfer as in heat transfer, and is definitely the relevant fuel-flow variable. Furthermore, an additional statement of the surface-to-volume ratio is unnecessary, since this information is also given in the Reynolds number. Appendix B ANALOG SIMULATION IN AN IN-PILE LOOP-LIQUID.SALTS FUEL STUDY E. R. Mann F. P. Green R. S. Stone Reactor Controls Department, Instrumentation and Controis Division An analog simulation of an in-pile loop experi- ment for ART fluoride fuel was performed by means of a portion of the Reactor Controls Com- puter to determine the optimum fuel and coolant flow rates and the temperature variation of the fuel as it traverses the loop for each of 16 flow combinations. Constant coefficients for the de- scriptive equations and a linear plot of the forcing function, flux, Fig. 17, were provided by D. F. Weekes. This simulation has provided a series of 16 curves of fuel temperature vs instantaneous position of the fuel within the 205-cm ‘‘active’’ portion of the loop and 16 corresponding curves displaying the radial heat transfer vs fuel position. The specifications given state that the proposed fuel loop will conform to the following equations (the quantities 6, and 6, may be defined as Tf - T9 and T - Tg, respectively; all other symbols are defined in the nomenclature list in 16 “‘Derivation of Heat Transfer Equations'’): 40, (26) -—;::B‘gb-—azy , 0 0 RECORDER M -50v BIAS Fig. 19. 18 Block Diagram for In-Pile Loop Simulation. calibrated time constants over wide ranges has not been previously reported, although it has been conventional for some time with the ORNL simu- lator. The method is described in Appendix C. The values of 2, and a, are such that G, varies between 0 and 1, and G, varies between 1 and 2. The quantity a is set to 7.52, and may vary between 0 and 1 (fraction of full-scale). The addition of potentiometer P makes it possible to vary the effective value of R, from 750,000 ohms to infinity with a 25,000-ohm potentiometer. Each of the resistances R, and R have four different values and are put into the circuit in the form of lumped constants, chosen by a four- position switch. Pertinent values, both given and calculated, are presented in Table 4. The quantity 20.,/a,0, is a correction coefficient needed in connection with boundary conditions. The simulation of y required the breaking up of each run into two equal parts. An exponentially decaying function describes y in the first half, the time constant in each case set by potenti- ometer A, in amplifier No. 3, whose gain is less than 1. An exponentially increasing function describes y in the second half, the time constant in each case set by potentiometer (1 + A.) in amplifier No. 4, whose gain is greater than 1 and less than 2. Because of a small discontinuity in y at the mid-point, the simulation must be stopped and a new initial condition for y set on potenti- ometer Y. This control is necessitated by the boundary conditions imposed, which are: 1. coolant to enter at each end at the same temperature (Gao = 0,505) and leave at the center, 2. fuel to enter at one end and leave at the other, with no net change in temperature (Ofo = 0[205). Since there are two distinct and separate coolant streams, entering at either end and merging to exit at the mid-point of the loop, there is a discon- tinvity in 6_ (and hence in y, since 0, is a continuous function) at s = 102.5 em. This requires a correction at mid-point, which may be calculated as follows. Let Y102.5 Ad ¥1g,.5 be the values of y just before and just after the discontinuity, respectively. From the differential equations, it can be shown by integration that az + aa 0 Yio2.s = Yo 2, 1102 a .8, 102.5 - [ b ds , aa, 0 ) CL2 - aa 0 Yio2.5 = Yo a,a /102.5 2 a 33‘ 205 - ¢pds . &1%9 Yy02.5 Since the flux distribution is symmetrical about s = 102.5 cm, it follows that 2a3 0 (39) ¥io2.s = Y1025 ~ 55 %025 - 1%2 The volt-box input to the 6, generator was used only at the initiation of the second half of the run in order to start the fuel temperature at the tinal value which is attained during the first half. Amplifier No. 5 was used for isolation, and ampli- fiers numbered 6 and 7 were used to invert the y and 8, signals and to transpose these outputs to the center of the recorder scales. At the start of a run, switches 2 and 3 were closed. This set 6 =0 and allowed y, to be set at some tentative value by means of potenti- ometer Y. Switches 2 and 3 were then opened and the run started. At mid-point the calculation was stopped, and switches 3 and 4 were closed. Potentiometers T and Y were then used to set 6/102.5 = 0/102,5+ and Yi02.5 = Y102.5 aa, /102.5 °* 19 0¢ TABLE 4. NUMERICAL DATA USED IN ANALOG SIMULATION OF IN-PILE LOOP G G a 2a 1 2 R R 3 Case Ref Rea a a a B a a a 4 5 - 3 2 1 1 1 2 3 3 5 (1= 75a;) (1 +75a,) (7.5a)) (10’8, (0°)/a, a,a, 1 1,500 10,000 0.0109 0.0379 0.0080 2.4 0.221 0.190 1.660 0.278 0.860 2 20,000 0.0092 0.0589 0.0060 0.85 144 | o 1yay 0.110 0.310 1.450 0.442 118K 4.35M 0.665 3 30,000 0.0089 0.0744 0.0049 11.4 0.079 0.332 1.368 0.558 0.603 4 60,000 0.0075 0.1060 0.00175 8.0 0.037 0.438 1.131 0.795 0.402 5 3,000 10,000 0.0114 0.0208 0.0102 20.4 0.221 0.145 1.765 0.156 1.86 6 20,000 0.0098 0.0342 0.0079 12.4 0.110 0.265 1.592 0.256 1.53 0.42 0.011 . 7 30,000 0.0097 0.0451 0.0071 9.4 116 0.079 0.272 1.532 0.338 238K 8.61M 1.45 8 60,000 0.0082 0.0707 0.0042 6.0 0.037 0.385 1.315 0.530 1.06 9 6,000 10,000 0.0127 0.0108 0.0110 19.6 0.221 0.048 1.825 0.081 3.88 . . . . . . . . .28 10 20,000 0.0100 0.0183 0.0090 0.212 11.6 0.0053 0.110 0.250 1.675 0.137 471K - 17.2M 3 11 30,000 0.0099 0.0246 0.0085 8.6 0.079 0.258 1.638 0.184 3.16 12 60,000 0.0083 0.0408 0.0060 5.2 0.037 0.378 1.450 0.306 2.47 13 10,000 10,000 0.0115 0.0065 0.0112 19.4 0.221 0.138 1.840 0.049 6.50 14 20,000 0.0099 0.0111 0.0094 0.127 114 0.0035 0.110 0.258 1.705 0.083 186K 285M 5:50 15 30,000 0.0098 0.0151 0.0091 8.4 0.079 0.265 1.682 0.113 5.45 16 60,000 0.0080 0.0258 0.0068 5.0 0.037 0.400 1.510 0.194 4.11 Once this adjustment was made, switches 3 and 4 were ned, switch 1 was thrown from ¢, to Lo and the second half of the calculation was run. This procedure was continued for successive runs until a value of y, was found such that 0]205 = 0]0 and Y205 = Yo The results of this procedure are illustrated in the offf®d curves (Figs. 20—-27) and in Table 5, which lists the initial heat transfer and the maximum temperature excursion for each case, along with an estimated statement of accuracy for these two parameters. TABLE 5. RESULTS OF THE ANALOG CALCULATIONS R R Yo A9, Curve Number* ef ea (w/em # 3&) ©c + 1) urve Number 1,500 10,000 54.5 101.7 1 20,000 49.0 99.5 2 30,000 47.0 98.4 3 60,000 43.0 91.5 4 3,000 10,000 55.0 51.5 5 20,000 52.0 48.3 6 30,000 50.8 48.3 7 60,000 47.0 46.7 8 6,000 10,000 57.0 255 9 20,000 53.0 25.5 10 30,000 52.5 25.1 11 60,000 49.0 24.3 12 10,000 10,000 58.0 26.0 13 20,000 53.5 24.9 14 30,000 54.0 23.9 15 60,000 51.0 23.8 16 *See Figs. 20-27, 21 SSD-B-!E?Z SSD-B-1363 ORNL-LR-DWG-3783 ORNL-LR- DWG -3792 55 : N CURVE Ref / No. 45—+ 1 1,500 5 3000 0T 9 6000 3 10,000 . / (1IN o -] /N o 10 N @ (&