MAFRT iy MARMET A ENERGY ?l"sL M-'lfl'f'u RO i 3 4456 D3yg5p; g 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. ORNL-1535 This document consists of 136 pages. Copy ;‘57 of 208 copies. Series A. Contract No. W-7405-eng-26 THERMODYNAMIC AND HEAT TRANSFER ANALYSIS OF THE ATIRCRAFT REACTOR EXPERIMENT Bernard lubarsky NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS B. L. Greenstreet AIRCRAFT NUCLEAR PROPULSION DIVISION OAK RIDGE NATIONAL LABORATORY DATE ISSUED AUG 10 1953 OAK RIDGE NATIONAL LABORATORY Operated by CARBIDE AND CARBON CHEMICALS COMPANY A Division of Union Carbide and Carbon Corporation Post 0Office Box P 0ak Ridge, Tennessee MARTIN MARIETTA ENERGY SYSTEMS LIBRARIES T B0 3 445k 0349507 3 - -3 O W N~ 9-14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24, 51-53. 54. 55. 56. 57-68. 69. 70-77. 78. 79. 80-84. 85. 86. 87-88. 89-94, 95. 96. 97. ?QEDJO_—‘ECUJ>.F‘EQDEODJ:UFJFJDJ ORNL 1535 Special INTERNAL DISTRIBUTION G. Affel 25. H. F. Poppendiek S. Bettis 26. P. M. Reyling P. Blizard 27. H. W. Savage C. Briant 28. E. D. Shipley B. Briggs 29. J. A. Swartout E. Center 30. H. L. Watts B. Cottrell 31. A. M. Weinberg D. Cowen 32. G. D. Whitman A. Cristy 33. G, C. Williams K. Ergen 34. C. E. Winters B. Emlet (Y-12) 35. E. Wischhusen P. Fraas 36-40. ANP Library L. Greenstreet 41-45. Central Files R. Grimes 46. Central Files, ORNL R.C. E. Larson 47. Metallurgy Library N. Lyon 48. Reactor Experimental D. Manly Engineering Library L. Meem 49-50. Central Research Library J. Miller EXTERNAL DISTRIBUTION Air Force Engineering Office, Oak Ridge Air Force Plant Representative, Burbank Air Force Plant Representative, Seattle ANP Project Office, Fort Worth Argonne National Laboratory (1 copy to Kermit Anderson) Armed Forces Special Weapons Project (Sandia) Atomic Energy Commission, Washington Battelle Memorial Institute Bechtel Corporation Brookhaven National Laboratory Bureau of Aeronautics (Grant) Bureau of Ships California Research and Development Company Carbide and Carbon Chemicals Company (Y-12 Plant) Chicago Patent Group Chief of Naval Research Commonweal th Edison Company FOREWORD The Aircraft Reactor Experiment utilizes the circulating fluoride-fuel as the primary reactor coolant. It is necessary, however, to employ an additional coolant whose primary function is to cool the reflector and pressure shell. Although liquid sodium will be used as the reflector coolant, the use of NakK had been assumed during the preceding year. Consequently, aconsiderable amount of consistent, detailed data on the performance characteristics for the reactor system using NaK as the reflector coolant has been assembled. These data are presented in this report. A sufficient number of calculations based upon the use of sodium has been made to assure that the performance with sodium will not deviate significantly from that calculated for NaK. Sodium 1s being used 1n preference to NaK because it can be more easily sealed at the pump shaft. CONTENTS INTRODUCTION . REACTOR Pressure Pulse Resultlng from a Sudden Change 1in React1v1ty Core Power Distribution . .. Temperature Profile 1in a Typlcal Sectlon of the Core Lattlce . Flow of Reflector Coolant Through Core Heat Removal by the Beflector Coolant. . Pressure Drop in Fuel Manifolds and Core Tubes . Temperature Gradients in Thermal Sleeves . Formation of Nonplugging Solids 1n Fuel Tube 1in the Event of a Small Leak FUEL HEAT DISPOSAL SYSTEM .. Performance of Fuel Heat Disposal System . . Temperature in Fuel System Because of Afterheat 1in the Event of Complete Pump Failure . REFLECTOR COOLANT HEAT DISPOSAL SYSTEM . ROD AND INSTRUMENT COOLING SYSTEM. Cooling of the Control Rods and Instruments Cooling of the Safety Rods Cooling of the Regulating Rod Cooling of Fission Chambers Helium Pressure Drops Division of Flow of Helium . . . .o .o Performance of Rod and Instrument Coollng System Heat Exchanger MONITORING AND PREHEAT SYSTEM Heat Loss Through Insulation . Reactor Preheating . . . Helium Leakage Through Clearance Holes 1n the Reactor Thermal Shield Space Cooler Performance .. . . Temperature Patterns 1n the Monltorlng Annulus in the Event of Heat Failure HELIUM SUPPLY AND VENTING SYSTEM . True Holdup of Fission Gases 1n Tanks e e e Temperatures in the Helium Vent Lines Containing Fission Gases Vacuum Pump Performance PAGE 11 13 17 19 33 38 41 43 43 49 54 64 64 65 66 68 73 76 76 79 79 81 87 90 92 103 103 107 111 Vi1l DUMP AND FILL SYSTEM . Fuel Dump Tank Cooling . Heating of Fill Tank with Centrally Located D1p Tube OTHER INVESTIGATIONS . Afterheat in Fission Products .o . Temperature Difference Between Thermocouple on plpe Wall and Bulk Fluid . REFERENCES . viil 117 117 119 122 122 123 127 Chapter 1 INTRODUCTION The Aircraft Reactor Experiment (ARE) is an experimental, high-tempera- ture, circulating-fuel reactor being constructed by the Aircraft Nuclear Propulsion Division of the Oak Ridge National Laboratory. The fuel is a mixture of fused fluorides, including uranium tetrafluoride; the moderator 1s beryllium oxide; and the structural material 1s Inconel. Figure 1 shows a schematic diagram of the reactor, the heat disposal equipment, and the other process equipment necessary to the operation of the reactor; also shown in Fig. 1 are the design-point pressures, temperatures, and flows at various polnts 1in the system. This report contalns a summary of the more pertinent analytical investigations of thermodynamic and heat transfer properties of the ARE. Considerably more investigations have been carried out than have been presented; the investigations omitted fall in one of the following categories: 1. investigations relating to systems and items of equipment not actually used 1n the ARE, 2. 1nvestigations relating to systems and 1tems of equipment used in the ARE but with different fluids than those actually used, 3. 1investigations in which estimated fuel properties were used that were found to be incorrect when additional experimental determi- nations of fuel properties were made, 4. routine calculations of tempera- tures and pressures at various points of the system that were of interest only to the detail designer. For convenience, the investigations are presented as they relate to the following subdivisions of the ARE: Reactor Fuel heat disposal system Reflector coolant heat disposal system Control rod cooling system Preheating and monitoring system Helium supply and vent system Fi1ll and dump system the are The physical properties of materials used in the reactor given i1n Table 1. TABLE 1. PROPERTIES OF MATERIALS MATERTAL THERMAL CONDUCTIVITY VISCOSITY SPECIFIC HEAT DENSITY REFERENCE® [Bew/bhr*£e? (°F/fe)) (1b/hr*ft) (Beu/1b*°F) (1b/£e>) 1. Air 0.0156 at 90.3°g 4.54.x10'§ at 90, 3°F 0.2399 at 90.3°F 0.0722 at 90.3°F 1 0.0180 at 190.3°F 5.15x 10 at 190.3°F 0.2409 at 190.3°F 0.0611 at 190.3°F 2. Aluminum 116 at 64°F 0.2220 at 32°F 168.5 at 68°F 2 119 at 212°F 0.2297 at 212°F 3. Beryllium oxide 0.84 at 1100°F 0.46 at 1100°F 142 3; 68°F (Porosity 3 0.73 at 1300°F 0.48 at 1300.F o 0.68 at 1500°F 0.50 at 1500°F 1770;t 68°F (Porosity 4. Copper 222 at 64°F 0.1008 at 30°F 555.0 at 68°F 2 220 at 212°F 0.1014 at 212°F 5. Fused fluorides 1.5 30.3 at 1150°F 0.26 187 21.8 at 1325°F 16.5 at 1500°F 6. Helium 0.0885 at 100°F 0.050 at 100°F 1.24 0.0098 at IOOZF 4 and 2 0.1250 at 550°F 0.075 at 550°F 0.0054 at 550°F 0.1650 at 1200°F 0.101 at 1200°F 0.0033 at 1200°F 7. Inconel 12.4 at 1200°F 0.109 at 77 to 212°F 530 5 13.1 at 1472°F 8. Insulation {(cf., chap. 6) 9. NaK 14,10 at 212°F 0.496 at 752°F 0.210 at 752°F 48.4 at 752°F 6 15.38 at 752°F 0.353 at 1292°F 0.209 at 1112°F 46.1 at 1022°F 0.213 at 1472°F 43.9 at 1292°F 10. Stainless steel 10.4 at 300°g 0.1178 at 212§F 489 at 32°F 7 and 8 15.7 at 1500°F 0.1519 at 752°F 11. Steel 26 at 212°F 0.1178 at 212°F 489 at 32°F 8 21 at 1112°F 0.1519 at 752°F 12. Water 0.343 at 32°F 2.43 at 68°F 0.99947 at 68°F 62.36 at 68°F 9 0.363 at 100 °F 1.59 at 104°F 0.99869 at 104 °F 62.35 at 104°F 0.393 at 200°F 1.13 at 140°F 1.00007 at 140°F 62.26 at 140°F *The references are given at the end of this report, TG VALVE BACKUP SYSTEM : TO STACK ¥ 2-in. GATE VALVE § 2rin GATE EX(STING EQUIPMENT SHOWN DOTTED [o Cha SURGE TANK 3 ————— 1 - \ | ! \ 4-in. PIPE === RESERVOIR ———— e R : | r‘*\' e - T \ —: h‘\ | | o= - o ~ 55-90! DRUM A S L 6-in. GATE VALVE 4 Lo | w2 ; [ —) T e % Ga-ing P, | g1z lp2 lelg i ______ HOATE ~F Wy w wi ! » Ya-in, PIPE i_ A _ianvst | : g’ % 21z 2is i & —_— - — W =3 o gl | TEST M35 PP T o iz ol S e ‘%I Y L _ i . i wia w |G w & z PRESSURE h T | 3o 3w g~ g e a Y] i SWITCH | | VALVES TO POND <. & | ol o 5 ' [ 3-in.PIPE_| ] "8 » s v S S 5 | PITS e g < - e x | r g ~N " £ L - “| (0 55-gal DRUM QUTSIDE OF BUILOING NoKk v T SUMP L CATCH BASIN AMBIENT I ) vT (3E6E) Y o =S = ] Ecouomzen TO LEAK OETECTOR SYSTEM - (T o NoK SURGE TANKS AND SUPPLY FOR [PXT] N & - l// ) (=} — | 4~ USED DURING PRETEST PERIOD - SUPPLY HEADRER (FUEL) SUPPLY HEADER Hilll source o E o TO FUEL ENRICHMENT SYSTEM z : 5 B Qa £ L e 1480 TO ORAIN f 33 F TO ORAIN FREEZE VALVE 5 FILL = _ FILL LINE XD I = LINE =z z = FILL E}—‘ - - [ LINE - w 3 2 Ha d? . - VAPCR TRAP : th A TANK NO.3 TANK ND.2 TANK NO, 4 TANK NO.4 TANK NO.5 TANK NO. 6 ‘\ Nak FUEL CARRIER FUEL CARRIER Na No No He {e2] 5 . & “ BULKHEADP‘ . $ g I ] i > | - _!! o \JQ r — T @ FROM OUMP-TANK PIT I MAKEUP HEADER — e 1 L -t H T H T ~{) R FILL AND 2000 FILL AND " DUMP LINE DUMP LINE NOTES: TO : Q FLOW IN gpm —(F— FuEc NGRMAL OFERATING POSITION FLOW CONDITIONS ARE BASED ON THE ASSUMPTION o FROM He SUPFLY TRAILER OF VALVES THAT THE COOLANT HAS THE FOLLOWING PROPERTIES: He SCRUBBER - RESERVE MANIFOLD | PRESSURE IN psig ——Na}—— SODIUM p =187 brtt3 ———1=<3+—QPEN .~ o, —{ne)— HELIM #% 7 TO 43 cp 4T OPERATING CONDITIONS 12 He BOTTLES /N TEMPERATURE IN °F —(w WATER Cp= 0.26 Btu/ib-°F . —er——pt— CLOSED PRESSURE IN INCHES OF WATER, GAGE —@\r— AUXILIARY COOLANT VOLUME OF MAIN SYSTEM {APPROX.): Yt Low . VT VAPOR TRAP — < THROTTLING INTERNAL - 1513 \( } IN cfm EXTERNAL 6.0 12 TOTAL: 7.5t "y s g. 1. Reactor and Heat Disposal Equipment. Chapter 2 REACTOR PRESSURE PULSE RESULTING FROM A SUDDEN CHANGE IN REACTIVITY The self-controlling features of the ARE are due to the expansion of the fuel with increasing temperature. A transient increase in reactivity produces an attendant increase 1in temperature that increases the volume of the fuel. Since the reactor has a relatively fixed volume, some of the fuel i1s forced out of the core and the reactivity is reduced. The entire process occurs 1n a very short time, and therefore 1t 1s necessary to know what pressures will be set up in the fuel tubes when the fuel 1is rapidly forced out of the core. Figure 2 shows the reactor and connecting piping to the surge tanks. The fuel can expand out of the reactor 1n either direction, but since the path to the surge tank in one direction (upstream) is considerably shorter than in the other, i1t will be assumed that all the excess fuel takes the shorter path to the surge tank (this is a con- servative simplification). Further assumptions that have been made are: 1. The fuel 1s incompressible. 2. The pressure pulse 1is of suffi- ciently short duration that the fuel in the external piping remains es- sentially fixed in temperature. 3. The Ltemperature and power variations 1n the reactor core will be neglected; all the reactor fuel 1s assumed to be at the mean reactor temperature, and the power generation in the fuel 1s always equal to the mean power generation. 4. The effects of the pressure pulse on the fuel pumps will be neg- lected. Precisely what effect this pulse would have on the pumps 1s unknown, but the pulse will probably be of sufficiently short duration that no permanent damage will be done. Figure 3¢ 1is a schematic diagram of the system to be analyzed. There are two, distinct cases to consider: the reactor in which the temperature and the density of the fuel change with time and the external piping 1in which the temperature and density of the fuel are constant., The reactor will be considered first (Fig. 3b). The impulse-momentum equation for any section 1s (1) - F dt = d(mv) where F = differential force on fuel volume, 1b, t * time, sec, m = mass in fuel volume, slugs, v = velocityof fuel volume, ft/sec. For a fuel volume of cross section 4, thickness dx, and position x, (2) m = pA Ax where © = mass density, slugs/fta, A = tube cross-sectional area, ft?, x = distance along the tube measured from the reactor outlet, ft, Since the fuel is incompressible, all the incremental fuel volume being generated between zero and x by in- creasing temperature must pass acCcross x (on the way to the reactor inlet and thence to the surge tank) as rapidly as the i1ncremental volume 1s being generated. The rate at which incre- mental volume is being generated between zero and x 1is (3) 4V BA 40 dt 7 de where V = volume from x = 0 to any arbi- trary x, ft3, coefficient of volumetric ex- ™ E pansion, per 'F, 8 = fuel temperature, °F, Since the rate at which the incremental volume is being generated must be equal to the rate at which the volume 1s crossing x, (4) vA = [BA df VR TR df v o= v - v, = Bx— o = B P where v is the incremental velocity (v - v,) 1n ft/sec and the subscript 0 refers to conditions at time zero. The impulse-momentum equation, Eq. 1, may be rewritten for the volume A Dx as dv dm (5) AF = m— + oy — dt dt Differentiating Egqs. 2 and 4 gives d d (6) ‘—m = A Ax P dt dt and dv dv d?5 (7) — T — = dt dt P dt? '’ and substituting Egs. 2, 4, 6, and 7 in Eq. 5 gives d26 (8) -=AF = pA Ax [(Bx dt? d d + A Ay —§ or AF d%6 dp do dp —— = A /61' o — + — + ‘Uo — . Ox dt? dt dt dt Dividing both sides by A and letting Ax approach zero gives (9) -— — = - — = Bx(p — 1 dF dP d?g A dx dx dit? de d +-—E ? + v ap dt dt 0 dt ' The may be expressed 1in terms of the temperature: where P is pressure in lb/ft?, mass density, P, Fo 1+ 56 - 5,) Differentiating Eq. 10 gives (10) o = do P48 17 d (11) ;fi . - t [1+8(8 - 8,)) Substituting Egs. 10 and 11 in Eq. 9 - gives 4?0 - d o dt? 0 t (12) - — = BaL——— dx 1+ 80 - 6,) dg\? pofi (;;) (1 + 88 - 6,))2 d voPol T [1 + B8(8 - 6,)]2 Integrating Eq, 12 from x = 0 to x = L and rearranging slightly gives fipoL2 d?o - P, = 2(1 -89, +80) | 42 do\? ve dB 85) 7 dt L dt (13) P, 1 - 5o, + B0 where the subscript m refers to condi- tions at x = 0 and the subscript L refers toconditions at x = L. Equation 13 with L set equal to the length of the reactor tubes gives the variations with time of the pressure differential across the reactor core, For the external piping (Fig. 3c), where the temperature of the fuel is assumed constant, Eqs. 1, 2, and 5 are valid. However, Eq. 3 1is not valid, because no incremental volume is gener- ated 1n the external piping. The - external piping, however, must pass all the incremental volume generated 25 ft—0in. UNCLASSIFIED DWG, E-A-3-1-51A MM TEST PIT FLOOR ELEV. 831 fr—0Qin. BLOCK ELEV. 832 ft—0in. —— 5ft—Gin.———= THERMAL SHIELD 7 ~ ELEV. 72 //l,//l/ 839 fr—9% in 6ft—6%in. [ Gy ELEV. 832ft—73% in..__ T < -~ { { I 7 S \_\\\\\\\\\\\\\\\\\\\\\\\\\\‘\} JELEV 840 ft—3 in. s ELEV. 834 ft—7:n. (ELEV. 834 ft—4in. / / / NaK DRAIN LINE SHIELDING PLUG T ELEv.8a2ft-gin DUMP TANK ROOM FLOOR ELEV. 828 ft-0in. 7 45¢ K N i I 7 2 e S R IRl ;fl < / TANK 1 [ | /\ XELEV, 831 ft—10¥g in. \_/' A e [ T T e ‘ Z At rEEs I T T L 0 =y [ e ey —ELEV. B34 ft—a s in. L ii\\\\\\\im! I“I : R T O, N N 1 —_— ™ R R OlOOOOOGOGOSTSESSSSESEEEE E E S N < AN S ELEV. B33 ft— T, N @\\\\\\\\\\\\\\\\\\\\\\\\\\\N\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ . A M) TR A ALt Rl TR f I, % ARSI R ELEV. 842 ft—0in. A R D i el e i R i o L 0 PR RO PAT AN FT P SEH PRI 7000 Ak BLOCKS FUEL DRAIN LINE SHIELDING PLUG RESERVED FOR g B8 = NN L\ \ N [ !'|'|‘ @mw,mm,n‘111[““" || W ELEV. 832ft—3in \ii\\ I' N T e P T T T IO — \ (] FUEL ENRICHMENT STORAGE TANK & LOOP NO.{ ELEV. 835ft—0Qin. HEAT EXCHANGER PI1T FLOOR ELEV. 831ft—0in. NaK PURIFICATION SYSTEM ELEV 840 ft—0in. — LOOP NO. 2 ELEV. 835f1—0in. —-——— 7 [ FUEL ENRICHMENT TRANSFER TANK — 30 ft—0Qin. 2. Im! 19098 MANIFOLD, 2 IN PARALLEL (EQUIVALENT TO &ft OF 2-in. IPS SURGE PLUS 22 ft OF 2-in. IPS) PUMP _ TANK —O{ ] 9 ft OF 1%-in-0D 1PS 2 IN PARALLEL REACTOR 39 ft OF 1.235-in-0D x 0.0680-in-WALL IPS PUMP SURGE 6 IN PARALLEL TANK (a) N XN—— - = X=0 {c) Fig. 3. Reactor and Connecting Piping to Surge Tank. (a) Schematic diagramof system. (b) Internal reactor piping. (c¢) External piping. in the core, and therefore Eq. 4 may be rewritten for the external piping: dg dt ' BV dé 7 o=y -yl = e— — ° A" dt where V_ is the fuel volume in the reactor core in ft® and the prime refers to values 1n the external piping. Equation 6, of course, becomes dm (15) =0, dt (14) v'A" = BV and Eq. 7 becomes dv' BV, d%0 4t A’ di? Substituting Egqs. 2, 14, 15, and 16 in Eq. 5 gives (16) pv, d*6 (17) AF' = p'A' Dy — A' dt? Since p' is constant and equal to o, Eq. 17 may be rewritten as ( ) 1 AFI AP: pO,BVC d29 18) - — —— - -~ - ___° ___ A" Ax Ax A' g2 or, by letting Ax approach zero, dPl pO’BVc dza dx A dt? Integrating Eq. 18 from x = 0 to x = L' gives p BV L' d?0 (19) P -PL: = —— n ' 2 A dt Equation 19 with L' set equal to the length of a runof external piping gives the variation with time of the pressure differential across the piping. In addition to the pressure dif- ferential set up by the inertia of the fuel (Eqs. 13 and 19), there are pressure differentials resulting from the change in friction pressure drop assocliated with change in velocity. These pressure differentials may be evaluated by methods similar to those used above, except that the impulse- momentum equation (Egs. 1 and 5) 1is replaced by the customary Fanning equation for the friction pressure drop: de Af pv? - povg (20) — S T, dx D 9 where Pf = change in friction pressure drop, 1b/fe?, f = friction factor, D = tube diameter, ft. Substituting Eqs. 4 and 10 for the reactor core into Eq. 20 gives do 2 dP, g5 |P0 Pr ot v . (21) 2 =L = L, dx D 1+B(9—90) or do\? 2_2 (&Y + Py 2py |7 (dt> dx D Integrating with respect to x from x = 1+8(6 - 4,) 0 to x = L gives d6\? d a + 2, 24 2
LT 2t Vo calculations is longer than the actual length to account for bends, exits, entrances, etc,, the change in friction pressure drop in the core calculated by using Eq. 22 must be corrected: (23) [Py, - (P,),] corrected - —1 - L [(Pf)m— (Pf)L} 3 where Le 1s the equivalent length for the friction pressure drop, ft. The change in friction pressure drop in the external piping is calcu- lated in the following manner. Equation 20 is valid, and substituting Eq. 14 in Eqv 20 and noting that p' = 0, glves v do\? dP} 2f’p0 ¢ Jt (24) = dx D' - 28V v d9 V. — ¢ O d + . Al Integrating from x = 0 to x = L' gives (25) (Pf)"l - (Pf)L dO\? do 2fp, L' |(PYe T, Ve 77 = + 2 __" D A o Ty 10 /32L3 (22) ( 100 | 3 Since the equivalent length of piping for friction pressure drop - USL . 1+ 86 -4,) and (26) [(P})m - (P_If)L]corrected _ eq : ' - [Py, = (Pp) I Hence, 1f the variations of &, df/dt, and d?9/dt* with time are known, " the total pressure pulse can be calcu- lated because all other quantities are known. The variation of the tempera- ture and its first two derivatives with respect to time, as a result of a 0.5% step increase in reactivity, were evaluated on an electronic analog computer. The results are shown 1in Fig. 4. The other constants required for the evaluation of the pressure pulse are: = 0,0407 ft? (6 tubes in parallel, 1.255 in. ODby 0,060-in. wall), 8 x 10-° I | T il per °F, vy = -3.70 ft/sec, Py = 5.81 slugs/ft?, d, = 1325°F, L = 42 f¢, A" = 0,0233 ft? (1 pipe, 2 in, IPS), 0.0283 ft? (2 pipes in parallel, 11/2 in. IPS), vy = =6.45, -5.31 ft/sec, 1,71 ft?, 28, 9 ft, = 0.0929 f¢, 0.0075, 52 ft = 0,1721, 0.1341 f¢, 0.0058, 0.0062, = 43, 15 ft, 300 280 260 240 220 200 180 160 140 1380 —— 120 1370 +— 100 1360 — 80 8, RATE OF TEMPERATURE RISE (°F/sec) 1350 — 60 1340}— 40 1330 — 20 8, TEMPERATURE RISE {°F) 1320 — 0 | ]|6 scaLel=[8 scaLe] o 02 04 06 TIME {sec) 0 0.050 0100 0150 0.200 DWG. 19300 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 -200 -400 4, RATE OF CHANGE OF TEMPERATURE RISE (°F/ seca) -600 - -800 -1000 -1200 -1400 -1600 -{800 0.250 0.300 0350 0400 0.450 0.500 TIME (sec) Fig. 4. Temperature Rise, Rate of Temperature Rise, and Rate of Change of Temperature Rise vs. Time, Ak/k = 0.005. The final results of the evaluation of Egqs. 13, 19, 23, and 26 are shown in Fig. 5, where the 1incremental pressure at the reactor outlet (position of maximum incremental pressure) 1is plotted against time. The maximum incremental pressure encountered 1s Data from ARE simulator. about 27 psi, and it occurs about 100 msec after the introduction of the step increase 1n reactivity. CORE POWER DISTRIBUTION The power distribution in the ARE reactor was estimated theoretically, 11 30 s | 2C TOTAL MOMENTUM EXTERNAL TO REAGTOR- FRICTION EXTERNAL TO REACTOR PRESSURE INCREMENT (psi) 3 FRICTION IN REACTOR | MOMENTUM _5 IN REACTOR ¥ -10 N% -20 | | 0 04 0.2 0.3 0.4 0.5 TIME (sec) Fig. 5. Incremental Pressure at Reactor Outlet as a Result of a Ak/k of 0.005 vs. Time. and the estimate was checked experi- mentally by the physics groups of the Laboratory, The power distributions used 1in the calculations in this report are presented in Figs, 6, 7, and 8. Figure 6 shows the variation of fission heat generated in the fuel with distance from reactor center; Fig, 7 shows the variation of neutron heating of the moderator; Fig. 8 shows the variation of gamma heating (average, based on the assumption that the reactor 1s homogenized). The maximum of the neutron, and gamma heating are given in Table 2. and average values fission, 12 t.3 DWG 12100 Pl [T | | ! : ) L | ; 12 o ; — ——t- — | SEE TABLE 2 FOR VALUES OF &, AND &, b 2 S LT ol AL S 4 g e e e 10 e ,,44;77:7 — 'i___‘ —— T i ‘ ._.1__i__. J“?ii _‘\‘\\ | | ]: : ] | ' : ! -‘ o9l - L] 207} — Lo b ; NG g C 1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 {7 18 {9 DISTANCE FROM CENTER (in) Fig. 6. Fission Heat Generated in Fuel as a Function of Distance from Reactor Center. Ve — — ‘ i | i i : . i : . mEJU;—~4fi+flA+fl$\-L~w‘wiw b o SEE TABLE 2 FOR VALUES OF A, AND A, | : | | . : ] l ¢ | L ; O12345678910111213141516171819 DISTANCE FROM CENTER {in.) Fig. 7. Neutron Heatingof Moderator as a Function of Distance from Reactor Center. 10 T o - 08— - [ . E e (] : : i : i " : £ 06— - -——1 Y < o 2 — 5 ‘ : ‘ ‘ % O 4! I T T sy e "r i P T D ‘—‘—: K : | | i g SEE TABLE % FOR VA:LUES OF K AND Ky et o f%: 02~ - TL e b4 . — L w A ) + i e : { 0 2 4 & 8 10 12 14 15 18 DISTANCE FROM CENTER (in) Fig. 8. Gamma Heating as a Function of Distance from Reactor Center. TABLE 2. MAXIMUM AND AVERAGE VALUES OF FISSION, NEUTRON, AND GAMMA HEATING IN THE ARE AXIAL RADIAL MAXTIMUM AVERAGE TYPE OF HEATING HEATING HEATING MAXIMUM- MAXIMUM- (kw/in.>) (kw/in.?) TO-AVERAGE TO-AVERAGE ’ ' RATIO, Ka RATIO, Kr Fission (in fuel only) 2.78 1.22 1.55 1.48 Neutron (in moderator only) 0.012 0.0052 1.55 1.66 Gamma (average for homogenized reactor) 0.024 0,011 1,32 1.82 TEMPERATURE PROFILE IN A TYPICAL SECTION OF THE CORE LATTICE Heat is removed from the moderator region of the reactor core by the fuel (Fig. 9). is transferred across the outer surface of a column of beryllium oxide blocks, the heat removed by the fuel flowing in the tube through this column would be the heat generated within the fuel, the metal of the tube, the NaK filling the gap between the tube and the column of blocks, and the blocks. For this hypothetical case, the tempera- ture profile existing between the center line of the fuel tube and the outer periphery of the blocks can be calculated. In a case in which no heat In the actual case, heat 1s trans- ferred i1nto the through the “boundary’ between the moderator and the reflector, and through the upper and lower surfaces of the moderator region. Thus, the calculated temperature profile has no meaning other than to show the maximum tempera- ture gradients that can exist in the rod holes, components of the moderator region. For the hypothetical case, the maximum temperature gradients will exist at the point of maximum heat generation. There fore, for the temperature profile calculations, heat generation rates corresponding to the maximum values expected 1n the reactor used. core were If the heat generated in a hollow cylinder is transferred through the inner surface, the temperature gradient between the outer and inner surfaces of the cylinder 1s given by @1y o7 = = L e 5% | 2 re re re nri , where AT = temperature difference, °F, G = heat generation rate, Btu/sec'fta, k = thermal conductivity, Btu/sec* ft? (°F/ft), r. = inner radius, ft, r = outer radius, ft. o On the other hand, the temperature gradient necessary for the transfer of heat across the hollow cylinder 1s Q - (28) AT = Q, = heat transferred per foot of length, Btu/sec, 7 = thickness (ro - ri), ft, A = mean area per foot of length, fo?, 13 THERMOCOUPLE LAYOUT CORE ASSEMBLY REFLECTOR CODLANT TUBES PRESSURE SHELL BOTTOM HEADER FUEL TUBES D!! !336A REGULATING ROD ASSEMBLY ~_ ——TUBE EXTENSICN __——— THERMAL SHIELD AP - - P THERMAL SHIELD TOP —-FUEL INLET MANIFOLD / SAFETY ROD GUIDE SLEEVE SAFETY ROD ASSEMBLY TOP HEADER TOP TUBE SHEET | HEATERS BeQ MODERATOR AND REFLECTOR A THERMAL SHIELD 5 ASSEMBLY 5 1 i 1 1 e 80V in. REF - BOTTOM TUBE | " shEET 1 _ —sTUD -SUPPORT ASSEMBLY T FUEL QUTLET : MANIFOLD - B—— e T~ _THERMAL SHIELD THERMAL SHIELD CAP BOTTOM ] o ‘‘‘‘‘‘ < 2 M) o \ . \ \ - \SUPPORT ASSEMBLY HELIUM MANIFOLD QMG SCALE IN INCHES ASSEMBLY SEQUENCE STEP 1: ASSEMBLE REACTOR ASSEMBLY TO HELIUM MANIFOLD TUBES. STEP 10: TEST PER TESTING SCHEDULE, STEP 2: SET THERMAL SHIELD GAP AND THERMAL SHIELD BOTTOM N STEP f1. INSTALL HEATERS, CONNECT AND TEST. PLACE AND SLIP TUBES THROUGH. STEP 11a: INSTALL THERMOCOUPLE LAYOUT. STEP 3: INSULATE MANIFOLD TOP AND BRAZE TO TUSES. STEP 12 ASSEMBLE THERMAL SHIELD BOTTOM. STEP 3a © INSERT SPRING AND SHOCK TUBE. STEP 13: ASSEMBLE BALANCE OF THERMAL SHIELD ASSEMBLY , THERMAL STEP 3b: ASSEMBLE ANO ADJUST ORIFICES SHIELD TOP AND THERMAL SHIELD CAP AND WELD CLOSED. STEP 3¢ : COMPLETE MANIFOLD, STEP 14: SEAL ALL JOINTS OF ASSEMBLY OF THERMAL SHIELD ASSEMBLY , STEP 4: ASSEMBLE REACTOR ASSEMBLY WITH SUPPORT ASSEMALY, THERMAL SHIELD CAP, THERMAL SHIELD BOTTOM, THERMAL SHIELD STEP 5: ASSEMBLE STUD WITH REACTOR ASSEMBLY AND SUPPORT TOP AND THERMAL SHIELD CAP WITH INSULATING CEMENT, J-M ASSEMBLY . NO. 400 OR FQUIVALENT. STEP 6: ASSEMBLE THERMAL SHIELD CAP WITH HELIUM MANIFOLD, STEP 15: INSULATE HELIUM MANIFOLD WITH 2-in. LAYER J-M SPONGE FELTED STEP 7 ASSEMBLE THERMAL SHIELD CAP LOOSELY WITH COCLANT LINE INSULATICN, SEAL ALL JOINTS WITH INSULATING CEMENT, J-M ANNULUS OF REACTOR ASSEMBLY. NO. 400 OR EQUIVALENT. STEP B: WELD TUBE EXTENSION TQ SAFETY ROD GUIDE SLEEVE AND STEP 16: SEE OPERATING PROCEDURE. INSTRUMENT GUIDE SLEEVE , 6 REQ'D. STEP 9: CONNECT ALL PIPING, 14 Fig. 9. Vertical Cross Section of Reactor. when heat 1s both trans- There fore, ferred across and generated within a hollow cylinder, Qt G 1 (29) AT = e o + r? 1n — 0 r. 1 The temperature at any radius in a hollow cylinder internal heat generation and the heat in which there 1is is transferred through the 1inner surface 1s given by G |1 (30) T = — |= (r? - r?) 2k |2 : 9 r + r® ln —| + T, | o r. l t where T = temperature at any radius r, °F, r = any radius within the cylinder, ft, Ti-=?temperature at r, °F, The heat gernerated per foot of length of the cylinder can be calculated from (31) Q= Gr(r? - r2) r where Q 1s the heat generated per foot of length, Btu/sec. The calculations of temperatures and temperature differences were made from the following data for beryllium oxide, NaK, and the metal tube. Beryllium Oxtde Block. The beryllium oxi1de block 1s hexagonal in cross section (3.73 in. across flats). For simplicity in calculation, the block was assumed to be a circular cylinder of equivalent cross-sectional area, with an outside radius of 1.960 1in, and an inside radius of 0,630 inch, The temperature difference between the outer and inner surfaces is due entirely tointernal heat generation. Therefore, G |1 T S B - 2 2 2 AT = 5; 9 (ri - ro) tor: ln‘:f . i NaK. The outer and inner radii of the NaK annulus, measured from the center of the cylinder, are 0.630 and 0,618 in,, respectively., NaK 1s nearly stagnant, the tempera- ture gradient through the NaK 1is Since the Q ¢ |1 r, AT = —— +— | = (r2-r2)+r? In k 2k | 2 ' ° ° r. L T m where . is the heat generated 1in the beryllium oxide. Metal Tube. The outside radius of the metal tube 1s 0.618 in., and the inside radius is 0.558 1inch., The expression for the temperature gradient in the tube 1s the same as that for NaK, except that Qt is the heat gener- ated in the beryllium oxide plus the heat generated in the Nak, The amount of heat generation 1in the fuel 1s proportional to the length of time the fuel resides in the reactor core. Thus high-velocity fuel will have less heat generated within 1t than fuel flowing at a low velocity and, correspondingly, 1ts temperature will be lower. Upon looking at the velocity profile of fuel flowing in a fuel tube, 1t 1s seen that the maximum velocity 1s at the center and that the minimum velocity is at the tube wall. From this, 1t that a temperature gradientwill exist between the outer surface and the center of the fuel. This temperature gradient can be determined, and the expression (r, - T_,.)/Gr?, in which T is the temperature of the outer surface of the fuel, °F, and T ., 1s the tempera- ture of the fuel at the center of the tube, °F, has plotted as a function of Reynolds’ and Prandtl’s (10) can be seen been moduli by Poppendiek and Palmer, The fuel also has a temperature gradient between the center and outer surface, which 1s given by k = — 0. 0. b= 0.023 = NS-® N34 15 where h = coefficient of heat transfer by convection, Btu/sec*ft?«°F, A = area of the inside surface of the metal tube foot of length, ftz, D = hydraulic diameter of the fuel per tube, ft, Ny = Reynolds’ modulus, Np, = Prandtl’s modulus, Q, = heat generated in the beryllium oxide plus the heat generated in the NaK plus the heat gener- ated in the metal tube, From this it is seen that the total temperature gradient in the fuel 1is t AT = — + AT (resulting from internal hA heat generation). For the fuel, the physical charac- teristics are: Radius, ry 0.558 in. Temperature, T 1170°F Viscosity, # 8.27 x 10~3 1lb/sec* ft Density, £ 187 1b/t? 1400 TUBE WALL 1360 0.26 Beu/1b*°F 4,17 x 10°* Btu/sec'ft2 (°F/fe) The following are the maximum expected heat generation rates for the various components: Specific heat, €p Thermal conductivity, k COMPONENT ¢ (Btu/seceft”) BeO 62.21 NaK 41,47 Metal tube 41, 47 Fuel 4838 The results of the calculations of temperature differences for the various components are: COMPONENT AT (°F) Fuel 81.08 Metal tube 22,97 NaK 3.08 BeQ 108,00 Total 215.13 Thus the maximum temperature 1is 1170 + 215 = 1385°F. A plot of distance from fuel tube center is shown on Fig. 10, temperature vs, DWG, 19103 1320 © o Ld g g 1280 jaed L a = 58] — 1240 1200 1160 0 1.0 20 RADIUS (in.) Fig. 10, Temperature Profile in Core Lattice. 16 FLOW OF REFLECTOR COOLANT THROUGH CORE In the ARE, the pressure shell, the moderator, and the thimbles of the control rod and instrument holes are cooled by the circulation of NaK, The NaK circuit (reflector coolant cir- cuit) is shown in Fig. 1. The coolant enters the pressure shell at the bottom, flows through the lattice, and leaves at the top (Fig. 9). The flow through the core lattice 1s divided among the annulus between the outer periphery of the reflector and moderator can and the pressure shell, the tubes leading through the reflector blocks, and the annuli around the rod and instrument holes. For adequate cooling of the moderator and pressure shell, it 1is necessary to have only a minimum amount flowing in the around the rod and instrument holes. The additional heat that must be removed from the thimbles will be carried away by the helium that cools the rods and instruments. To obtain this minimum flow, orifice plates (Fig. 11) were placed in the annuli. of coolant annuli There will be a pressure drop in the fluid when it enters the pressure shell because of expansion, and when it leaves there will be a further pressure drop because of contraction. In the spaces between the tube sheets and the pressure shell above and below lattice, which will act as plenum chambers, the coolant velocity will be effectively Thus the pressure drop in these regions will the core ZeT O. be very small. The pressure drop in the coolant flowing through the core lattice will be due to contraction, friction, and expansion. Since the pressure drop of the fluid inside the pressure shell 1is due almost entirely to that i1n the core lattice, the flow through the various paths will be directly proportional to the respective resistances of the paths, The loss in pressure by contraction is given by (32) AP = k where k_ is a constant given by McAdams (cf., p. 122 of ref. 11); the expansion pressure drop 1s given by plvy - vy)? (33) AP e 2g and the friction pressure drop for turbulent flow 1n either a tube or an annulus 1s given by (34) o, = apt 2 f 7 p 2 The equation for the friction factor 1is 0.046 (35) f=— 0.2 NR The meanings and units of the symbols 32 through 35 are: used 1n Egs. AP = pressure drop, lb/ft?, f = friction factor, dimensionless, L = length, ft, D = hydraulic diameter, ft, o = density, 1lb/ft3, v = average velocity, ft/sec, g = gravitational acceleration, 32.2 ft/sec?, kc = constant, dimensionless, v, = average linear velocity upstream, ft/sec, v, = average linear velocity down- stream, ft/sec, Np. = Reynolds’ number. The subscripts have the meanings: following ¢ = contraction, e = expansion, f = friction, All the annuli around the control rod and instrument holes have the same dimensions: the outside diameter, D , is 3.652 in, and the inside diameter, Di’ 1s 3.000 i1nches. There are two instrument holes, three safety rods, and one regulating rod; thus there are six holes and six corresponding annuli, Where the NaK enters at the bottom of the annuli (Fig. 9), there are orifice plates (Fig. 11). These orifice plates reduce the outside diameters of the annuli to 3.140 in,; the length of each orifice plate 1s 1.00 in,; and the length of the remainder of each annulus 1s 35.25 inches., The annulus 17 81 UNGLASSIFIED e @ DWG.E-A-1-24 3930, N %D e | J -~ 35640 in. 0.060 in. PARTS LIST INCONEL TUBE GOIL A INCONEL TUBE CCIL B INCONEL. INSTRUMENT TUBE SUB-ASSEMBLY INCONEL CAN BeO REFLECTOR EDGE BLOCK BeO REFLECTOR BLCCK BeO CORE BLOCK INCONEL REFLECTOR COOLANT TUBES INGONEL. CORE SLEEVE INCONEL SAFETY ROD GUIDE SLEEVE INCONEL TOP TUBE SHEET INCONEL BOTTOM TUBE SHEET INCONEL SUPPORT STUDS INCONEL SPACER INCONEL ORIFICE PLATE __/,//® = Aoy S - -=-2.035in. ey l IR /{ e e o e e - {% NN NN R e NS (® ' 4 O @O~ OO s WM - 4 ", . s " | | N o ASSEMBLY SEQUENGE STEP {: WELD ITEMS 8,9 AND 15 TO ITEM 2, 9 AND 15 WELDED TOGETHER TO ITEM 12 STEP 2: ASSEMBLE ITEM 13 WITH ITEM {2 STEP 3: ASSEMBLE ITEMS 1 AND 2 WITH ITEM 12, THEN ITEM 14 WITH ITEMS 1,2 AND 8 STEP 4: ASSEMBLE ITEM 7 WITH ITEMS { AND 2 STEP 5° ASSEMBLE ITEM 6 WITH ITEM 8 STEP &° ASSEMBLE ITEM 5 . ’i ;///’5,//,;”' N e > STEP 7° ASSEMBLE AND WELD ITEM 4 TO ITEM 12 () 7 S NN % SOENSRONNNNN 4 STEP 8: WELD {TEMS 8 AND 9 TO ITEM 1 §§§g§§\s STEP 9: WELD ITEM 4 TO ITEM {f ;/,7;/,/// Fig. 11. Core and Reflector Assembly Elevation Section. between the pressure shell and the outer periphery of the moderator can has an outside diameter of 48.57 in.: the gap width 1s 1/16 in.; and the path length through this annulus is 36.25 inches. In the reflector region, 79 tubes, one through each column of beryllium oxide blocks. Each of these has an inside diameter of 0.49 in., and 1s 36.25 in. long. The coolant is carried to and from the pressure shell by 2 1/2-1n. schedule-40 pipe. Since the NakK flowing through the reactor pressure shell and core lattice is almost isothermal, there are the physical properties were considered to be constant. The values of density and viscosity used were, respectively, p = 44.5 1b/ft3 and pmo= 0.36 1b/hr: ft . By using Egqs. 32 and 33, the inlet and outlet losses of the pressure shell were calculated to be AP (inlet) = 156.3 1b/ft? and AP (outlet) = 78,15 1b/ft? , From Eqs. 32 through 35 and the assumption that the distribution of flow through the core lattice depends only on the relative resistance of each path, the distribution of flow was found, by trial and error, to be: FLOW RATE PATH T (ft3/sec) Large annulus 0.108 Tubes through reflector 0.272 Six annuli 0.120 The pressure drop through the lattice, which 1s the loss in pressure experienced by the fluid flowing through one path, was found to be AP = 19.49 1b/ft? . If the pressure drop i1in the spaces above and below the core lattice 1is neglected, the total pressure drop 1is AP = 253,9 1b/ft? = 1.76 lb/in. 2% . HEAT REMOVAL BY THE REFLECTOR COQLANT A cross section of the reactor 1is shown in Fig, 9; in Fig., 12. Molten NaK is circulated through the reactor to remove the heat generated i1n the reflector and to cool the pressure shell and the walls of rod and instrument holes. In passing through the reactor, heat is removed a plan view 1s shown from the following sources in the reactor by the NakK: 1. heat generated in the reflector, 2. heat generated in the pressure shell, 3. heat generated in the Nak, 4, heat transferred from the reactor core a. through the serpentine elbows, through the tube sheets, c¢. through the “boundary’ between the core and the reflector, d. through the walls of the rod and i1nstrument holes, The NaK i1in the interstices of the moderator blocks 1n both the reactor core and reflector is almost stagnant and, for the purposes of the following calculations, is assumed to be entirely stagnant, Jt 1s assumed that the electric heaters on the pressure shell add sufficient heat to the system to Just balance the heat loss to the environment; therefore it 1s also assumed that there 1s no net heat flow across the outside of the pressure shell. Heat Generated in the Reflector. The following values for gamma and neutron heating of the reflector were obtained from the section on “Core Power Distribution.” Gamma Heat Generation: Peak gamma heating (at center of core), Btu/sec.in.3 0.023 Ratio of maximum gamma heating at a radius of 18 in. to peak gamma heating 0.20 Maximum gamma heating at a radius of 24 1in. 0.0 Ratio of maximum gamma heating at any radius to average gamma heating at the same radius 1.32 19 DWG.E-A-1A THERMAL SHIELD ASSEMBLY PRESSURE SHELL TOP HEAD ASSEMBLY ........ FUEL OQUTLET MANIFOLD SAFETY ROD EXTENSION GUIDE INSTRUMENT TUBE EXTENSION GUIDE Fig. Neutron Heat Generation: Peak neutron heating in beryllium oxide (at center of core), Btu/sec-in. Ratio of maximum neutron heating at a radius of 18 in. to peak neutron heating Neutron heating of the reflector at a radius of 22 1/2 in. Ratio of maximum neutron heating at any radius to average neutron heating at the same radius 20 12. INGHES 6 9 2 Plan View of Reactor,. Neutron heating aqccurs only in the beryllium oxide, which constitutes about 78.5% of the reactor. 0.011 It is assumed that within the reflector the gamma and the neutron heat generation vary linearly with 0.30 radial distance. That this assumption 1s fairly valid may be observed from 0.0 Figs. 7 and 8. The following equations for the average gamma and neutron heat generation at any radius within the 1.55 reflector can be written: (36) g, =0.00460 -0.000767 (R - 18) , - 18 22.5 , where q = heat generation, Btu/sec-in.?3, R = radius, 1inches. The total heat generation, Q, 1is 24 (39) Q, =.L8 [0.00460 - 0.000767 (R - 18)] 27R dR = 40,7 Btu/sec , 22.5 40 = 0.00210 (40) @, =f "I - 0.000467 (R - 18)] 27R dR = 9,5 Btu/sec , (41) Q = Qy + Qn = 50,2 Btu/sec . The heat generated in the reflector is removed by the NaK through various interfaces; the temperature limitations of the beryllium oxide and associated structure are sufficiently far above the NaK temperature that temperature patterns in the reflector need not be calculated. Heat Generated in the Pressure Shell. The heat generated in the Inconel pressure shell 1s due to gamma attenu- ation and fast-neutron scattering. The actual variation of heat generation with position in the top head is shown in Fig., 13. The curve may be approxi- mated by the exponential relationship (42) q'= 13,200 ¢-9-20= where 9" = heat generation, Btu/hr-ft?, x = distance from inside surface, ft. The heat generation in the bottom head and barrel is actually less than this, it 1s assumed that the curve may be used. The total heat generation, Q, in a flat plate of thickness 7 is given by but to be conservative, (43) Q = 13,200 e~ %2°% gy 0 = 1450 (1 - ¢~%207) | where 7 1s in feet. The structed of 2-in.-thick plate reinforced to 4 1in, locations 1in the heads. 43 for thicknesses, T, 1/3 ft gives Eq. and respectively, If the barrel 1s treated as a flat plate, thick material is 72.5 ft?, total area of the 4-1in.-thick material is 9.5 generation is 95,300 Btu/hr, Btu/sec. but because Fig, conservative value 1s desirable. Temperature of Pressure Shell. Inasmuch as the allowable design stress Inconel pressure shell 1s con- in thickness at critical Evaluation of of 1/6 and Q = 1135 Btu/hr- ft?2 Q = 1380 Rtu/hr-ft? , the total area of the 2-1n.- and the ft?2., Therefore the total heat or 26.5 This value 1s probably high, 13 1s approximate, a in the pressure shell is a function of the pressure shell temperature, the temperature pattern in the pressure shell head (the most critical portion of the pressure shell from the stand- point of both stress and temperature) must be calculated,. The as a flat plate internal heat generation. pressure shell will be treated in which there 1is One side of the plate is insulated and the other side (44) is cooled by circulating Nak. The differential equation, then, 1is: d26 q' dxz- k- where x = Btu/hr- ftd = heat generation, 13,200 ¢~ 720 T - T , x Nak temperature in pressure shell at position x, of NakK, thermal conductivity of Inconel = 11 Btu/hr* ft? (°F/ft), distance from 1nside surface, ft. temperature The boundary conditions are: df — =0 , at x = T , dx dé h — =—26&, at x = 0 , dx k 21 o HEAT (watts /cm3) 22 DWG. 19301 5 * TOTAL HEATING SHCULD BE INCREASED APPROXIMATELY 10% TO ALLOW FOR FAST-NEUTRON SCATTERING 2 10! TOTAL HEATING ¥ 5 2.5-Mev GAMMA (CORE) 2 1072 5 7-Mev GAMMA (CORE CAPTURE GAMMAS 2 CAPTURE PLUS INDUCED ACTIVITY FROM GAMMAS IN SHELL 1073 0 2 4 6 8 10 12 THICKNESS OF SHELL {cm) Fig. 13. Heat Generated in Pressure Shell at 3-Megawatt Power Level. where h 1is the heat transfer coef- ficient of NaK in Btu/hr-ft?-°F. The heat transfer coefficient, h, may be calculated by the following formula: kNaK (45) h (5.8 + 0.02 Pe®?®), where knag = thermal conductivity of Nak, D = NaK passage equivalent diameter, Pe = Peclet’s number for NakK. To assure a conservative value for the heat trans fer coefficient, the hy- draulic diameter of the NaK passage without the tube elbows was used as the equivalent diameter of the NaK passage. The diameter and other values are D = 0.667 ft, kyag = 16.0 Btu/hr-fe? (°F/ft), Pe = 148, using a velocity of 0.1 ft/sec (cf., chap. 2, “Flow of Reflector Coolant Through Core ), Therefore h = 166 Btu/hr-ft2-°F, The differential equations and boundary conditions thus become d?6 (46) = 1200 =920 dx ? and dé (47) — =0 , at x = T , dx dé (48) — = 15.16 , at x = 0 , dx The solution 1is, of course, obvious: dé (49) -E— = 130.5 e %% + cy x where, from Ea. 47, c, = -130.5 e” 9207 and therefore d6 d_ = 130.5 (6'9.201 _ 6‘9.207') , x (50) 6 = —14,19 ¢79-20= - 130.5 x e~ 9%+-207 4 c, c, = 8.64 (1 - e %) + 14.19 6 = 14.19 (1 — ¢™9:20%) - 130.5 x e-9-207 + 8.64 (1 — e~ 2-20%) The temperature at x = 7, which 1s, of course, the maximum temperature difference, can be determined: (51) 6&_ = 22.83 (1 — e %207) - 130.5 7 e~ 9207 For 7 = 2 in., B = 13.2°F; for 7 = 4 in., 8 = 19.8°F. As a check on the calculation, 6 _, = 8.64 (1 - e79-207) = 6,78 , for 7 = 1/6 ft , = 8.23 , for 7 = 1/3 ft , he oo = 166 0, = 1130 , for 7 = 1/6 ft , 1/3 ft These values check very closely the heat generated per square foot in the 1370 , tor T two different sections, The pressure shell, therefore, will be about 5 to 20°F hotter than the NaK. lleat Generated in the NaK. The calculation of heat generation 1in the NaK in the reactor circuit is rather complex, and only a gross estimate of the heat generation is available. The maximum heat generation in the NaK will probably be of the order of 10 Rtu/sec- ft®, with the average heat generation being of the order of 3 Btu/sec* ft®. Since there is approxi- mately 10 ft® of NaK in the pressure shell, the total heat generation in the NaK will be of the order of 30 Btu/sec. The total heat added to the re- flector coolant circuit by heat generation in the reflector, pressure shell, and NaK 1s Q = 50.2 + 26.5 + 30 = 106.7 Btu/sec This heat addition 1s independent of NaK temperature. Heat Transferred from the Reactor Core. Heat is transferred to the NakK in the reflector coolant circuit from the reactor core, The boundaries 23 across which fhe heat 1s transferred are the serpentine elbows, the tube the boundary between the core and the walls of the rod and instrument holes. Serpentine Elbows. The fuel tubes that (Fig. 9); there are six tubes in parallel, There are therefore sixty 180-deg bends or elbows pressure shell, 30 below 1t. In addition, between the core and the pressure shell, s1x straight sections at the inlet of the tubes and six straight sections at the outlet. The length of the 180-deg elbows is 8.5 in., for the elbows above sheets, and the reflector, are wound as serpentine coils pass through the core 11 times between the core and the 30 above the core and there are the core and 6.5 in. for elbows below the core; the straight sections are 4 i1in, long above the core and 3 in. long below 1t. The tubes have an outside diameter of 1,235 in. and 0.060-in, walls. The total length of the bends and the internal and external areas of the bends are 6.5 8.5) 4 3> L = 30— + =2 ) 4+ g2+ =2 19 12 12 192 = 41.0 ft , 1.235 A . = 41,0 x 7 x = 13,3 ft? | ex 12 1,235 - 0.120 A, =410 x 7 x —m — — 1n 12 = 12,0 ft? The fuel-side heat transfer coef- ficient can be calculated by first calculating the heat transfer coef- ficient for a straight pipe and cor- recting for the effect of the bend: ! Dl (52) hf=hf, H where hf = fuel-side heat transfer coef- ficient, Btu/sec*°F, h} = heat transfer coefficient in a straight section, Btu/sec*ft?-°F, D. = tube inside diameter, Dy = bend diameter, h, = h'(1 + 3 L.115 = 2.04 h' f_f 05 _o4.' 3.75 f 24 (53) k% = 0.027-/i> Re Pr}“" fi)“’“ \D f Hs/f where Ref = Reynolds’ number for fuel = 10,600, Prf = Prandtl’s number for fuel = 3.78, 0.14 <fi> = 0.96, Moo f 0.004409, TN o |~ \_/ “—h I Therefore h} = 0,303 Btu/sec-ft?2-°F, h 0.618 Btu/sec*ft?*°F, (hA)f= 7.42 Btu/sec*°F, ), The value of the NaK-side heat transfer coefficient 1s somewhat in doubt be- 0,135, cause very little work has been done on the heat transfer coefficient of ligquid metals flowing across round tubes, For an approximation, the formula for flow inside a round tube will be used, with the outside diameter of the tube being considered as the equivalent diameter: . I 0.8 (54) k. = N K <7 + 0,025 PeNaK> , where PeN“(= Peclet’s number for NaK = 22,90, 0.0432 D Nak Therefore hNflK = 0.316, (hA)NaK = 4,20 Btu/sec*°F, 1 <-> = 0.238. h4 NakK The tube wall resistance is DO ln — 1 D (55) — == 0,130 , hA 2k L ‘metal where D, is the outside diameter; and the over-all resistance 1is oo () (x) « (&) ) metal 0.503 . For the calculation of the effective temperature difference between the fuel and the NaK 1t 1s assumed that the NaK temperature 1s constant and 1s the same as the mean temperature of the This simplifying to some 1lnaccuracles NaK 1in the core. assumption leads in the calculation of the heat trans- ferred to the NaK; however, in view of the extremely complex flow of the NaK through the reactor, it i1s doubtful whether any approximation would be the variation in the fuel temperature from 1150 to 1500°F is due primarily to heating in the core, the arithmetic-average temperature difference between the NaK and the fuel should be used. The arithmetic-average elbow temper- ature 1s about 1330°F, The effective temperature difference and the heat the NaK through the are in the more valid. Since rejected to serpentine elbows given following tabulation for various mean temperatures: MEAN NaK AVERAGE TEMPERATURE HEAT REJECTED TEMPERATURE DI FFERENCE TO NaK (°F) (°F) (Btu/sec) 1300 30 60 1200 130 258 1075 255 507 1000 330 656 800 530 1054 Tube Sheets. The tube sheets are the metal plates at the upper and lower boundaries of the core through which the fuel tubes pass (Fig., 9). Figure 14 shows a cross section of a typical fuel tube and 1ts associated moderator blocks and tube sheet section., Heat 1s generated 1n the moderator and trans- ferred to the fuel and the NaK; 1in addition, heat flows from the fuel to the NaK through the moderator blocks. The differential equation and hboundary the two-dimensional conditions for system shown 1in Fig. 14 are given 1in the following: %68 9% q' (57) A Ox? dy 2 k where — 0 g =T - Tk °F» T = temperature at any point (x,y), OF, Ty.k temperature of the NaK, °F, g’ = heat generation in moderator, Ptu/sec- ft3, k = thermal conductivity of moder- ator, Btu/sec*ft? (°F/ft). OWG 19104 TUBE SHEET NaK FLOW / . | :fié::::::j x | g | M x | 2 | q f 1 s |l D i o i = ‘ % i | o @ > X e L TR e N REACTOR CENTER LINE Fig. 14. Cross Section of Moderator Block Showing Tube Sheet and Fuel Tube. The heat generation in the moderator block 1s assumed to be constant in the x direction and to the y direction 1in accordance with the axial moderator heating curve found in the The vary 1in section on power distribution. 25 boundary conditions are a6 (58) — =0 , at x = 0 , Ox o6 (59) — =0 , at y = 0 , dy h a8 f (60) 5;'= T (9 T Thak = TS> , at x = a , h o NakK 61 — = - g = (61) 5 . , at y b No closed or series solution for this boundary value problem could be readily found; consequently, solutions to specific numerical problems were undertaken by the relaxation method. Figure 15 shows the temperature pattern across the tube sheet face of atypical moderator block, as found by this method, for several NaK temperatures. The heat loss from the section of the tube sheet adjacent to one fuel tube and moderator hblock and the total heat loss from both tube sheets, which 1is 132 times the loss from one of the sections, are tabulated in the follow- Nak TEMPERATURE HEAT LOSS PER pap,; peaT LoOSS a SECTION ("F) (Btu/sec) {Btu/sec) 900 1.86 246 1075 1.15 150 1250 0.25 33 Boundary Between Core and Reflector. The fuel tubes at the periphery of the core (near the reflector) are at a considerably higher temperature than the reflector, and they transfer heat into the reflector through the beryl- lium oxide blocks., An estimate of the heat transferred into the NaK circuit by this method has been made. The system of fuel tubes, NaK tubes, and beryllium oxide blocks was simplified and considered as a hollow beryllium oxide cylinder with internal heat generation in which the inner surface 1s washed by fuel and the outer sur- face 1s washed by NaK. The actual heat transfer coefficients of the fuel and the NaK in the tubes were calcu- lated and, from these coefficients, hypothetical heat transfer coef- ficients on the sides of the cylinder were computed so that ing: (62) R*A* = hA Dd! 15105 l—~e—TUBE (¢ AT O} ~=— ~TUBE (4. AT 3.75)% mafl°” 1300 \ / e 1250 “ 1200 / w \ o 2 b ,—’/////// x 1075 R S 100 A\ / w - // | J t000 \\\\\‘h“‘- 900 _—___—____,,,/// --———-_— 900 0 05 { 1.5 2.0 2.5 30 3.5 RADIAL DISTANCE FROM CENTER OF FUEL TUBE (in) Fig. 15. Temperature Pattern Across Tube Sheet Face. 26 h* = actual heat transfer coef- ficient, Btu/sec* ft?:°F, A* = actual heat transfer area, ft?, h = hypothetical heat transfer coefficient, Btu/sec* ftQ'OF, A = hypothetical heat transfer area, ft2, The mean radius of the peripheral fuel tube circle 1s about 15 1in, and there are 29 tubes; the mean radius of the inner circumference of the NakK tubes 1s about 18 1/2 in. and there are 35 tubes; and the reactor core 1s 36 in., 1n height. Therefore the actual heat transfer areas are (63) A * 2 Af 25.8 ft* | * _ 2 . ANaK = 11.86 ft° ; and the hypothetical heat transfer areas are il 7DLN (64) A = 2nrL - 2 Af = 23.6 ft* , - 2 ANaK = 29,1 ft© , where D = tube 1nside diameter, ft, tube length, ft, number of tubes, L N ro= = average radius of tube caircle, fe. The heat transfer coefficients 1in the tubes are found as follows: 1. For the fuel tuhles . kf w 0.14 (65) hy=10.027 — Re}-B pr}x’3 <—~> D ’usf where k thermal conductivity of fuel, Btu/sec* ft? (°F/ft), Ref = Reynolds’ number for fuel, Prf f I} Prandtl’s number for fuel, H . : : <~—> ratio of viscosity of fuel at B /g bulk temperature to viscosity : at surface temperature, For a fuel velocity of 3.7 ft/sec and a Df of 0.09285 ft, the values of the terms in Eq. 65 are o H 1 2,98 , hy = 0.373 2. For the NaK tubes * kNaK (66) hy, , = b, (7.0+0.025 Pey: &), where Pe \ is Peclet’'s number for NakK. For a NaK velocity of 3.0 ft/sec and a DNaK of 0.03582 ft, the values of the terms 1n Egq. 66 are PeNaK = 236.4 %* hy.o = 1.093 The hypothetical heat transfer coef- ficients are therefore h*A* hf =%f = 0.4-08 f and . . b _ hNaKANaK - 0. 44 NaK A = 0.446 NakK The differential equation for steady- state heat conduction with internal heat generation 1s ! (67) vip = - - BeO where T = temperature at any polint in the BeO, °F, g’ = internal heat generation, Btu/sec* ft3, kpeog = thermal conductivity of BeQO, Btu/sec- ft? (°F/ft). Although g’ varies with radial distance and kBeo varies with temperature, both will be assumed constant and equal to their average values., This simplifying assumption undoubtedly results 1in some error and the following solutions, accordingly, are only estimates: qg' = 7.74 Rtu/sec* ft? ? 27 and ko.o = 0.0054 Bru/sec*ft? (°F/ft) . The solution of the differential equation for the i1nfinite cylinder case 1S dT “ (68) —_ = =717 + — , dr r (69) T = -358.5 r? + ¢ + , Inor c, where r 1s the radial distance from the center of the core in feet and €, and ¢, are arbitrary constants, The boundary conditions are h dT (70) — = - f (1460 - T) , dr BeO at r = 1.25 ft (the mean fuel temperature in the peripheral! tubes 1s 1460°F), (11) 2L - nex (T - T,..) o T ‘NaK ! dr kBeo at r = 1.5417 ft (TNaK 1s the mean NaK temperature). The values of ¢ by using the , and ¢, are obtained boundary conditions: (72) c, = 4.3823 TNaK ~ 5008.,53 and (73) c, = 3072.71 - 0.93146 T Nak (the solution requires that many significant figures be carried). The temperature differences at the ReO-to- fuel and BeO-to-NaK interfaces and the heat removed from the fuel and added to the NaK are given in Table 3. It 1s obvious from the data in Table 3 that heat 1s transferred from the fuel to the NaK and that all the heat generated 1n the beryllium oxide goes into the NaK. A simple check of the numerical work, by the method of superposition, 1s therefore possible: (74) Q5.0 q'W(rfiaK—r;)L = 59.5 Btu/sec, fp.0 = temperature difference across the beryllium 28 oxide resulting from internal heat generation only = 61.1°F, PR |- — n 0.1039 | f 1 (——) = 0.0771 |, hA NakK 1 <——> = 2.060 , hA'BeO 1 <——> = 2.241 hA'f-NaK The fuel-to-NaK temperature differences for the various NaK temperatures are given in Table 4. As can be seen, the results quite well with the results given in Table 3. A portion of the heat transferred agree to the NaK comes from heat generated in the beryllium oxidein the reflector, as previously discussed. It 1s therefore necessary to subtract from the heat transferred to the NaK an amount equal to 2 Q:?_m[(}f_-__s_) 12 18. 0 \? - — X 3 = 4.65 Btu/sec 12 The net heat added to the NaK 1s then TNaK (QNaK)net 800 322 1000 233 10675 199 1200 143 1300 99 Walls of the Rod and Instrument Holes. through the reactor core and pressure shell to admit control rods and nuclear instruments (Fig. 16). In each hole there are three concentric tubes (Fig. 17); NaK flows through the passage between the outer There are six vertical holes two TABLE 3. TEMPERATURE DIFFERENCES AND HEAT TRANSFERRED AT THE Be0-TO-FUEL AND BeO-TO-NaK INTERFACES TEMPERATURE DIFFERENCE (°F) 5 Tyag (°P) Qs ) QNaK( ) Opeo = Unax * ¢ () BeO- to-Fuel BeO-to-NaK e a f 800 ~27.77 25.20 -267.4 326.7 59.3 1000 ~-18.49 18.31 ~178.0 237.4 59.4 1075 ~15.01 15.73 ~144.5 203.9 59. 4 1200 -9.21 11.42 ~88.7 148.0 59.3 1300 -4.57 7.97 -44.0 103.3 59.3 (G)Qf = heat transferred to the fuel, Btu/sec, (b)QNaK = heat transferred to the NaK, Btu/sec. (C)QBeO = heat generated in BeO, Btu/sec. TABLE 4. TEMPERATURE DIFFERENCES AND HEAT TRANSFERRED AT THE FUEL-TO-NaK INTERFACE TEMPERATURE DIFFERENCE _ - 1§BK FUEL-TO-NaK, 6, \ o gf“Na§ = "Beo T ) ek Ppnak = Fpeo) | Ovax = 0p * Opeo (°F) (°F) - ("F) (Btu/sec) (Btu/sec) 800 660 598.9 -267.2 326.7 1000 460 398.9 -178.0 237.5 1075 385 323.9 -144.5 204.0 1260 260 198.9 —88.7 148. 2 1300 160 98.9 ~44.1 103.6 tubes and removes the heat that would otherwise be transmitted to the hole from the reactor; the passage between the inner two tubes 1s packed with insulation; helium flows inside the inner tube and cools the rod or instrument and the inner tube wall. Heat 1s therefore added to the NaK from the reactor and removed from the NaK by the helium. Since the two instrument holes are located in the reflector and the heat addition to the NaK from the reflector has already been accounted for in the calculation of heat generated 1n the reflector, only the heat added to the NaK in the four control rod holes remains to be calculated. The calculation of the heat removed from the NaK by the found and Instrument helium in the six holes can be ‘‘Rod ” in chap. 35, Cooling System. Each rod hole through the reactor 1s surrounded by six beryllium oxide blocks, each of which contains a fuel tube (Fig. 16). The mean fuel tempera- ture 1n the fuel tubes 1s about 1200°F. As a simplification (similar to that used 1n the calculation of heat transfer across the boundary of the core and reflector), the holes and associated structure were considered as a hollow beryllium oxide cylinder with internal heat generation and with the 1nner surface washed by NaK and the outer surface washed by fuel. 29 TUBE COIL B {INCONEL) TUBE COIL A (INCONEL) 0 o O o o O o — 5 o o o o O O © o Fig. 16. There is some overlapping of fuel tubes in the sense that some of the tubes are members of the tube sets encircling more than one rod hole. This effect was neglected i1inasmuch as the heat added to the NaK in the rod holes smaller 1n magnitude than the heat added elsewhere and, a rough estimate of the heat additionis all that 1s necessary. 1s considerably hence, The actual heat transfer coefficient in the fuel tubes was calculated and, from this coefficient, a hypothetical heat transfer coefficient on the side of the cylinder was computed so that: (75) h*A* = hA 3 30 DWG. 15847 —INSTRUMENT TUBE (INCONEL) ——_> REF_ECTOR EDGE BLOCK { BERYLLIUM OXIDE) \\\\\\ - REFLECTOR BLOCK {BERYLLIUM OXIDE) _.—-CORE BLOCK {BERYLLIUM CXIDE) REFLECTOR COOLANT TUBES {INCONEL) — GAN (INCONEL ) ——— CORE SLEEVE (INCONEL) SAFETY ROD GUIDE SLEEVE ({INCONEL) ] SGALE IN INGHES Plan View of Reactor Core Lattice, where h* = actual heat transfer coefficient, Btu/sec'ftz'oF, A* = actual heat transfer area, ft?, h = hypothetical hecat transfer coefficient, Btu/sec'ftz'oF, A = hypothetical heat area, fe 2, The inside radius of the outer NaK-containing tube 1s 1.826 1in.; the mean radius of the fuel tube circle i1s 3.75 in.; and the height of the reactor core 1s 36 1inches. The heat transfer coefficients and transfer DWG. 12106 ;// 72 _ DIATOMACEOUS EARTH Fig. 17. Cross Section of Helium Passage and Sleeve, areas are therefore: 1. For the NaK annulus (76) ANnK = AaaK = 7TDNaKL ! (77) hNaK = h;aK “NaK 0.8 ) (5.8 + 0.020 Pel:2) Nak where D = equivalent diameter, ft, L = length of reactor core, ft, k = thermal conductivity, Btu/sec-ft? (°F/f¢e), Pe = Pelcet’s number. For a NaK velocity of 0.81 ft/sec, an Ay.x = Af.x of 2.87 ft?, and a Dg.x of 0.0543 ft, the values of the terms in Egs. 76 and 77 are PeNaK = 97,4 , hy.x = hy . x © 0.530 Btu/sec* ft?* °F. 2. For the fuel tubes (78) A? = WDfLNf ; (79) Af = 2erL , (80) h; kf [ 0.14 = 0.027 — Re%® pr /3 (——) , Df f f N = number of tubes, r = mean radius, ft, Re = Reynolds’ number, Pr = Prandtl’s number, (fi;> = ratio of viscosity of fuel at f bulk temperature to viscosity at surface temperature. For a fuel velocity of 3.7 ft/sec, an A* of 5.25 ft?, an Af of 5.90 ft?, and a Df of 0.09285 ft, the values of the terms in Eqs. 78, 79, and 80 are Re = 7970 , Pr = 5.02 , h% = 0.294 Btu/sec* ft2-"F h, = 0.262 Btu/sec* ft?+°F The differential equation for steady-state heat conduction with internal heat generation 1s i (81) V2T= - 1 ’ kBeO where g' = internal heat generation, Btu/sec* ft?, = thermal conductivity of BeO, Btu/sec* ft? (°F/ft). Although q' varieswith radial distance kBeO and ky,, varies with temperature, both will be assumed constant and equal to their average values. This is done for simplicity and undoubtedly results in solutions that are only approximate. The values are g' = 39.8 Btu/sec*ft? and k.o = 0.0058 Btu/sec:ft? (°F/ft) . The solution of the differential 31 equation for, the infinite cylinder case 1s dT ¢y (82) — = 3431 r +—, r r (83) T = 17155 r* + ¢, In r + ¢, , where T = temperature, °F, r = radial distance from center of core, ft, ¢; and ¢, = arbitrary constants. The boundary conditions are dT hyak (84) — = (T - Ty K) , dr kBeO ) at r = 0,15217 ft, -h dT (85) -7 (1 - 1200) dr kg.o at r = 0,13250 ft (the mean fuel temper- ature 1s approximately 1200°F), Solving for ¢; and ¢, by using the boundary condition gives (86) c, = 1573.87 - 1.1596 T, , (87) c, = 3110.40 - 1.2666 T, (the solution requires that many significant figures be carried). The temperature differences at the BeO-to-NaK and BeO-to-fuel interfaces and the heat added to the NaK and to the fuel are given in Table 5. The values given in Table 5 are for one of the four rod holes. A check of some of the numerical work, by the method of superposition, is possible: QBeO The temperature difference from the fuel to the NaK across the beryllium oxide because of internal heat gener- ation only is 131,7°F when all the generated heat enters the NaK, and -88.8°F when all the generated heat enters the fuel, q'W(ri—rfiaK)L =27.9 Btu/sec The resistance to heat transfer between the NaK and the fuel 1is 1 <__> - 0.6574 | . hA N a K 1 <—A> = 0. 6475 ’ h f 1 (-) = 6.5818 | hA BeO 1 (——) = 7,887 hA f-Nak The fuel-to-NaK temperature differences for the various NaK temperatures are given 1n Table 6. results As can be seen, the agree qulte well with the results given 1in Table 5. TABLE 5, TEMPERATURE DIFFERENCES AND HEAT TRANSFERRED AT THE BeO0-TO-NaK AND BeO-TO-FUEL INTERFACES TEMPERATURE DIFFERENCE (°F) TNK (OF) QN K(G) Q (b) QBO=QNK __Q (C) & BeO-to-NaK BeO-to-Fuel a f © a f 800 40.74 -22.01 61,97 ~33.,97 28,00 1000 24,06 -5.57 36. 60 —8.60 28,00 1075 17.80 0.60 27.08 0,93 28.01 1200 7.38 10, 87 11,23 16,78 28.01 1300 ~0, 96 19,09 ~1, 46 29,47 28.01 (a) - Quag = heat transferred to NaK, Btu/sec. (b)Qf = heat transferred to the fuel, Btu/sec. ( C)QBeO = heat generated in BeO, B:u/sec. 32 TABLE 6. TEMPERATURE DIFFERENCES AND HEAT TRANSFERRED AT THE FUEL-TO0-NaK INTERFACE Tyak ef-NaK GENERATED ef,NaK = %Be0 Qf Onak (°F) (°F) HEAT ENTERS (°F) (Btu/sec) (Btu/sec) 800 400 NaK 268.3 -34.0 62,0 1000 200 NaK 68, 3 -8.7 36.6 1075 100 NaK and fuel 1200 0 NaK and fuel 1300 ~100 Fuel -11.3 +29.3 -1.4 The heat removed from the NaK by the helium flowing through the rod holes is calculated in chap. 5, ‘Rod and Instrument Cooling System,” for the various rods and instruments. Summary. A plot of the heat added to the NaK circuit vs, the mean Nak temperatures for the various sources of heat addition is shown in Fig. 18, A plot of the net heat that must be removed from the NaK in the reflector coolant heat exchangers vs. the mean NaK temperature is shown in Fig. 19, By cross-plotting these two figures, the mean NaK temperature 1s obtained; the cross-plot is shown in Fig, 19, The mean NaK temperature 1is about 1172°F, and at that temperature, 640 Btu/sec (675 kw) 1s removed from the reactor by the reflector cooling system. The minimum and maximum NakK temperatures are about 1105 and 1235°F, respectively (Fig. 1). The maximum pressure-shell temperature 1s about 20°F greater than the maximum NakK temperature (see previous work in this section) and is therefore about 1255°F, PRESSURE DROP IN FUEL MANIFOLDS AND CORE TUBES The fuel flows from the heat exchangers through the surge tanks and pumps and into the inlet manifold of the reactor, whereit i1s distributed into the six parallel passes through the core lattice. Upon leaving the core lattice, the fuel enters the outlet manifold. From the outlet mani fold, the fuel is returned to the heat exchangers. For a fuller under- standing of the circuit, see Figs. 1 and 9, The problem is to determine the pressure drop (or drops) of the Da! 19107 700 600 500 400 300 200—— HEAT ADDED TO NaK IN REACTOR (Btu/sec) 100 SHELL, AND NaK O [ TRANSFERRED TO HELIUM IN - ROD-COOLING SYSTEM -100 900 1000 1100 1200 1300 MEAN NaK TEMPERATURE (°F) Fig. 18, Heat Removed by NakK. 33 DWG. 19108 1400 r 1200 \ HEAT ADDED TO NeK IN REACTOR 1000 \ \ ! 800 HEAT TRANSFERRED (Btu/sec) 600 \ HEAT REMOVED FROM NaK IN HEAT EXCHANGERS 400 200 | 0 I 900 1000 1100 1200 1300 1400 MEAN NgK TEMPERATURE {°F) Fig., 19. Heat Added to and Removed from NaK vs. Temperature. fuel from the time 1t enters the inlet mani fold until 1t leaves the outlet mani fold. The pressure drop of the fuel in flowing through the i1nlet manifold, core lattice, and outlet manifold 1is due to factors: curvature of the tubes or pipes, contraction losses, expansion losses, and losses 1n the pipe fittings and square elbows. The formula for loss 1in pressure because of friction 1is five friction, L 2 op, = 45 =2 (88) , D 2g where f 1s the friction factor given by f= 0.046/Ny? for turbulent flow. (") The curvature loss 1s given more simply by 2 v (89) 6P, = k2 2g In this expression, k_ is a constant that 1s taken from the curves of Cox, 34 Glen, and Germano (cf., p. 191 and 193 of ref. 12). The expression for contraction loss 1s very similar to that for curvature; pvy 2g where k 1s a constant that 1s dependent AP = k X (90) 1 upon the ratio of the smaller area to the larger. Values for k are found in the work of McAdams (cf., p. 122 of ref. 11). The loss caused by expansion 1s determined from (v, = v,)? (91) AP = p 2g a fitting or square elbow 1s calculated by using the frictiondrop equation and replacing L by L,; that is, The pressure drop 1n L 2 AP, = 4f S EY (92) . F D 2g The L_,'s for square elbows and various fittings are given in ref. 13; they depend upon the tube or pipe size. The symbols used i1in the equations above have the following meanings and units: AP = pressure drop, lb/ft?, f = friction factor, dimensionless, L = length, ft, D = hydraulic diameter, ft, £ = density, lb/fta, v = average velocity given by fe? of fluid per second/ft? of cross section, ft/sec, g = gravitational acceleration, 32.2 ft/sec?, k = constant, dimensionless, kc = constant, dimensionless, v, = average linear velocity upstream, ft/sec, v, = average linear velocity down- stream, ft/sec, L_ = equivalent length of straight pipe, ft, Np, = Reynolds’ number. The subscripts have meanings: the following f = friction, ¢ = curvature, X = contraction, Y © expansion, e = equivalent, F = fitting. In the pressure drop calculations, it was assumed that the flow of fuel would be equally distributed between the six passes through the core. Although this 1s a reasonable as- sumption, 1t 1S not qulte true, as will be demonstrated by the calculated data. The same value of density was used throughout the calculation, but the viscosities corresponded to the mean temperatures in the inlet manifold, core lattice, and outlet manifold. The properties used were: Density, p 187 1b/ft> Viscosity, p Inlet manifold 12,5 cp Core lattice 9.0 ¢cp Outlet manifold 6.8 cp The flow rate of the fuel was considered to be 0.150 cfs. Figure 20 shows sketches of the inlet and outlet manifolds. In this figure, the outlets of the 1nlet manifold are numbered 1 to 6 and the inlets of the outlet manifold are numbered corre- spondingly. Thus outlet 1 of the inlet manifold 1s connected by a tube to inlet 1 of the outlet manifold, etc., and the fluid paths from the entrance tee of the 1nlet manifold to the exit tee of the outlet manifold are given designations such as “l1-1.7 The geometries of the two manifolds are shown in Figs. 21 and 22. The these manifolds were calculated by using Eqs. 88 through 92. The tubes carrying the fuel through the core lattice are often referred to as “serpentine” tubes because each tube has 10 bends and 11 straight lengths. For each tube the equivalent straight length 1s L = 42,20 f¢. pressure drops 1n The pressure drop for each path through the system being considered was easily calculated by using the equal flow rate assumption and Eqs. 88 and 89. O The results are tabulated in Table 7. Of course, as can be seen, the flow will not be distributed equally among the six parallel paths through the core lattice. In fact, the flow rate may vary as much as 2.5%. Thus a maximum temperature difference of the order of 9°F may exist in the fuel exit temperatures from the various DW!. i9109 tubes. INLET MANIFOLD OUTLET MANIFOLD Fig. 20. Fuel Manifolds. 35 9¢ INCONEL CONCENTRIC \ REDUCER 1'% x 1-in. IPS~ INCONEL WELDING COLLAR INCONEL LEG {-in. IPS SCH 40 INCONEL LEG —~_ ; 1Y% -in. IPS SCH 40 . | T AL 2 | x o N SECTION A-A INCONEL STRAIGHT TEE 2x2x2-in. IPS——____| DWG. E-A-1-1-3 B —INCONEL LEG 1-in. IPS SCH 40 1.049-in.D REAM TO 1.053-in. AFTER WELDING \ ey 2 | INCONEL CASING TUBE 3l-in. 0D x Yg-in. WALL INCONEL. LEG 7Y, - R 2-in IPS SCH 40 S INCONEL OQUTLET LINE 2-in. IPS 5CH 40 ™ &:s < "o ——INCONEL CONCENTRIC " REDUCER 2 x 1%~ in. IPS INCONEL LEG 1‘/2-1‘n. IPS 5CH 40 Fig. 21. Fuel Outlet Manifold. O 24 in. D500 OWG D-A-1-1-1-3A LINLET LINE 1% IPS SCH 40 PIPE ECCENTRIC REDUCER 12 IPS = 1 IPS—— -~ _REDUCER 2IPS - 1% IPS INLET LEG o 1 IPS SCH 40 PIPE- - L - TEE 2x2x2 e 1‘//} «~—INLET LINE 2 IPS SCH 40 PIPE “ COVER REMOVED iN THIS VIEW—— - \‘\\\‘ o f ; - i} /.‘ .. 59 / e / - - /.r/ // . . \ i | ‘ / — 21 H‘ COVER. BODY ST T— : f | | f | \ > \\ | ! i 5 MINLET LINE \ INLET LINE 1 | i ‘ N TEE : ‘ | 1 e ! } | h : 1 ‘ \SLEEVE NOTES: - et ALL MATERIAL 1S INCONEL. | | i | | | ALL DIMENSIONS ARE IN INCHES. \ | | Fig. 22. Fuel Inlet Manifold. 37 TABLE 7. PRESSURE DROP IN FUEL MANIFOLDS AND CORE TUBES PRESSURE DROPS (lb/ftz) TOTAL PRESSURE DROP 1-1 627.17 613.0 172.5 1413 9.81 2-2 605.7 613.0 155.7 1374 9.54 3-3 627.7 613.0 155.7 1396 9.70 4-4 627.17 613.0 172.5 1413 9.81 5-5 605.7 613.0 121.90 1340 9.30 6-6 627.17 613.0 121.0 1362 9. 46 TEMPERATURE GRADIENTS IN THERMAL where SLEEVES The fuel tubes pass through the pressure shell heads in the manner shown schematically in Fig. 23a. The sleeve connecting the pressure shell and fuel tube 1s at the pressure shell temperature at one end and at the fuel tube temperature at the other end. At the fuel tube outlet, the fuel tubes are at 1500°F; the pressure shell temperature at this point 1is difficult to determine, but it 1is probably not less than 1150°F, The sleeve gains heat from the fuel tube through the NaK between the tube and sleeve; the NaK i1s assumed to be stagnant. Heat lost by the sleeve to the surrounding helium atmosphere may be neglected because the helium is at about 1200°F, The problem was simplified by considering the sleeve, the fuel tube, and the NakK between the sleeve and the fuel tube as a single cylindrical tube. The temperature was assumed to be constant across any cross section of this cylindrical tube, and an thermal average conductivity for the tube was used. (The conductivities of NaK and Inconel are nearly equal.) The differential equation governing the flowof heat in the sleeveis (Fig. 23b) d*T 2 (93) ~ka = hc(1500 - T) dx 38 k = thermal conductivity of the composite tube, Btu/hr*ft? (°F/fc), a = cross-sectional area of the composite tube, ftz, BWG. 90 13, in. e 1 %, ~in-IPS SLEEVE PRESSURE SHELL FUEL TUBE —=— { A--‘ 125N | . 1 PRESSURE SHELL /COMPOS!TE TUBE —h (&) FUEL Fig. 23. Thermal Sleeve. ’s s T = temperature, °F, x = distance from pressure shell, ft, h = fuel heat transfer coefficient, Btu/hr+ ft?: °F, ¢ = circumference of inside of fuel tube, ft. The boundary conditions are (94) T = 1150°F, at x = 0 , (95) T = 1500°F, at x = 0.1146 . The fuel heat transfer coefficient maybe evaluated by using the following formula: k 0,14 (96) h=0.027-—ae°-spr‘/3 , D v 3 where k = thermal conductivity of the fuel, Btu/hr-ft? (°F/ft), D = fuel tube inner diameter, ft, Re = Reynolds’ number for the fuel, Pr = Prandtl’s number for the fuel, (L il ratio of fuel viscosity at bulk Fs temperature to fuel viscosity at surface temperature, For this case, k = 1.5 Beu/hr-ft? (°F/ft), D= 0,0929 f¢, Re = 14,100, Pr = 2,85, 0.965 ST LE \___/o o F-Y i h = 1250 Btu/hr-ft?:°F, In Eq. 93, k = 13.7 Btu/hr*ft? (°F/ft), a = 0.0129 fg2, c = 0,422 ft; therefore 2T 6 - 2980 T = -4.48 x 10 dx? The solution of Eq. (97) 97 1is (98) T=c, e~®H%r+ 1500 , The first boundary condition, Eq. 94, gives (99) ¢, * ¢, = =350, The second boundary condition, Eq. 95, b 654 I+Cz gives (100) 520 ¢, + 0.001923 ¢, = 0 . Therefore c, = 0,001294 and c, = - 350 Thus Eq. 98 becomes (101) T = 0.001294 54-6=x - 350 e=%%-6x 4+ 1500 and the first derivative of T with respect to x 1s 54,64« dT (102) — = 0.07065 e dx + 19,110 e Plots of Eqs. 10l and 102 are shown in Fig. 24, The maximum temperature gradient is about 1600°F per inch. -54. 6! Temperature in Fuel Tube Elbows as a Result of Afterheat of Residual Fuel. There 1s a possibility of fuel remaining 1in the U bends of the reactor fuel tubes after dumping. This residual fuel will rise in temperature because of internal heat generation, and it 1s desirable to know the maximum temperature that will be attained. Since the activity of the fuel decreases with time after shutdown, an equilibrium will be reached when the heat generation rate 1s the same as the rate of the heat Once this equilibrium has been the fuel temperature will loss. reached, decrease. The total heat generation rate of the fuel is given 1in another portion of this report. From this, the heat generation rate of the fuel in a U bend 1is volume of fuel in U bendx total fuel volume where Q = heat generation rate, Btu/sec Qf = total heat generation rate of fuel, Btu/sec. The temperature rise in the U bend will be greatest when the reflector coolant system 1s filled with helium (Fig. 9). Under this condition, heat 1s removed from the tube by free convection and radiation. The free 39 DWG. 19111 1600 2000 1500 1600 £ T ,///// 5 £ 1400 1200 ~ w = o =2 > / L é 3 i S = w ~ 1300 800 % \\ c @ w a \ s L - 1200/ : 400 \\ 1100 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 DISTANCE FROM PRESSURE SHELL (in.) Fig. 24. Temperature and Temperature Gradient in Thermal Sleeve vs. Distance from Pressure Shell. convection loss 1s (104) q, = hAG where q, = heat transferred, Btu/sec, h free convection heat transfer coefficient, Btu/sec*ft?+°F, A= surface area of tube, ft?, ¢ = temperature difference between the surface of the tube and the helium, °F. The radiation loss 1s given by 0.173 3600 4 4 « (Tsink> “1'\7100 / "~ \Too ’ € = radiation emissivity, di- mensionless, absolute temperature of the surface of the tube, °R, (105) g4 = where tube 40 T,;,x = absolute temperature of the sink (surrounding material), °R. The total heat loss 1s (106) q = g9, 1t qp Jakob has given Nusselt’s number (cf., p. 525, Fig. 25-1, of ref. 14) as a function of the product of Grashof’'s and Prandtl’s numbers. The value of Nusselt’s number for the existing helium conditions was taken from Jakob’'s work, and the free- convection heat transfer coefficient was determined. The temperature change of the fuel and the metal of the tube per unit time 1s (107) pr =279 chp where AT = temperature change, °F/sec, chp = summation of heat capacities of fuel and metal of tube, Btu/°F, w = weight of material, lb, ¢, = specific heat of material, Btu/lb- °F. The data required to make the calculations are listed 1n the follow- ing tabulation; only the portion of the tube that 1s below the tube sheet 1s considered: 1. For the metal tube, Area, A Volume of metal 0.226 ft? 1.86 in.° 0.307 1b/in.> 0.11 Btu/1b*°F Density, p Specific heat, ¢, 2. For the fuel, Volume of fuel Density, p 4.74 % 1073 f£¢3 187 1b/f¢? Specific heat, c, 0.26 Btu/1b*°F Total fuel volume of entire system 7.75 fi° The temperatures of the fuel at various times after shutdown were calculated by numerical methods for sink temperatures of 1200 and 1300°F, The calculated data for the two sink temperatures are given in Fig. 25. 1600 DWG 19112 1500 /z§\ 1.64 x 107 0.85 x 107 Equivalent diameter, ft 0.0929 0. 0929 Reynolds’ number 7700 14, 100 Prandtl's number 5.20 2.85 u 0,14 — 0.97 0.97 p's Heat transfer coef- ficient, Btu/hr*ft2*°F 945 1260 The solution of the differential equation, Eq. 108, 1s df q'x (112) —_= - t o, , dx k 2 q x 2k The boundary conditions, Egs. 109 and 110, give (113) g = - + c,x + €, (114) c, = 0, q.rT2 q"T (115) c, = + —, 2k h and Eq. 113 becomes 42 ! ! - (116) 6= (72 - 27 + 12 2k h The maximum temperature in the solid occurs at x = 0; therefore qr7_2 q"T = + = + — + (117) T, = Oha* T, ot T Ty where T ., ° maximum temperature 1in the solad, °F, Tf= temperature of the flowing o fuel, °F. A tabulation of values of some of the terms of Eq. 117 for values of 7 of 0.1 and 0.2 in. is presented below: Tf, °F 1170 1490 T, in 0.1 0.2 0.1 0.2 2 9'7’ o , °F 380 1418 197 787 2k 4'7' —\, °F 145 289 56 112 h T , °F 1694 2878 1743 2388 max The values for the maximum temper- atures of the solid indicate that unless the solids found when NaK and fuel are mixed have a lower melting point than that of Inconel there 1is danger that a small leak might result 1in the formation of a solid deposit which would reach a high enough temperature to melt the Inconel tube wall. Chapter 3 FUEL HEAT DISPOSAL SYSTEM PERFORMANCE OF FUEL HEAT DISPOSAL SYSTEM Heat Transfer. The heat added to the fuel 1n the reactor 1s disposed of by circulating the fuel to a heat exchanger where 1t gives up its heat to helium. The hot helium 1s then passed through a heat exchanger where it gives up 1ts heat to water. The fuel and helium recirculate; the water 1s dumped. There are actually four fuel-to-helium heat exchangers and four helium-to-water exchangers. These exchangers are arranged (Fig. 1) so that all four fuel-to-helium exchangers are 1n parallel on the fuel side and all four helium-to-water exchangers are in parallel on the water side. The helium circuits are arranged so that there are two parallel circuits and each circuit contains two fuel-to-helium and two helium-to- water exchangers in series (the exchangers alternate, of course). Figures 26 and 27 show the details of the two types of heat exchangers. The performance of the fuel heat disposal loop over a range of operating conditions 1s calculated below. The fuel heat disposal obeys the following relations: system (1) Q = Wf ¢ (Tf - Tf) , (2) Q = wHe CHe (Tl;e - THe) ! (3) Q=W ¢ (T -T) , (4) Q = hf-He Af-He 6f-He ! (5) Q - hHe-w He s w He-w ! where Q = heat transferred, Btu/sec, W = weight flow, 1b/sec, T' = maximum temperature, _F, T = minimum temperature, F, ¢ = specific heat, Btu/lb-*°F, h = heat transfer coefficient, Btu/sec‘ft2'°F, A = heat transfer area, ftz, § = effective log mean temperature difference, °F, and the subscripts refer to f = fuel, He = helium, w = water, f-He = fuel-to-helium heat exchanger, He-w = helium-to-waterheat exchanger. The heat disposal systemis operated with the following restraints and conditions: 1. The fuel flow 1s held fixed at 28.2 1lb/sec. 2. The water outlet temperature 1s thermostatically controlled and held fixed at 135°F. 3. The water inlet temperature will vary with the time of year, but for this analysis 1t has been assumed to be fixed at 70°F. 4, The mean temperature of the fuel 1s fixed because the reactor 1is sel f-controlling to a constant mean temperature. The design mean tempera- ture is 1325°F. Calculations were also carried out for mean temperatures of 1225 and 1425°F ¢to give some indication of the effect of a change in mean fuel temperature. The helium weight flow 1s the independent variable; the flow 1s controlled by variable speed hydraulic motors which drive the two helium blowers. The dependent variables are Q, W, T}, Tf, T;e, and Ty _. Thus there are six unknowns and si1x equa- ti1ons: the five equations listed above and the one i1nherent i1n the fourth condition, namely: T + T f f (6) ———= a constant . 2 Before these equations can be solved, the heat transfer coefficients and areas must be calculated for the two exchangers. The over-all hA’s are (1) (hA), . 1 1 1 -1 = + + (hA) (hA) g, (hA) J f-He 43 vy ————2f1 3in —— e e e in. = g S - 2Y-in. SCH 160 INGONEL s PIPE FOR MANIFOLDS - e o MATERIAL AND MATERIAL SPEGIFICATIONS DESGRIPTION MATERIAL SPECIFICATION QUALITY B SHELL, TUBE SUPPORT PLATES | STAINLESS STEEL | ASME-5A-240 | GR 5 TYPE 304 f MANIFOLD , WELD ELL AND NICKEL , CHROME PIPE AND IRON ASTM*B-16? INGONEL SHELL SUPPORTS, MANIFOLD SUPPORTS, FLANGE BARS AND | STAINLESS STEEL |COMMERGIAL | TYPE 304 BAGKING BARS 6 in— . 16 in_44444““ - - : TUBES N FOME | ASTM-B-167 | INGONEL | FINS _ | sTANLESS STEEL | TYPE 304 - BOLTS STAINLESS STEEL | ASME-SA-193 | GRADE B-B ”””””””””” 'DESIGN DATA SEGTION G- { | DESIGN PRESSURE SHELL SIDE 6 in WATER 2. DESIGN PRESSURE TUBE SIDE 25 psi < 3 DESIGN TEMPERATURE SHELL SIDE 1500 °F 2 WY e @ 4. DESIGN TEMPERATURE TUBE SIDE 1500 °F ~ 5. HYDROSTATIC TEST PRESSURE TUBE SIDE 500 psi . -3~in. TAPPED HOLES o ’ Y, in, E 38-g-in | et | . _ 2% 1 FOR GAP BOLTS f% 20 7 in. 77_:: “A;"'""'fff'fff” i E fi o] Lo o o o o Q o , Lo A D e e e - o T | j T T A € | o |- ——— i + 1 TUBE VENT AND i Yy |0 o ‘F\:\l - / - T T T 7 DRA!N,? STRAIGHT A \/ “ i ™ e e . LENGTHS " " S oL = N (U ‘ l ¥ 5] T [ q’ | T HET —_— Pl e | | : ;/,fmj'—l%;_f I-in. OD NO. 12 BWG o = - - : T N M ; (‘: | | . INGONEL TUBES, 43 c R } ) G | o~ | ||+ STRAIGHT LENGTHS, | u ] - 1 || | 2=inOD STAINLESS o |- - - \ (J O | | | STEEL FINS 0.024-in I i _ i ! ! [ | | THICK . "I [ | I \ A e P! ! TP — — SUPPORT PLATE TO | ! ; A = | b—— 1. ! - =—lerr— — = BE GUT IN TWO | M | | A e S SEGTIONS AND | | 0 1 N o | o o - WELDED TOGETHER | | ! T | . AFTER ASSEMBLY—. | | A% St || S s — i 0O 1. . . - F o= (T I 0 - ! - 1 L — —-- £ ! ‘ 1‘ O‘/- f/\/;_—“ — e = O } c | H} — ——————— — w L | o R | ! - 4 Y _ P | o l fiv[} - S - @ : 1 } L 5 L i T — T T — 1 - © Lo o Q\ ' o < 2 e . / L N . e ey 6 _ I 54 ~in. OD ¥ 0065 WALL L] %8 * 17pmin. BAR DRAIN TUBE SECTION E-E Fig. 26. Fuel-to-Helium Heat Exchanger. 2 ft—a'gin- T i = 1 o | =z w i - : ¢ =Z 5 . =" £ rc\]> &L = " g w [ | e - ul = < L 3 ft=2 in——————e UNCLASSIFIED DWG. A-3-2-214 "~ Y- in DIA. RODS “Yg-in. THICK FULL FACE ASBESTOS CLOTH GASKET. 5 Y 0 0 C 0 0.0.0 0 O “Yg-in. THICK FULL DURABLA GASKET Yp-in WIDE AT PARTITION. | r | | e 2 H=B Y i e e e — 3ft—2'% in. e ‘ ' 3, . P DESIGN DATA *"—'[ =— 29 in. i = % T - - T SHELL | TUBES } © ! O; DESIGN PRESSURE 6-in Hy0 | 50 psi b = o s, DESIGN TEMPERATURE | 1S00°F | 340°F = —_ 3 o } l ] ! ; ° FEET ] L | ; ; o i f T T 0O 0 & 0 0 0 0 0 0 O 1 1 0 ! HALF VIEW CF STAT. HEAD WITH COVER REMOVED MATERIAL AND MATERIAL SPECIFICATIONS DESCRIPTION MATERIAL SPEC. QUALITY SHELL FLANGE AT TUBE SHEET, GAS INLET FLANGE, ASME Sa— SHELL AND SHELL COVER PLATE, BLANKING-OFF PLATE, |STAINLESS STEEL | 40 GRS TYPE S-304 TUBE SUPPORT BAR, BACKING-UP BAR. STAT. HEAD PLATES, STAT. HEAD FLANGES, GAS GUTLET ASME FLANGE, STAT. HEAD PARTITIONS, STAT. HEAD TIE PLATES,| FIREBOX STEEL Ao GRADE C STAT. HEAD COVER PLATE, TUBE SHEET. 3-in,, 150 Ib. WELDING NECK FLANGE. FORGE STEEL ASME SA-{BI GRADE 1 3-in SCH. 40 PIPE. SEAMLESS STEEL | ASME SA-106 GRADE A TUBES, TUBE BENDS. SEAMLESS STEEL | ASME SA-179 MIN WALL FINS COPPER COMMERCIAL STAT. HEAD GASKETS. DURABLA COMMERCIAL SHELL GASKET SMEARED BOTH SIDES WITH PLASTISEAL. | ASBESTOS CLOTH | COMMERCIAL BOLTING FOR TUBE SHEET AND SHELL FLANGE. STAINLESS STEEL | ASME SA-193 B8 NUTS AT TUBE SHEET AND STAT. HEAD COVER PLATE. BETH OIL QUENCH | ASME SA-194 CLASS 2H BOLTING FOR STAT. HEAD COVER PLATE. ALLOY STEEL Fig. 27. Helium-to-Water Heat Exchanger. ro 4L 45 and (8) (hA),, _ w 1 1 1 ]! = + + { (hA),, (hA)_ (hA) } ’ He= w where the subscript m refers to the metal of the tube wall. The heat transfer coefficients of the fuel are calculated from the curve of ref. 11 (p. 193). The heat transfer coefficient of the water 1is k ; 6,14 (9) h =0.027 —* Re%:8 ppi/3( L w D v w /-Ls w v (15)) (Sieder-Tate relation where k = thermal conductivity, Btu/sec* ft? (°F/ft), D = equivalent diameter, ft, Re = Reynolds' number, Pr = Prandtl’s number, L = viscosity at bulk temperature, 1b/hr* ft, p, = viscosityat surface temperature, 1b/hr- ft. The liquid-side areas are: (10) Af = WDfo_He and (11) A, = 7D Ly, where L 1s the total effective length of the heat exchanger tubes 1n feet. The resistance of the metal 1s DO In 'B“ f/f-He 1 (12) { J = ()] o 2k ae Ly, and Do In| — Df He.w (13) |——— = , {(hA).J 27T(km)l'le-w LHe w He - w - where D is tube outside diameter 1in feet. The heat transfer coefficients on the gas side are taken from a corre- 46 lation by Kern of data by Jameson and Tate and Cartinhour (cf., p. 555 of ref. 8). Kern’s correlation curve may be approximated by the following equation: (14) h He k 0,14 He Ret723 p 173 [ K D eHe I‘He s He /J": He = (0. 092 where DHe for the fin and tube con- figuration 1s defined as 2(A0+Af) (15) Dy, = —— . , € m(projected perimeter) where A = tube outside bare area, ft2, 0 A, = fin area, ft?, and the projectedperimeter 1s the sum of all the external distances 1in the plan view of the finned tubes (ft). The mass velocity used i1n the Reynolds’ number is computed from the free flow area 1in a single bank of tubes at right angles to the gas flow. The helium—-side heat transfer area 1s (16) Ag, = A, + an f ’ where i 1s the fin efficiency.(16) Table 8 lists the pertinent infor- mation obtained from the heat exchanger designs (Figs. 26 and 27) and Egs. 7 through 16. Values are given for three different flow rates of helium and of water; curves were plotted from these values and used 1n the solution of Egs. 1 through 6. The data of Table 8 were used to solve the six simultaneous equations (Eqs. 1 through 6} for various values of the independent variable - helium weight flow. (Inasmuch as the water heat transfer coefficientis a function of the water flow rate, 1t was necessary to assume a water flow rate for each helium flow rate and solve the equations by i1teration.) The results of the solution of Egqs. 1 through 6 are shown in Figs. 28 and 29, where the heat transferred, maximum fuel temper- ature, and maximum and minimum helium TABLE 8. HEAT EXCHANGER DATA FUEL-TO-HELIUM HELIUM-TO- WATER HEAT EXCHANGER HEAT EXCHANGER . Tube outside diameter, in. 1.0 0,625 Tube wall thickness, in, 0.109 0,049 Tube material Inconel Steel - Fin outside diameter, in. 2.0 0.75 Number of fins per inch 7 16 Fin thickness, in. 0.024 0,014 | Fin material Stainless steel Copper | Tube transverse pitch, in. 2,75 2,25 Tube longitudinal pitch, in, 2.43 1,47 Number of tubes per exchanger 43 360 Number of tubes transverse to flow (per exchanger) 9 12 Exchanger height, in. 24,75 27.0 Exchanger width (also active tube length), in. 26,25 27.5 Total active tube length per exchanger, ft 93.65 825 Liquid flow area per exchanger, fe? 0.01006 (First bank 0.0545 group*), 0,00671 (Second bank group*) . Liquid flow rate per exchanger, lb/sec 7.05 10,61, 7.08, 3,54 Liquid velocity, ft/sec 3.74, 5.61 3.11, 2,08, 1.04 Reynolds’ number 5890, 8840 19,000, 12,700, 6,340 . Liquid heat_transfer coefficient, Btu/sec* ft?*°F 0.24, 0,38 0.27, 0.20, 0.11 Liquid heat Eransfer area per exs- changer, ft 11.15, 8,02 114 (hA) || 414 PeT exchanger, Btu/sec*°F 2.676, 3.048 30.8, 22.8, 12.5 Total 5.724 (1/hA) |; .uiqa Per exchanger, sec*°F/Btu | 0.175 0.0325, 0.0439, 0,080 (1/hA). per exchanger, sec*°F/Btu 0.137 0.00456 Helium-side equivalent diameter (DHe)’ in. 1, 447 0.670 Helium free flow ratio 0.575 0.71 Helium flow area per exchanger, fe2 2,60 3.66 | Helium flow rate per exchanger, 1b/sec 1.5, 1.0, 0.5 1.5, 1.0, 0.5 Helium Reynolds’ number 4050, 2630, 1290 1330, 860, 420 Helium heat transfer coefficient, 0.0083, 0,0061, 0.0080, 0.0059, 0,0035 Bru/sec*ft?+°F 0.0036 Fin efficiency 0.37, 0.43, 0.55 1.0, 1.0, 1.0 | Helium heat transfer area,** 2 115, 131, 162 402, 402, 402 | (hd),, per exchanger, Btu/sec*°F 0.955, 0.800, 0.580 3.22, 2.37, 1.40 i (1/hA),_ per exchanger, sec* F/Bru 1,05, 1.25, 1.72 0.310, 0,422, 0.714 *The liquid sideof the fuel-to-helium heat exchanger is divided into two groups of tubes. The first bank group has three tubes in parallel and is connected in series with the second bank group, which has two tubes in parallel. . 44 % ) ea’ varies with helium flow rate because the fin efficiency varies with helium flow rate {(cf., Eq. 47 700 — ‘ E—— OWG 19113 MEAN FUEL TEMPERATURE (°F | | | | T 1600 - e 1500 1400 1300 MAXIMUM FUEL TEMPERATURE (°F) 1200— 3000 T = 2 L D 2000F-- - I gy i | L w) : : S ' ' ] g 1000— e b T o - L O 2000 4000 6000 8000 10000 HELIUM VOLUMETRIC FLOW (cfm) Heat Transferred and Helium Fig. 28. Maximum Fuel Temperature vs, Yolumetric Flow. temperatures are plotted against helium volumetric flow for the three different values of mean fuel tempera- ture investigated. At design point, by the reflector coolant cooling circuits. Therefore, 1s to be removed by the fuel. Film Temperature. Because the fuel hasa high melting point (about 970°F), the minimum fuel film temperature must be calculated to determine the situation with respect to freezing of the fuel film. The minimum fuel film tempera- ture at any point may be calculated from the relation 700 kw 1s removed and rod 2300 kw Q (17) T =T -, fmin fbulk (hA)f where Tf = minimum fuel film temper- min ature at the point 1in question, °F, 48 DWG. 19114 900 BOO 700 600 < | o QUTLET OF FUEL-TO-HELIUM EXCHANGER ..D_ 500 b < o> & 5 [ a : = Pa i bog = 400 - O 2 5 % - | MEAN FUEL @ S | TEMPERATURE T @ {°F) 300 o L g o 200 j 160 INLET OF FUEL=TO-HELIUM E o 2000 4000 6000 8OO0 HELIUM VOLUMETRIC FLOW {cfm) 10,000 12,000 Fig. 29. Maximum and Minimum Helium Temperature vs. Helium Volumetric Flow. Tf = bulk fuel temperature at the bulk . . : OF point in question, . The other symbols mean the same as they did previously, except that the fuel heat transfer coefficient, hf' must be evaluated locally, that is, at the point 1n question. Several critical points were investigated 1in the fuel-to-helium exchanger, and a plot of the lowest of the temperatures vs. helium volumetric flow (and various mean fuel temperatures) is shown 1in Fig. 30a. Pressure Drop. The pressure drops in the fuel and in the helium have been calculated for the exchangers. The fuel pressure drop was calculated by using the customary Fanning equa- tion¢!!) for the straight sections, and the curves presented by Cox and Germano¢1%) for the bends, exists, and entrances. Since the fuel flow 1is constant and the properties do not vary substantially i1n the range of mean fuel temperatures considered, the DWG. 19415 1500 - , | | ] : | | — i S 1400 xr——-—-————------ e ey | o | @ 2 | g a g 1300 N ™ i | I = co 3 N . MEAN FUEL 1200 S TEMPERATURE (°F }| > \‘\ s l =~ 1425 Z 100 \ 1 | = \\\\\J o] s (G’) \ | 1000 I T~ 1225 | =T e Q) i [&) 2 Sr—1 % o = o O| 5T @ wE ol / o8 ‘ p A ” s | & T3 | | oz FUEL-TO- HEL UM EXCHATEEB//’ %04 | | oo o // HEL {UM - TO- WATER ! EXCHANGER (5) | C | ‘ | i | 0 2000 4000 6000 8000 10,000 12,000 HELIUM VOLUMETRIC FLOW (cfm) Fig. 30. Minimum Fuel Film Tempera- ture and Helium Pressure Drop vs. Helium Volumetric Flow. fuel pressure drop 1s constant and equal to about 17 psi1. The pressure drop in the helium was calculated by the method given by Gunter and Shaw: ¢17) H, = viscosity at surface tempera- tures, lb/hr-ft, D;. = equivalent diameter (cf., Eq. 19), ft. The equivalent diameter in the Gunter-Shaw correlation 1s , 4 X net free volume (19) DH = , © A, + A f © where Af and A have the same meanings as previously. The values of Dy, are 0.0438 ft for the fuel-to-helium exchangers and 0.1365 ft for the helium-to-water exchangers. The friction factor, f, which is a function of Reynolds' number, 1s evaluated from the Gunter- Shaw correlation. The helium pressure drop 1s plotted against helium volu- metric flow for both exchangers 1in Fig. 30b. The helium pressure drop 1s not greatly affected by the mean fuel temperature, and thus the curves of Fig. 30b are valid for the range of mean fuel temperature considered. The pressure drops in the fuel and in the helium for the remainder of the fuel and helium circuits have been calculated by using the Fanning equation and the Cox and Germano data. Figure 1 shows the pressure at various points in the fuel circuit. The fuel pressure drop external to the heat exchangers is 40 psi; the total fuel pressure drop is 57 psi (Fig. 2 shows the fuel piping). Figure 31 shows the (18) AP = 5,305 x 10°1'° ;. < AP = pressure drop, in. of H,0, f = friction factor, Gy, = helium unit weight flow, 1b/sec* ft2, LP = length of helium flow path, ft, s = average helium specific gravity, S, = transverse pitch, ft, S, = longitudinal pitch, ft, @ = viscosity at bulk temperature, 1b/hrft, 2 ! > . fGHeLp DHe 0.1 Sl o " 0.14 \ S, 3: ’ p’s He helium ducting for the fuel circuit. The pressure drop external to the heat exchangers and the total pressure drop are plotted against helium volu- metric flow in Fig. 32. TEMPERATURE IN FUEL SYSTEM BECAUSE OF AFTERHEAT IN THE EVENT OF COMPLETE PUMP FAILURE If there were a complete power failure and all the fuel remained 1n 49 50 ELBOW He TO H,0 HEAT EXCHANGER-— = UNCLASSIFIED DWG. D-A-3-2A ELBOW HEAT BARRIER HEAT BARRIER te——He TO Hy0 HEAT EXCHANGER i /FUEL TO He ! HEAT EXCHANGER L 7 / / / /1/ ( TRANSITION PIECE ELBOW Fig PLAN ELEVATION 31. Helium Loop for Fue —— HELIUM BLOWER -———HYDRAULIC MOTOR L 1 Circuit. DWG. 19116 2.5 i / o oJ T £ 20 | 0 /1 O ' ; : £ 15 - ’ Y, > | 2 T = @ | : | : / 5l o 1.0 S ; : gl T g‘ : oD / 2 05 5 ql i [0 i | l | ; NGERS EXTERNL\L 10 HE AT EXCHA | - 0 2000 4000 6000 8000 10000 HELIUM VOLUMETRIC FLOW (cfm) Fig. 32. Helium Pressure Drop vs. Helium Volumetric Flow. the system, 1t would be desirable to know the maximum temperature the fuel would attain (Fig. 1). The tempera- ature rise 1n the fuel will be due to internal heat generation. However, since the heat generationrate decreases with time after shutdown, at some temperature an equilibrium will be reached between the heat generated and the heat lost from the system. The maximum fuel temperature will be attained at equilibrium. reached, As soon as the maximum has been the temperature will decrease. The total heat generation rate of the fuel 1s given as a function of time after shutdown in chap. 9. Heat is lost from the components of the fuel system by free convection to the helium in the pits and by thermal radiation to the equipment and walls. This heat loss is given in chap. 6. The change in temperature of the fuel and metal of each fuel system component per unit time 1s Qf "Ql (20) AT = 2we P and (21) © _ volume of fuel 1n component < 0 total fuel volume £ where AT = temperature change, °F/sec, total heat generation rate 1in the fuel, Btu/sec, heat generation rate in the fuel in the component, Btu/sec, Q, = heat loss from the component, Btu/sec, Zwfl;= heat capacity of component plus fuel, Btu/°F, w = weight of material, 1b, c, = specific heat of material, Btu/1b- °F, The most critical pointsin the fuel system under the condition postulated are those with the smallest surface- to-volume ratio. The components in this categoryare the reactor (Fig. 9), the surge tanks (Fig. 33), and the 2-in. pipe lines. Table 9 gives the data needed to calculate the temperature rise 1in these components. TABLE 9. DATA FOR CALCULATION OF TEMPERATURE RISE OF VARIOUS COMPONENTS 2we FUEL VOLUME TEMPERATURE COMPONENT (Btu/sec) (£.9) AT FAILURE (°F) Reactor 4166 1. 96 1400 Surge tank 48. 6 0. 83 1150 2-in. pilpe (per foot of length) 1.52 0.023 1500 51 S NOTES: ALL DIMENSIONS ARE IN {NCHES ALL MATERIAL S INCONEL WELDING CAP 6% oD x % THiCK HANDHOLE 6% 0D x Y% walLL WELDING CAP 10Y% 0D x 1 THICK -7 SPARK PLUG PROBES #4mm SPECIAL -~ - UNCLASSIFIED DWG E-A-3-1-33A LIQUID-LEVEL WELL 3PS x 18% LONG—={ TANK SHELL 10%2 0D x 24 LONG — AR £ 4! BAFFLE PLATE B LIQUID-LEVEL STATIC LEG 3% IPS x 26 LONG—-~—| LIQUID INLET AND LIQUID QUTLET ROTOMETER 2% SCH 40 3 1PS — ———fi ] LR 90° ELL- WELDING CAP 1050 OD % ¥ THICK %_-, - 5 [ - ,._;_.- e 8 . - - __—:‘ e 9 . . ‘,__.....__ - I 26 . S Fig. 33. Fuel Surge Tank. —-WELDING CAP “Jo'% 0D x 1 THICK s For the metal c, = 0.11 Btu/lb-°F, o = 0.307 1b/in. 3, . and for the fuel c, = 0.26 Btu/lb*°F, o = 187 1b/ft3, The total volume of fuel 1n the system was taken to be 7.75 ft3, and the sink temperature was takenas 130°F or 590°R. The maximum temperature to be expected 1in each component was calcu- lated numerically by using Eqs. 20 and 21, The following results were obtained: E COMPONENT MAXIMUM TEMPERATUR (°F) Reactor 1400 Surge tank 1900 2-in. pipe 1520 Curves of temperature vs. time after shutdown are shown in Fig. 34. G. "7 1900 e 1800 ( 1700 ] SURGE TANK# 1600 L & 2-in. PIPE o < 500 & % a p- LJ - REACTOR 14009 <> 1/ 1300 1200 — ¢ 1100 f 10 102 10> 1ot 10° TIME {sec) Fig. 34. Component Temperature vs. Time after Shutdown. 53 Chapter 4 REFLECTOR COOLANT HEAT DISPOSAL SYSTEM The heat added to the reflector coolant (NaK) in the reactor is dis- posed of by circulating the NaK to a heat exchanger where it gives up its heat to helium., The hot helium is then passed through a heat exchanger where 1t gives up its heat to water. The NaK and helium recirculate: the water 1s dumped. There are two NaK-to-helium and two helium-to-water 1) so that the liquid sides of each pair of ex- changers are in parallel. The helium two para]_le] circuilts, and each circult contains one exchangers exchangers arranged (Fig. circuit consists of NaKk-to-helium and one helium-to-water heat exchanger in series. Figures 35 and 36 show the details of the two tvpes of heat exchangers. The per- formance of the NaK heat disposal loop over a range of operating conditions 1s calculated below. The NaK heat disposal syster obeys the following relations: (1) @ = Fyak CNak (7\Iax - Ty.x) > (2) Q = Wfle Che (THE - THe) ) (3) Q=W,c, (T, - T,) (4) Q - hNaK-He ANaK-He rNal‘{-He ’ (5) Q - hHe-w AHe-w 6He-w ' where ) = heat transferred, Btu/sec, W = weight flow, lb/sec, T' = maximum temperature, °F, T = minimum temperature, °F, h = heat transfer coefficient, Rtu/sec* ft? (°F/ft), = heat transfer area, ftz, = effective log mean temperature difference, °F, and the subscripts refer to DA | NaK = Nak, He = helium, w = water, NaK-He = NaK-to-heliumheat exchanger, He-w = helium-to-water heat ex- changer, 54 The heat disposal system 1s operated with the following restraints and conditilons: 1. The NaK flow 23 lb/sec. 2. The helium volumetric flow per exchanger 1s held fixed at 2000 cfm at This fixes 1s held fixed at blower inlet temperature. Wy, once Ty is known, _ 3. The water outlet temperature is thermostatically controlled and 1is held fixed at 100°F. 4. The water inlet temperature will vary with the time of the year, but for this analysis it has been assumed to be fixed at 70°F. The heat transferred is chosen as the independent variable in the system, by the heat This I NaK' since 1t 1s determined added to the NaK in the reactor. leaves as dependent variables T TNaK’ Tée, Ty, and W _. There are therefore five unknowns and five equations (Egs. 1 through 5). Before can be solved, the heat transfer coefficients and areas must be calculated for the exchangers. these equations two heat The over-all hd4's are: (6) (h), . . o (hA)NaK (hA)He (hA)m NaK-He and (1) (ha), e, o @, G, G, where m refers to the metal of the tube wall, The liquid-side heat transfer coef- ficients are: kNaK 0.8 (8) hyak = (7.0 + 0,025 Pe”* %) Nak S¢S EWG. A-3-3-21A 17 ——I 4l SUPPORT PLATES MATERIAL AND MATERIAL SPECIFICATIONS ———————————————— PART MATERIAL SPECS. QUALITY SHELL, TUBE SUPPORT PLATES. STEEL ASTM A-283 | GRADE C MANIFOLD, WELD ELL, AND REDUCER. | NICKEL , CHROME, IRON | ASTM B-167 | {NCONEL SHELL SUPPORTS, FLANGE BARS ~ BACKING BARS AND AIR STOPS. STEEL ASTM A-283 | GRADE C TUBES NICKEL, CHROME, IRON | ASTM B-167 | INCONEL MANIFOLD CAP AND TRANSITION. NICKEL, CHROME, IRON | ASTM B-167 | INCONEL FINS STAINLESS STEEL TYPE 304 MANIFOLD SUPPORTS STAINLESS STEEL TYPE 304 INCHES 2 0 4 8 12 16 VENT TUBE NOTE. ALL DIMENSIONS IN INCHES. SECTION A-A c ‘1 25%, 39Y% __J‘ 16Y, 21, 16 Yy SECTION C~-C ELEVATION Fig. 35. NaK-to-Helium Heat Exchanger. 9¢g WG I'l---!-lt“.;lflu lg-in TH'E. FULL FACE ASBESTOS e o MATERIAL AND MATERIAL SPECIFICATIONS Yo % 1-in BAR WELDED TO . —- DESCRIPTION MATERIAL | SPECFICATION | OQUALITY _ BLANKING-OFF PLATE - | = SELL, SHELL OOVER B, | T—@—' b : BLANKING-OFF &, TUBE | ) f SUPPORT BAR, BACKING-UP - i BARS FOR SHELL FLANGE, | swEEL ASTM - A-283 | GRADE C : SHELL REINFOR(ING BARS, | = SHELL SUPPORT R, ‘ , WA BAFFLE BOX . | STAT. HD FLANGES, SUPP'T [ | R'S, STAT HD P ; 5 | | - STAT WD TIE RS, STAT, HO. e DO |ASTM-5-285 | GRADE C 1 %% -in BARS WELDED TO — COVER R, TUBE SHEET STAT | X -in WELL | | O R'S i APIERET TLAtET—= | | - B50-1b WELDING NECK FLANGE, FORGE STEEL |ASTM-A-181 | GRADE | L [~ .’ . < 1'5-in 5CH 4D PPE | SEAMLESS STEEL| ASTM-A-106 | GRADE A = | .| H-'_ — o T = | I = | i i B e TUBES | SEAMLESS STEEL| ASTM-A-1T9 | umy. wall : ' E | | : | | s FING | COPPER COMME RCIAL ¥ 1 | | ! (11 ' STAT HD GASMETS DURSBL A COMMERCIAL \ — | | | g oa. -4 !;L‘s-rn THE ~in BLANKING-OFF PLATE- , e—————y TAT - iy : | ‘ J ‘ i 1 j“r SHELL GASKET &F TUBE SHEET ASRESTOR Lo msm% | | | 1 ye TAP BOLTS AT BLANKING-OFF BLLOY STEEL COMMERTIAL | ‘ . | | | :s,l_l_T BAFFLE : f | | . BOLTING AT STAT HD AND | asTh- | 125000 TS | L ' T SRET ALLOY STEEL | ASTM-8-93 B7| \65000 e i | TiE AOCS, SPACERS AND NUTS STEEL | COMMERCIAL | i . = T i MUTS AT TUBE SHEET AND BETH OIL A | | bl _Ir::- CNVER i APE UENCH | ASTM-a-134 |cuass 21 e | | | | i t | ! T & 4 Ii ] 1) Ya-in TH'N FuLL F{E‘E ASBESTOS fil iy ba-it. DIA VENT HOLE ke, g — 8N~ 0Tg In = _l—in THK DURABLA GASKEY - —t r | DESIGN (ATA SHELL TUBES | CESISN PRESSURE 6 o WATER SCips CESIGN TEMPERATURE 000°F 340°F < | HYDROSTATIC TEST PRESSURE 75 psi 2 DESIGN TEMPERATURE AT TUBE SHEET BSO"F e MANXIMUM METAL TEMPERATURE SHELL SI0E SO0™F 2 SOE FLEVATION Zf I%-in o Yy-in X 2-in STEFENMG BAR e ! Ya-in Doa DR HOLE S x1% ~in BAR ALL AROUND DPENING BOTH SIDES ¥5g-in TH'K DURABLA GASKET t% -0 IS0HD F5 WELDING NECK FLANGE- Fig. 36. Helium-to-Water Heat Exchanger. (Lyon equation(%)) and k 0.1 (9) h, = 0.027 — Re®8 Prls3 (—“) ! p, * ® Hs w w (Sieder-Tate equation(!3)), where k = thermal conductivity, Btu/sec* ft? (°F/ft), D = equivalent diameter, ft, Pe = Peclet’s number, Re = Reynolds’ number, Pr = Prandtl’s number, [ = viscosity at bulk temperature, lb/hr- ft, ft, = viscosity at surface tempera- ture, 1b/hr-ft, The liquid-side areas are (10) Avex = ™yak Inax-ne and (11) A, =7D, Ly .y s where L 1s the total effective length of the heat exchanger tubes in feet. The resistance of the metal 1s DO In 1 DNaK NaK-He (12) |—— = (hA)m NaK-He QW(km) NaK-He LNaK-He and DO In D 1 He - (13) [____ ] v w ’ (hA)m He-w 27T(km)He-w LHe-w where DO is the tube diameter 1in feet. The heat transfer coefficients on the gas side are calculated in a manner identical to that used for the fuel heat disposal system calculations (cf., Egs. 14, 15, and 16 of chap. 3). Table 10 contains alist of pertinent information obtained from heat ex- changer designs (Figs. 35 and 36) and the heat transfer relations discussed above. Values are given for four different flow rates of helium and four different flow rates of water; curves were plotted from these values and used in the solution of Egs. 1 through 5. The data of Table 10 were used to solve the five simultaneous equations (Egs. 1 through 5) for various values of the independent variable - heat Inasmuch as the helium flow 1s constant (see the helium weight flow transferred. volumetric restraint 2), cannot be precisely determined until the helium temperature at the blower (Ty,) is known. It was necessary therefore to assume a helium weight flow for each power and to solve the equations by i1teration. The results of the solution of Egqs. 1 through 5 are shown in Figs., 37 and 38, in which the minimum and maximum NaK and helium temperatures are plotted against heat transferred. The mean NaK temperature is also shown 1in Fig. 37. The pressure drops in the NaK and in the helium have been calculated for the exchangers. The NaK pressure drop was calculated with the use of the customary Fanning equation‘!!) for the 2000 | i | i | i / 1800 i - | [ 1600 e f 5 MAXIMUM ! ‘ ? MEAN ~ | MINIMUM 1400 T | // o ‘ ! W 1200 . ey 0 i = : <[ m ' L o = 1 & 1000 i x ! o g 800! 600 0 200 400 600 800 1000 HEAT TRANSFERRED (kw) Fig. 37. NaK Temperatures vs. Heat Transferred in Heat Exchangers. 57 TABLE 10. HEAT EXCHANGER DATA NaK-TO-HELIUM HEAT EXCHANGER HELTUM-TO-WATER HEAT EXCHANGER Tube outer diameter, in. Tube wall thickness, in. Tube material Fin outer diameter, 1in. Number of fins per inch Fin thickness, in. Fin material Tube transverse pitch, ft Tube longitudinal pitch, ft Number of tubes per exchanger Number of tubes transverse to flow (per exchanger) Exchanger height, in. Exchanfier width (also active tube length}, in. Total active tube length, ft Liquid flow area per exchanger, £t 2 Liquid flow rate per exchanger, 1b/sec Liquid velocity, ft/sec Peclet’s number Reynolds’' number Liquid heat transfer coefficient, Btu/sec: ft2' °F Liquidheattransfer.areaperexchanger,ft2 (hA)liquid per exchanger, Btu/sec'°F (l/hA)liquid per exchanger, sec- F/Btu (l/hA)! per exchanger, sec'oF/Btu Helium-side equivalent diameter (DHe)’ in. Helium free flow ratio Helium flow area per exchanger, ft2 Helium flow rate per exchanger, 1lb/sec Helium Reynolds’' number Helium heat transfer coefficient; Btu/sec- ft2-°F Fin efficiency Helium heat transfer area,* fr 2 (hA)He per exchanger, Btu/sec'°F (1/hA)y, per exchanger, sec’ °F/Btu 1.0 0.109 Inconel 2.0 7 0.024 Stainless steel 2.75 2.43 75 13.75 16.25 101.6 0.0503 11.5 4. 97 790 0.830 20.8 17.3 0.058 0.126 1. 447 0.575 0.893 0.33, 0.22, 0.11 2,230, 1,470, 720 0.0063, 0.0046, 0.0028 0.43, 0.50, 0.60 142, 162, 190 0.889, 0.743, 0.526 1.12, 1.35, 1.90 0.625 0.049 Steel 0.875 12 0.010 Copper 2.80 1.684 180 6 16.8 17.0 255.1 0.0273 16.67, 10.0, 6.67, 3.33 9.89, 5.40, 3.91, 1.96 49,300, 29,600, 19,700, 9,860 ¢.610, 0.406, 0.290, 0.168 35.2 21.5, 10.2, 5.92 0.047, 0.070, 0.098, 0.169 0.015 0.722 0.768 1.524 0.33, 0.22, 0.11 650, 430, 210 14.3, 0.0051, 0.0038, 0.0023 1.0, 1.0, 1.0 187, 187, 187 0.957, 0.709, 0.424 1.04, 1.41, 2.36 " “Area” varies with helium flow rate because the fin efficiency varies with helium flow rate. 58 JR— DWG. 19119 1800 1800 / 1400 1200 / = wl r e 1000 & / w a 2 MAXIMUM - < 800 2 | L I 600 / 400 / P— 200 flfifl@ia -——/ 0 0 200 400 600 800 1000 HEAT TRANSFERRED (kw) Fig. 38. Helium Temperatures vs, Heat Transferred in Heat Exchangers. straight sections and the curves pre- sented by Cox and Germano{1%) for the bends, exits, and entrances. Since the NaK flow 1s relatively constant, the NaK pressure drop is approximately constant and is equal to about 1 psi. The helium pressure drop is calculated in a manner identical to that used for calculating the helium pressure drop in the fuel system., The helium pressure drop 1s plotted against heat trans- ferred in Fig. 39. DWG. 19120 o HELIUM PRESSURE DROP {in HEO) Q \\ N o @ o o 0.4 0.2 HE LIUM -TO-WATER EXCHANG ER HELIUM - e =" EXTERNAL CIRCUIT 0 l [ 0 200 400 600 800 1000 1200 HEAT TRANSFERRED (kw) Fig. 39. Helium Pressure Drop vs. Heat Transferred. The pressure drops in the remainder of the NaK and the helium circuits have been calculated with the use of the Fanning equation and the Cox and Germano data. Figure 40 shows the NaK piping; Fig. 41 shows the helium duct- ing., The pressures at various points in the fuel circuit are shown in Fig. 1. The NaK pressure drop, exclusive of the heat exchangers, is 16 psi; the total NaK pressure drop is 17 psi. The helium pressure drop exclusive of the heat exchanger and the total helium pressure drop are plotted against heat transferred in Fig, 39, 59 UNCLASSIFIED DWG, A-3-3-5{A ELEV. B40 ft-6in ‘ [——! i i . . - - REFLECTOR COOLANT HEAT EXCHANGER LOOP T - /////////// T M////////////i///////////%/f i ELEV 832 119 Fg i /////// 0 | 9 R #/M/////////Y/////////////W//////// ’J’// v i ELEV. 832 f1-9%g in. i % ¢ OF TEE . - 7 Wl i W 7 = 7 21 | a=| fi 23 c Z L > | o ] ; - ouwl £ ; % l-ly-f//’mm/mx//mxmmmm%{fi N o £ R / ; i - J % /"'////l/#//l//f////lfllllffllfllflé'rz % — \! - REACTOR % | F L 7 © % . % ‘i ! E M ! / //[/[IlllllllllllIlllflfllfllllllfff‘y,,llf I i ! ) | = | FLOWMETER .| [ N : g T ‘ g ! g [l § : a 52 _ i NaK PURIFICATION SYSTE 7 !. g .fi 7 &L . e e T, ‘ A\ e wl £ . . _ELEV. 842 f1-3i L B % ?’ Hn % fiz oL © W é ///Illfllfllfll Illl/fl%fllfllllf’/f/j RTITE) J -“--I"/””/% L /’//,¢ St | e L - / REFLECTOR COOLANT ‘ é/ y z e — “’ 8 E / ’;f / : e ; f ////////// Z ‘ ;2 z % ONITORING He BLOWER é 1 : ! e ' P O / '/ ’ ) ' o i L i " ) | | / / o .’fi;m mfga/é___,_%-”,,u / '//////////// ' & & cievain- o [\ Qy d =T - / / Loy 1“ %W i tr 1 BLDG. ¢ / / . ,,,, / U ! ELEV 841 -3 | - | / ~ a1} - in. BLDG. ¢ : ! é T T ///////////‘Agwf/f////mfmmmmmf,,,é ‘ [ Ay, : A 4 % P DUMP VA ) dl | ELEV.838 fi-6in. - ? % : : ‘ / ; z é Vo ) / i I [R— S TTTSS e = - L 710 : - ) A - ELEV. 832 ft-9in, fimflm#flfilmmmwmfl// ! . ) . 7 Y ¢ OF TEE i SR Ry D , : MONITORING SYSTEM \\\\!\Q\\\\\\\\\w \“\\\. [ eSS ] NaK PURIFICIA_lON SYSTEM ==t < | | | I\I | MONITORING He BLOWER - WWW | VR - REFLECTCOR COOLANT PIPING == ///I/I/I/I//II//M’I LR R L ///‘ — \\\\\\\\\,\\K\\\\\\‘K\\\\\\‘\\\‘%\\\\k\\\\\‘\‘%\\\\\\&\\ T LR : : FLOWMETER : A \\\\ 3 ‘ Q / : R Z \\\\\ \\\ \\ \ \.: T & E S h NN | = = ol N - 3 W \ \ A . ) . \\ i > AN : el e J// ///// e —— // ~— @ < e /////// HEAT EXCHANGER INLET C.I: - ; ELEV. B39 ft-0in. « HEAT EXCHANGER OUTLET ELEV. 839 ft -1 in. REFLECTCR COOLANT HEAT EXCHANGER .——5 ft-0in. — -t 9 ft-0in. ] [2ft-2in. 9ft-2in. EDGE OF PLATFORM Fig. 40. Reflector Coolant Piping. UNCLASSIFIED DWG D-A-3-4-51A rem —— 14 ft-0%in REF. e ‘—— e 10 f1-10%in. — NO. 20-SM200 LAMSON BLOWER VICKERS HYDRAULIC MOTOR TRANSITION PIECE, 10-iniD TO 20'gx16% in 90° ELBOW, 20Ygxi6% in DUCT, 20% x16% x 1134-in. LONG DUCT, 20% x16% in x3 f1-0-in. LONG TRANSITION PIECE, 10-inID TO 20%x 6% in. GRISCOM-RUSSELL He TO H,0 HEAT EXCHANGER GRISCOM-RUSSELL NaK TO He HEAT EXCHANGER ORNL HEAT BARRIER 11 ASBESTOS GASKETS, REQUIRED DIA X Ygin. THICK NOTE: ITEMS NO 3,4,5 6, AND 7 ARE SAE NO. 10-20. O ® N O D DL - —7ft-3%in —— o -8 in.r 3f1-QYgin |~ | : I -2 ft-gin ELEVATION END VIEW Fig. 41. Reflector Coolant Heat Exchanger Loop. Chapter 5 ROD AND INSTRUMENT COOLING SYSTEM COOLING OF THE CONTROL RODS AND INSTRUMENTS There are six vertical holes in the reactor of the ARE (Fig. 16) into which a regulating rod, three safety rods, and two chambers fission can be lowered, when required. Helium 1s blown through the passages between the rods and i1instruments and annular the reactor to cool the various surfaces In the case of the rods, this cooling 1s desirable because the present, vanes on the rods slide 1n contact with the sleeve 1n the reactor; guide considerable uncertainty exists as to what would happen 1f this sliding con- to be made at the high temperatures 1in the reactor., The require cooling because the electrical tact were instruments insulators used 1n their construction emit false signals at temperatures above about 700°F, The rod and instrument cooling circuit each of 1000 cfm capacity, which blow helium through in the consists of two blowers, the annular passages reactor holes, and a heat exchanger which removes from the helium the heat picked up 1n the reactor holes. Although the blowers have a total capacity of 2000 c¢fm, they are operated so that the helium flow 1s 1000 cfm, Figure 1 shows a diagram of the rod and instrument cooling system. Figure 42 shows the dimensions of the helium passages through the reactor. Figure 17 shows a cross section of the helium passages and details of the sleeve 1n the reactor. This sleeve, is actually triple-walled. The as may be seen, helium passes between the 1inner wall and the rod or instrument 1n question, The space between the 1nner wall and the middle wall 1s packed with diato- maceous earth, which serves as thermal insulation between the reactor and the NaK from the reflector coolant flows between the middle and outer wall and rod or instrument hole. circuuil provides some cooling because 1t 1s 64 colder than the surrounding sections the 1000 may be ap- of the reactor core. Since cfm of helium available portioned differently to the various holes, the cooling of the holes was investigated for a range of helium flows. Also, at the time of the calculations, the mean NaK tempera- various ture was unknown and, consequently, a range of mean NaK temperatures was investigated. The cooling of the various rods and instruments will be considered separately and 1in the following order: safety rods, regu- The division of the total flow among the different holes will be discussed last. lating rod, fission chambers. DWG. 19421 PLENUM CHAMBER fee— 7 - 2%, 0Dx0.043 WALL BELLOWS 3Y%g ro@ _S A P \ i N ‘ o 297 ODx0.035 e —2.4500x0.035 WALL WAL~ N ‘ &< L & ROD SLEEVE—= = INSTRUMENT SLEEVE e | ! oot et i | RS TOP OF PRESSURE F___- sefl H'@ L sHELL b ‘ | * &\ 3.7500x0.049 | |1 1 ot TOP OF CORE WALL——L—-- ; ‘ 1 f LATTICE I ‘ - 3.000Dx0.085 {}=——3.75 0D x 0.049 WALL WALL = ; o 1} 1.75 0D x 0.035 WALL o L 2.46 0Dx 0.035 oo 300 0D x0.065 WALL WAL L ‘ | : BOTTOM OF DIATOMACEQUS | = 1 ,/ CORE LATTICE EARTH-T—L : T { | © I 1o i \\BOTTOM OF 3 2 9700x0035 | 258 1 PRESSURE SHELL WALL: 2y 2.97 0D x 0.035 WALL PLENUM CHAMBER i VARIABLE ORIFICE DIMENSIONS ARE IN INCHES Fig. 42, Rod and Instrument Sleeves. COQ LING OF THE SAFETY RODS During normal reactor operation, the safety rods are not in the reactor but are withdrawn into sleeves above the reactor. The safety rods themselves are 1n a cool area, and the only cooling problem, then, 1s that of cooling the sleeve i1in the reactor. The equations governing this process are quite straightforward and are listed below: (1) Q= We (T, - Ty, (2) Q = hAG + Q ’ (3) RA = | ——— 4 1 (hA) .o (hd)_ 1 1 1 -1 — o+ — oy , (hA), (hA)_ (hA),. where ) = heat transferred to helium, Btu/sec, W = weight flow of helium, 1lb/sec, ¢, = specific heat of helium, Btu/1b-°F, T' = maximum temperature, F, T = minimum temperature, °F, h = heat transfer coefficient, Btu/sec* ft? (°F/ft), A = heat transfer area, ft?, f = effective log mean temperature difference between the NaK and the helium, heat generated in the sleeve by nuclear radiation, Btu/sec, and the subscripts Q, = He = he lium, NaK = Nak, m = middle metal wallin sleeve, I = insulation (diatomaceous earth), n = 1inner metal wall. The various terms in Eq. 3 may be evaluated as follows: kNaK \ (4) hy . = (5.8 + 0.020 Pe®-#) | NaK where k = thermal conductivity, Btu/sec* ft? (°F/ft), D = equivalent diameter (four times hydraulic radius), ft, Pe = Peclet’'s number: (5) A = d' h %-:b Nak m ' where d' = tube outside diameter, ft, L = length of tube = pressure shell, ft; hei1ght of 1 In 2= (6) = -, (hA)m 27Tk L where d = tube inside diameter, ft: dm In o 1 n (7) = — (hA)I 277k (L d, In ~ 1 n (8) = ; (hA) 21k L kHe (9) hy = 0.023 ~D—Re°-3 Pelet for Re 2 2100 k}[e DHe 1/3 e = 1.86 — Re!/3 Pr1/3<——> , Dy L ’ - I for Re < 2100 (10) Ay, = 7d L Equations 1 through 10 and the dimensions shown 1in Figs. 42 and 9 were used to calculate the exit tempera- ture of the helium and the heat trans- ferred to the helium; an inlet helium temperature of 150°F was assumed. The properties of helium were eva luated at the mean helium temperature. The range of helium weight flows considered was from 0,005 to 0,100 1b/sec, and the calculations were made for mean NaK temperatures of 1000, 1150, and 1300°F, The of the com- putations are shown in Figs, 43, 44, and 45, resul ts of the sleeve wall can be calculated from the The maximum temperature 65 n DWG. ] 1400 7 1000 | g ! | | 9004~ ot 5.0 1200 ' e i /QTOTAL ’(T/ i : /////’ i T T ™o, To1aL ‘ i 1 eoo% | / } 1000 '/ 5 i / : _ § ‘ W 2 i ; ! = = 7ooé i | | 40 4 800 J , B ! = — | 1 2 | 2 ! \ ‘ : « o : ; E \\ N | 400 ) ‘ — \ - \\QTT TEMPERATURE \ 200 - =0 t ! t i | TEMPERATURE (°F)} Q, TOTAL (Btu/sec) | | | 0 80 100 ; 120 0 i HELIUM QUTLET TEMPERATURE o 20 40 60 ; HELIUM FLOW (lb/sec X 103) Fig. 44. Safety Rod Cooling at a | ; Nak Temperature of 1150°F. ; 1.0 0 0020 0.040 0.060 0.080 0100 HELIUM FLOW RATE {ib/sec) Fig. 43. Safety Rod Cooling at a 1800y . ‘O NaK Temperature of 1000°F. | | 1400} #70 following equation: 1200 6.0 . Q (11) (T ) = The . n max e (hA) . He 1000 —50 3 The helium heat transfer coefficient, g _ _ [% h, in Eq. 11 is evaluated by means of < 800 et e e 40 T Eq. 9, with the helium properties § \KMAXIMUMWALLTE‘MPERATURE B corresponding to the maximum helium M eoo N | _ J—fl——aog; temperature being used. The maximum \ wall temperature was evaluated by ‘. 50 . 400 — 2 using Eq. 11, and the results are ‘ N HELlUMOUTLETTl:MPERATURE | shown in Figs. 43, 44, and 45. | \‘< ! | 5 — o] 200 o COOLING OF THE REGULATING ROD | | During normal operation, the o} i o __io position of the regulating rod may O 0020 0040 0060 0080 0100 0120 vary from a position completely out HELIUM FLOW {ib/sec) of the reactor to a position where the midpoint of the stainless steel Fig. 45. Safety Rod Cooling at a slug is coincident with the center line NaK Temperature of 1300°F. 66 of the reactor. When the regulating rod is completely out of the reactor, the situation is exactly the same as that analyzed in the previous section on the safety rods, the triple-walled sleeve being i1dentical for the two types of rods. When the regulating rod 1s i1n the reactor, the situation 1s more complex; the case of the regulating rod all the way into the reactor, which is the extreme condition, HELIUM~, will be analyzed. The regulating rod hole will be divided into three sections in the reactor (Fig. 46). The top section of the rod hole is the section that contains the portion of the regulating rod which 1is in the reactor but contains no appreciable amount of neutron and gamma absorber. The middle section of the rod hole is the section that contains the portion of the regulating rod which contains DWG. 19125 CONTROL ROD |- TOP OF PRESSURE SHELL TOP OF LATTICGE 48.50 35.25 | INSULATION ¢ ‘/NCIK GAP Fig. 46. BOTTOM OF LATTICE BOTTOM OF PRESSURE SHELL Regulating Rod. 67 the heavy stainless steel slug. The bottom section of the rod hole 1s the section that contains no regulating rod. The governing the cooling process in the three sections of the rod hole are (12) Q= We (T, =~ Ty), , e 1 ;i =1,2,3, the symbols have the meanings as given previously and the equations where same subscript 1 refers to the sections of YR . the regulating rod hole: 1 = top section, 2 = middle section, 3 = bottom section; (13) Q, = (hA6 + Q. + q), , where g = the heat which must be removed from the rod, Btu/sec; (14) q; = (g, * qg), , where q, = heat generated in the rod by nuclear radiation, Btu/sec, qp = heat transferred from the sleeve to the rod by thermal radiation, Btu/sec; it may be noted that (qr)i=1 = 0 and qi'—'3 = 0: 1 . 1 (hA) g x (hA) (15) (hA), = 1 1 1 -1 + — + , (hA), (h4) (hA) . | where the various terms are evaluated exactly as the corresponding terms 1in Eq. 3; !’ (16) (0,), = il - 7T 3600 1 a1 — o+ [EN - € (A;)(g ) (qR)i=3 = 0 ’ where a = surface area of control rod, fe?, t' = maximum rod temperature, °F abs, t = minimum rod temperature, °F abs, € = emi1ssivity, | 68 It may be noted that the arith- metical-average temperature 1is used in Eq. 16 to evaluate the heat trans- ferred by thermal radiation. This 1is only an approximation, but a check that 1t 1s greatly 1in error. Equations 12 through 16 and the dimensions shown in Figs. 42, 46, and 47 were used to calculate for the various sections the has i1ndicated not too exit temperature of the helium and the heat transferred to the helium; an inlet temperature to the rod hole of 150°F was assumed. The prop- erties of helium were evaluated at the mean temperatures, and the values of Qr and q_ are shown in Fig. 48, The range of helium weight flows considered was 0.015 to 0.025 1b/sec; of 1000, as before. average NaK temperatures 1150, and 1300 were used, The results of the calculations are in Figs. 49, 50, 51, and 52, which show the helium temperature and the heat transferred to the helium at the end of sections 2 and 3 plotted against helium flow for the various shown NaK temperatures. The maximum temperature of the sleeve and the rod can be calculated from the following equations: Q (17) (T = A max = Ty )ies [(hA)He} and Q (18 ) o= (Th) . — e T T )i [(hA)HeJ,= the coefficients helium heat transfer are evaluated locally. {(Tn + T;>4 (t - tij} 200 200 /1, The results of the evaluations of Eqs. 17 and 18 are Figs. 49, 50, and 51. COOLING OF FISSION CHAMBERS The the reactor core during startup of the Again, also shown 1n fission chambers will be 1n 69 T T . . &Efi'&ffis 2TEEL . . ENQ'QDLES’ISLU%EELSLUGS STA'E‘[SEfiOSRTEEL 1% -in. 00 x 0.065-in. WALL x 170 in. ING ROD NOSE STAINLESS STEEL LOWER DRIVE TUBE TACK WELDAL WELD 5 1 - | — (1 “ ( UNCLASSIFIED DWG. D-A-2-5A RN /.. /v TACK WELD 69.031 in. 68.969 in. /:‘28312' DIA. 0.577 in. ' ' 0.547 in. SNUG FIT WITH LOWER MAKE FROM 1%-in. OD x Q.312-in. WALL DRIVE TUBE \ /15° 3-in. DIA. HOLE~ | [ ] B 7 7 77 6V 777 TR . _ ] 1265-in. o \ V _ ) ) ) . ( 1235-in. = ( c s S S 774 Z 77 Py 0125-in. MAX—={{=— L WELD AND 0.765~in. GRIND FLUSH 1140-in, 0735-in. 1410-in. 19g-in. OD x Yg~in. WALL x 69-in. STAINLESS STEEL UPPER DRIVE TUBE Fig. 47. Regulating Rod Assembly. ...... DWG. 19126 6.6 watts/linear in. DIATOMACEQOUS EARTH SLEEVE IN CORE REGION 56.2 watts/linear in. 4.0 watts/linear in. CONTROL ROD Fig. 48. Cross Sections of Sleeve, Nuclear Heat Generation Rates. reactor, but later they will be removed from the core the fission entirely. For following analysis, the chambers are considered as being in the core, which Each into is the most extreme condition, instrument hole 1s divided in much the same fashion as the regulating rod hole was divided. of the hole t he the fission chamber; sections The top section portion which the 1s contains 70 295 watts /linear in. r———~5.0 watts /linear in. 4.0 watts /linear in. SAFETY ROD Control Rod, and Regulating Rod Showing lower portion contains nothing (Fig. 53). to be used The equations in calculating the cooling requirements are - ’ - - (19) Q, = ch (Tge ~Tgedyr =1, 2, _ where the subscript i refers to 1 = top section . and 2 = bottom section; DWG. 19127 600 MAXIMUM WALL TEMPERATURE - 500 MAXIMUM ROD S TEMPERATURE ) 400 o HELIUM TEMPERATURE w T 300 2 <1 o w a S 200 ’_ 100 0 0015 0.020 0.025 HELIUM FLOW (Ib/sec) Fig. 49. Regulating Rod Cooling at a NaK Temperature of 1000°F. . WG. 19128 700 600 T\ \ MAXIMUM WALL TEMPERATURE MAXIMUM ROD 500 o=z TEMPERATURE & ~ 400 g 7T [+ E MAXIMUM HELIUM TEMPERATURE & o 300 = w ’— 200 100 0 ; 0.015 0020 0025 HELIUM FLOW (Ib/sec) Fig. 50. Regulating Rod Cooling at a NaK Temperature of 1150°F. o 700 MAXIMUM WALL TEMPERATURE eoo\\\* (\ \ [ - 400 2 a E MAXIMUM RCD YEMPERATURE z & 300 > — MAXIMUM HELIUM TEMPERATURE — 200 iCO 0 0015 0020 0025 HELIUM FLOW (Ib/sec) Fig. 51. Regulating Rod Cooling at a NaK Temperature of 1300°F. 850 800 7.50 700 @, TOTAL (Btu/sec) 650 1000°F _ ‘ 0.026 6.00 - - i —r O// ; f 550 | | l | ' 0014 0.018 0.022 HELIUM FLOW (lb/sec) Fig. 52. Regulating Rod Cooling at Various NaK Temperatures, 71 el DWG. 19131 | INSTRUMENT HELIUM TOP OF PRESSURE SHELL . : : TOP OF LATTICE | INSULATION 35.25 -t NaK GAP e | BOTTOM OF LATTICE V - ' BOTTOM OF PRESSURE SHELL Fig. 53. Instrument Hole. 72 (20) Q. = (hdO + qp), , where the symbols have the same meanings as before; Lo, (hA)y.x (hA)_ (21) (h4), - [ 1 1 1 -1 + + , (hA)I (hA)n (hA)He}_ where the various terms are also evaluated the same as in Eq. 3, except that the heat transfer coefficient 1in an annulus is given by k 0.14 /D 0. He He (22) h = 1.02 —— Re®-*5 <3i> ( ) D M l He where i = dynamic viscosity evaluated at the mean temperature of helium, lb/sec* ft, . = dynamic viscosity evaluated at inner wall temperature, lb/sec" ft, l = length of section, ft, df = outside diameter of fission chamber, ft, Grashof number; & — i dimensions of the sleeve are shown 1in Fig. 42, The calculations are based on the same NaK temperatures as used before, and the results are given 1in Fig. 54. Figure 55 shows the heat removed and the maximum temperature of the helium vs, helium flow rate for a NakK temperature of 1150°F, HELIUM PRESSURE DROPS The helium pressure drops in the safety rod, regulating rod, and instrument sleeves are calculated by 0.8 4 d ( ") Gr°:%5 | for Re < 2100 , dy using various helium flows and a Nak temperature of 1170°F. The equations governing the pressure drops are 1 pv? 24 AP, = Af — pv’ (25) " --ix. APC = X , 2 g r 4 4 (23) _0.173 2 (Tn + T, (tf * tf) " 73600 1 200 200 ’ where a, = surface area of fission chamber, fe?, ty = minimum fission chamber tempera- ture, °F abs, t} = maximum fission chamber tempera- ture, °F abs, €, = emissivity of fission chamber, € = emissivity of tube. The cooling requirement calculations for the fission chambers are made with the assumption that the bottom of each instrument (excluding nose) 1is at the center line of the core. Also, the maximum temperature of the instru- ment is taken to be 600°F, and the inlet temperature of helium 1is taken to be 150°F, The outside diameter of the instrument is 1.25 in., and the 2 (26) ap = Pr = Vo) e 2g L, ov? 27 AP = - . (27) , Af D 2 The symbols have the following meanings and units: AP = pressure drop, lb/ft?, f = friction factor, l = length of section, ft, l, = equivalent length, ft, D = hydraulic diameter, ft, v = average velocity, ft/sec, g = gravitational acceleration, 32.2 ft/sec?, constant, dimensionless, S I 73 v, * average linear velocity up- stream, ft/sec, v, = average linear velocity down- stream, ft/sec. The meanings of the subscripts are the following: f = friction, c = contraction, e = expansion, y = elbow, The friction factor, f, is given by (28) £ = lé‘, for Re £ 2100 , Re 0.125 f=0,0014 + —M8Mm — , (Re )?-32 for Re > 2100 , However, for an annulus 6 (29) f = , for Re £ 2100 . Re Values for X are given by McAdams (cf., p. 122 of ref. 11), and [, values are taken from ref. 13, DWG 19132 2.6 T 1.6 24 M mn ™ O O 1.C00 o ® @,TOTAL (Biu/sec) REQUIRED FLOW RATE (ib/sec X10%) 086 0.4 1.2 0.2 | 00 \ o {000 100 1200 {300 1400 NoK TEMPERATURE {°F) Fig, 54. Instrument Cooling. 74 Each sleeve is equipped with a variable orifice where 1t enters the the pressure bottom chamber., However, drops calculated here do not include the pressure losses across these orifices. The dimensions of the sleeves are given in Fig. 42, The lower end of the safety rod will be 1 in, above the top of the core lattice when the safety rod is in the “full out' position. The pressure drops were calculated for the rod in this position with helium flows varying from 0,005 to 0,090 Ib/sec. The safety rod dimensions are given in Fig., 56, and the results of the calculations are given in Fig, 37, The regulating-rod helium pressure drops were calculated for the rod 1in the “ full in”and’ full out” positions. The *“full out” position for this rod was taken to be the same as that for DWG. 15133 1.80 800 1.70 700 {60 600 / .. 150 500 © o o @ ) ‘ L 3 | : 5 o i | 5 4 1.agQ / ' -1400 (5 = \x\<:,,MAMMUM HELIUM i & TEMPERATURE = = L Q' | 1.30 /// ‘*~‘5=~¢300 120 4 ' 1200 110 100 | | | .00 f o 0 0.0020 0.0060 0.0100 HELIUM FLOW {Ib/sec) Fig. 55. Instrument Cooling with Bottom of Instrument at Center Line of Core and at a NaK Temperature of 1150°F. 5 BOTTOM INSERT NQOSE \ //‘ \\ \\ . \ A N / \ / RO SLUG WITH SF’ACERS—/ SLUG WITHOUT SPACERS ALTERNATE, 9 EACH, 18 TOTAL NOTE: INSERTS, NOSE, BRAIDED HOSE, TAIL AND COLLAR ARE STAINLESS STEEL Fig. 56. DWG. 19134 300 280 260 240 200 / 180 / 160 140 120 / / 80 / - / , / 20 PRESSURE DROP [lb/ft¢) 0 0.030 0.060 0.090 HELIUM FLOW (fb/sec) Fig. 57. Rod Sleeve, Pressure Drop in Safety the safety rod. Figure 58 gives the results drop com- from 0.015 of the pressure putations for flow rates to 0.025 1b/sec. The helium pressure drops for the instrument hole were also calculated AM. METAL BRAIDED HOSEfj Safety UNCLASSIFIED DWG D-A-2-4A TAIL--5 TOP INSET — / / / / s o . / 0156 in _. F s Z 00949 in Y CONNECTING ROD COLLARV'\ Rod Assembly. 135 55 — " / 40 3 Q & - = o o O x o ) x o ¥ 30 w o a ) g st o 20 e~ 10 0.015 0.020 0.025 HELIUM FLOW (Ib/sec) Fig. 58. Pressure Drop inRegulating Rod Sleeve. for the instrument in the ‘“full in” and in the ““full out’” positions. Here, the bottom of the instrument (excluding 75 above the top of the instrument nose) 1is 15 1in. pressure shell when the 18 in the “full out” position. The flow rates used 1n these calculations ranged from 0.0015 to 0,0100 1b/sec. The results of the calculations are given 1n Fig. 59, DIVISION OF FLOW OF HELIUM The flow of the helium to the various holes 1s apportioned so that the minimum flow to the instrument in the ““full is 0,005 lb/sec, and the minimum flow to the regulating rod in the ““full out” 0.034 1b/sec. The flow rates per hole for all combinations of reguTgyfinglwxlandinstrumentpositions, with the safety rod out of the are given 1in Table 11, C L 1in’’ position position 1s core, PERFORMANCE OF ROD AND INSTRUMENT COOLING SYSTEM HEAT EXCHANGER The control rods and nuclear instru- in the of the ARE are cooled by helium, which gives ments core up 1ts heat 1in a helium-to-water exchanger (Fig, 60), governing the performance of this heat exchanger The equations are (29) Q = Wfle CPHe (The - THe ) ’ (30) Q=4H c (T; - T) (31) (} = hAS | where @ = heat transferred, Btu/sec, W = weight flow, lb/sec, c, = specific heat, Btu/lb:°F, T' = maximum temperature, _F, T = minimum temperature, °F, h = over-all heat transfer coef- ficient, Btu/sec*ft?+°F A = heat transfer area, ftz, f = effective log mean temperature difference, The heat exchanger operates under the following restraints and conditions: 1. The helium flow is 1000 cfm at blower temperature. DWG. 19136 ] 18.0: | | | 16.0F—— e tmmed | % ‘ INSTRUMENT IN- : \ I 140 e 10.0 - PRESSURE DROP (Ib/f1°) @ @] 4*,]7 IR | . __i.__. . 20 INSTRUMENT QUT | 0.0060 HELIUM FLOW (Ib/sec) ©0.0100 Fig. Sleeve, 59. Pressure Drop in Instrument TABLE 11, HELIUM FLOW RATES IN ROD AND INSTRUMENT HOLES POSITION HELIUM FLOW (lb/sec) R lati Rod Inst t ; ceo avine 7o peramen Safety Rod Regulating Instrument Qut In Out In Rod x X | 0.035 0.034 0.005 X X 0,037 0.026 0.005 X X 0.037 0,026 0.005 X X 0.035 0.034 0,005 76 bt 3ft 5in. —-— 4*/4 in, ‘ 2 fr 8%in. } T \ri/ Z3—in. P.T. INLET fl ‘ ‘ /32 Yyin P, 5’//—2-m.ar.ouTLET E-m.RFINLETj\ GASKET [ | 1 'Z 4, in. T a'hin. | T -—-/// - * - i . OD___LL - UNCLASSIFIED DWG. 3-5-21A —— 4‘/4 N —-] -in,-THK. HEX. HEAD CAP SCREWS BONNET & in. Fig. 60. Helium-to-Water Heat Exchanger. 2. The water outlet temperature 1is 1 1 1 -1 thermostatically controlled and is (32) h4d = |—— t ; held fixed at 100°F., (hi)y, (W), (h4), 0.14 1/3 Bue /H 1/3 1/3 Pye - (33) hy, = 1.86 — Rey.” Pry, A DHe ’u's He ’ . 3. The water inlet temperature (McAdams, p. 190 of ref. 11), where | will vary with the season of the year, | but has been assumed to be 70°F for | this calculation. The rod cooling system heat ex- changer of three standard shell-and-tube heat exchangers arranged in parallel. The helium flows in the tubes, and the water flows the outside of the tubes. The follow- consists AaCross ing are pertinent physical dimensions of the exchanger; all values are for one of three units: The heat transfer coefficient may the Shell inside diameter, in. 6 1/8 Tube length, ft 3 1 Tube outside diameter, in. 0,375 | Tube inside diameter, in. 0.319 Number of tubes 116 Surface area per tube (inside), fr? 0.251 Surface area per tube {outside), fi2 0.295 Surface area (inside), fi? 29.1 . Surface area (outside), fr? 34.2 Baffle spacing, in. 2 Tube pitch (triangular pattern), in. 29/64 be evaluated from equlations: following the calculation 1ndicates that the helium flow is laminar; (34) h =— [— Re?: %% Pr!/3 Y DW ’LLS w v Y (Kern, p. 137 of ref. 8), where GWDW Re = , Fy 4 x f b = ree ared (free area ¢ wetted perimeter measured in a plane perpen- dicular to the tubes), dCB G = : p 1 27k, L (35) ) e ha m DHe In DW where kR = thermalconductivity,Btu/sec'ft2 (°F/ft), 77 D = equivalent diameter, ft, @ = viscosity at bulk temperature, Ib/hr-ft, #. = viscosity at surface temperature, 1b/hr-ft, Re = Reynolds’ number, Pr = Prandtl’s number, L = tube length, ft, G = unit weight flow, lb/hr-«ft?, d = shell inside diameter, ft, ¢ = tube clearance, ft, B = distance between baffles, ft, p = tube pitch, ft, and the subscripts He = helium, w = water, The helium and water heat transfer areas are tabulated above: 29,1 and 34,2 ft? per one unit of three, respectively, By using Egs. 29 through 35 and noting that the large number of baffles on the shell side makes the effective log mean temperature dif- ference almost equal to the log mean temperature difference for counterflow, the performance of the rod cooling system heat exchanger can be calcu- lated. Figure 61 shows the result of such a calculation: the helium inlet and outlet temperatures are plotted against the heat transferred. Some of the pertinent information not shown 1n Fig. 60 1s tabulated in Table 12, The heat removed from the core in the rod cooling circuit, calculated in the first section of this chapter, is about 25 Btu/sec. From Fig. 61, it may be seen that the minimum and maximum temperatures in the rod cooling heat exchanger will be about 110 and 240°F, respectively., The helium will actually pick up a considerable amount of heat between the heat exchanger and the 1nlet to the reactor and, con- sequently, the 1nlet and outlet temperatures of the heat exchangers wi1ll be greater than those listed above. The inlet temperature to the reactor will be about 150°F, 78 650 o | 550 4505 - DWG 19137 - | %onu- 250 — HELIUM INLET TEMPERATURE (°F) 150 —- HELIUM OUTLET TEMPERATURE (°F) O 20 40 60 HEAT TRANSFERRED (Btu/sec) 200 e 80 100 120 Fig. 61. Helium Inlet and Qutlet Temperature vs. Heat Transferred. TABLE 12, HEAT EXCHANGER DATA FOR HELIUM-TO-WATER HEAT EXCHANGER Helium flow area (total), f12 Helium velocity, ft/sec Helium Reynolds' number Helium heat transfer coef- ficient, Btu/sec*ft“*°F (hA)He, Btu/sec* F Water weight flow, lb/sec Water heat transfer cogf« ficient, Btu/sec*ft?*°F (hA)w, Btu/sec® F h4, Btu/sec'OF 0.246 65 950 0.0039 0.344 1.0, 2.0, 3.0 0.13, 0.19, 0.24 13.5, 19.8, 24.6 3.01, 2.99, 2.98 Chapter 6 MONITORING AND PREHEAT SYSTEM HEAT LOSS THROUGH INSULATION The heat loss to the environment of the various pileces of equipment in the three ARE pits is complicated by the fact that the pits are filled with helium. The helium tends the air in the pores of the insulation and thus to 1ncrease the thermal conductivity of the insulation. The for the thermal conductivity of porous 1insulating materials was derived by Maxwell and to replace following formula reported by Jakob (cf., p. 85 of ref, 14): akg 1 - {1 ~-——1% kS (].) k = ks ’ 1 + (a - 1)b where 3k a = , 2kt k s g V V p-—8& -y °* -1 _£2 V. Vg V. + Vg P k = thermal conductivity, Btu/hr-ft? (°F/ft), V = volume, ft3, o = density, lb/ft?, and the subscripts s = solad, g = gas, The ARE uses three types of insu- lation; diatomaceous earth and Superex for high-temperature insulation, and felted Asbestos-Sponge for lower- temperature insulation. The properties of these insulations are given 1n Table 13. By using the data of Table 13 and mean thermal conductivities of 0.033 and 0.021 Btu/hr-ft? (°F/ft) for the air in the high- and low-temperature the thermal can be insulation, respectively, conductivity of the solid, &k, determined from Egq. 1. Since k_ 1s known, k can be calculated for the case with helium in the pores by using 0.15 and 0,11 Btu/hr-ft? (°F/f¢), respectively, for the high- and low- temperature mean thermal conductivities of helium. The results of the calcu- lations are tabulated in Table 14, The the ARE piping and equipment 1s a com- insulation on the outside of bination of Superex and Asbestos- Sponge, and diatomaceous earth 1s used for i1nsulation i1n the control rod cooling loop. The heat loss to the environment through the combination Superex and Asbestos-Sponge insulation may be calculated from the following equations: 1. For insulating cylindrical shapes (1.e., piping), 2k O (2) _ LTRs Us , DS In DI s 2mk 6’(1-3 (3) — ¢ D In—" DI a=3s 4y . 0113 (Ts )4” 184 518 0.0055 Specific heat, Btu/ 1b*°F 0.38 0.15 1,24 T T e S e s s e et et SRy e eemmsne. . eeses e dd e e mmee e i e e b SRR e AR AR E i eesen e T T e e s aeaem et b ian et N WS b e Ry e AR R ...-...::..... ................ e et e e .....:..................... e by ...........................‘.............. T L 0 e e L, T T e e e T Ty Ty e L E e s ke 8 E R AR R 8 b8 8 A e e e b e e e a e e e e e e S e e e OO R L OO T g A e e e e a A by by e e o0 0 oaea e DR L SIS ey, Sl UNCLASSIFIED OWG. A-3-9-54A Sy aarEn ey KA CEa ey e s ery A e Saveereey e Sesaeaens v ane e e Cedenerane Swaee e, o 0 werveeey Seevaeas - — oy Ceessiany vavase ey e e earnn NesEaeres P00 " Saraane Ceersaan aanaany e veaany SO s LR e ST Sy e eaad RO e ey e ...... A SO0 warrerneos Vea e s e e e b aaan .......-:....... e's s s nedsats sy _'........-. ey AR ettt e e s Cesaaveasennntes e ee ey ey Sene e XA AR Yy e e v e ey e e Caan i AR A eae e e e eyt . ANNROOLO00 iy S e e e s eaner ey Saawansaaeenee i n e a ey eaeaa e e Ne sy es e aaansenaanss e ekaasAssRas v . hee A as e e e AOO0R0000N0 e oy e e e TS e X 0 e ey aa e na ey e a e R A v e e e aaa sy W e e e e e W e e e e raas et e AT e e e e e e e AOCOOCODLAD AONOnntn A0 e W e S e A ORI Ao e e e v e m et S e, e aaA Ay aay e aatn ke b AS i v a e e e aares Aea e A et R ey s ey Chebbantaereae e A S T e e e e e e e e Bhr A b NS e, . O e e aae e n e s e e s en e bbb e RN 0 eaa ey e _.....: e Ve . e e e Y e S S Crrr ey e an s e ey e s Seaen e e aeent e e ..:.:. aar e, ......... e ey DO . 'y - Cra e aeee e n e S e e DOOOCE RO OO RO ek e sy ey 0 ey OO D R e e e e e LG e e OO e a s s aa it OO e A n b ae et saan .. ae e na e e e e sk e ey e e ey e e avsesesiy araea e enany re e s n e OO et e e b d ey ...-...a......... e s Cereeaas ey e s e e e e e eaas vy e e e e e e v A e ay A AR ey e v ae . e wava e e, W e e AN aaaa e A a e e Yaneasearasesntet e e e e e e kA s b a A e e e ey awa ey ae e e an ek s sy Suwa e ae s A s AR R A n Ry a v e e, W e Y LSS e e e e e " ...:........... Yra e eaasaennye o0 weans e e A B Ry e e e e e e e e a e e A n e s Inside Shield. ing f Pip Composite Plan View o 63. Fig. 83 The temperature difference between any radial station in the reactor and the outside of the pressure shell when the reactor is in the quasi-stationary temperature state can be calculated from the following equation: dé Q (8) — = , dt (WCP)BEO'TL (WCP)IHC+(WCP)He where d@ = rate of temperature rise, dt °F/hr, of any point in the reactor (in the quasi-stationary temperature state), Q = heater input to the reactor, Btu/hr, W = weight of material in the reactor, lb, Cp = specific heat, Btu/lb*°F, and the subscripts BeO = beryllium oxide, Inc = Inconel, He = helium, The weight of the beryllium oxide in the reactor 1is approximately 5800 Ib; the Inconel in the pressure shell weighs about 7900 1b; the helium weight can be neglected., From Eg. 8, do 34,100 dt 5800 x 0.38 + 7900 x 0.15 - 10.1°F/hr . The temperature difference across any of the cylindrical shells may be approximated in the following manner: r nt+1 q, In — (9) ANO = , n 21k L n-1 d6 (10) q, = 34,100 - -’;1 (ch)i"é? , i = where A = radial temperature differential across a shell (in the quasi- stationary temperature state), OF’ = heat entering shell, Btu/hr, outside radius of shell, ft, k = thermal conductivity of shell, Btu/hr ft? (°F/ft), L = length of shell, ft, ~ il and the subscript n refers to the number of the shells, counting inward from the outside. (For a more accurate estimate, the fact that all the g, 1n FEg. 10 1s not transferred across shell n should be considered. The above approach 1s a conservative simplifi- cation, however, because i1t leads to larger values of A .) The results of the solution of Egs. 9 and 10 are shown in Fig. 64, which gives the difference in temperature (in the quasi-stationary state) be- tween the outside of the pressure shell and any radial position. The difference between the outside of the pressure shell and the center of the reactor is 162°F. The time required to reach the quasi-stationary temperature state may be readily calculated. The reactor 1is originally at some uniform temperature 04+ The quasi-stationary state is reached while the temperature of the center of the reactor remains fixed at €, and the outer shells heat up to a 0 temperature of N 1 (11) ¢ =6+ E AG . +— A ny 0 ) 1 2 n 1=nt1 where 6, = temperature of the nth shell at ! the beginning of the quasi- stationary state, N = total number of shells. The time required to reach the quasi- statlonary temperature state 1is, DWG. 19133 INCONEL PRESSURE SHELL —~=~ == SMOOTHED CURVE f;/ TRUE RA s HELIUM GAPS~ OUTSIDE OF PRESSURE SHELL AND RADIAL POSITION (°F) TEMPERATURE DIFFERENCE BETWEEN Q 4 B 12 16 20 24 28 RADIUS {in.) Fig. 64. Temperature Profile of Reactor Core and Pressure Shell (Quasi- Stationary State). 85 therefore, N L i=1 1 Q ! the time required to reach (We )y (8, ~84) t (12) t i} where t 1s the quasi-stationary temperature state in hours. This time was calculated from Eq. 12 to be about 10.0 hours. Thus, after about 10 hr, the tempera- ture of the outside of the pressure shell will be at about 162°F above ambient temperature, while the center of the core will still be at about ambient temperature. The actual ambient temperature in the pits will probably vary during the preheating period; most of the calculations of this report assume an ambient tempera- ture of 130°F in the pit. It was assumed for these calculations that the reactor and pit were both, at the until the reactor pressure shell outer temperature reaches 1200°F, During this period, quasi-stationary state, the temperatures are 1in the and every temperature in the reactor is raised . uniformly at the rate of 10.1°F/hr: (13) where quasi- period, 1200 - 292 10.1 t, is the time at the end of the stationary state. During this t, — t, 89.9 hr, - the electrical heater power must be continually increased as the pressure shell temperature increases to malntailn a constant rate of heat f1low power into the reactor. The heater must therefore be equal to 10 kw plus the heat loss through the 1insu- lation. insulation may function of reactor pressure outer The heat loss through the calculated as a shell temperature from the following be equations: Ay A 1 < 1 Ay \ €, G- _ (14) S hA (T, - T, ) il q 171 1 = THe 3600 — 4 “1 0.173 (15) g = h,A, Ty, - T,) ¢ 3600 1 4+ €1 kf (16) g =— A, (T, - T;) , 71 0.173 (17) q = h,A, (T, - Ta) + —ggaafesAs start, at a temperature of 130°F, The time required to raise the mean temper- ature of the reactor from 70 to 130°F is about 6 hours. It may therefore be considered that t 1s really about 16 hr and that at the end of the 16-hr period the reactor pressure shell outer temperature will be about 292°F and the center-line temperature will be about 130°F, The next period of the preheating process 1s the heating of the reactor 86 T where q."—' e~y () - (% T a ] heat loss through Btu/sec, heat transfer Btu/sec* ft?:°F, heat transfer area, temperature, R, thermalconductivity,Btu/sec‘ft2 (°F/ft), thickness, insulation, coefficient, ft2, ft, emissivity, and the subscripts l] = outside of reactor pressure shell, 2 = inside of thermal insulation, 3 = outside of thermal insulation, I = insulation, He = helium between pressure shell and thermal insulation, a = ambient, Equations 14 through 17 and the following data were used to calculate the heat loss through the insulation for various pressure shell tempera- tures: 1. € = 1.0, 2. The data of King(!?) were used to evaluate h, , 3. The dimensions of thermal insu- lation were: Outside diameter 76.25 in. Outside length 80.5 1in. Thickness 6 in. (4 in. of Superex, 2 in. of Asbestos-Sponge}) 4. The thermal conductivity value for the insulation, as found in the previous section on “Heat Loss Through Insulation,” was used. The results of the calculation are shown 1n Fig. 65, where the heat loss through the insulation 1s plotted against the reactor pressure shell outer temperature. Temperatures at other points 1n the reactor thermal insulation are shown by the dotted line. The last portion of the preheating process, that is, when the heater power is reduced to maintain the pressure shell outer temperature at 1200°F, 1is evaluated by a graphical method de- veloped by Schmidt.(2%) Asa simplifi- cation, each helium shell 1s divided between adjacent beryllium oxide shells, and the Inconel pressure shell is replaced by an equivalent thickness of beryllium oxide. The reactor 1s then treated as a homogeneous cylinder with a thermal conductivity equal to the average thermal conductivity of the composite beryllium oxide and helium shells. A plot of the tempera- tures in the reactor for the first 8 hr of the last portion of the pre- heating period is shown in Fig. 66. 1200 1000 800 c L w o 2 L 600 o w a = w - 400 / 200 / OF INSULATION __ e | [ | OUTER SIDE OF INSULZ e e AMBIENT TEMPERATURE 0 0 4 8 12 16 HEAT LOSS THROUGH INSULATION (kw) Fig. 65. Temperature of Outer Side of Pressure Shell vs. Heat Loss Through Insulation. After 8 hr, the temperature of the core center line is about 1125°F, A summary of the temperatures and powers in the entire preheating period is shown in Fig. 67. The maximum temperature gradient 1in the pressure shell at any time 1is approximately 6°F/inch, HELIUM LEAKAGE THROUGH CLEARANCE HOLES IN THE REACTOR THERMAL SHIELD The tubes which contain the control rods and fission chambers pierce the reactor thermal insulation at both the top and bottom, and there are six such tubes. Figure 68 shows a sketch of a typical tube and the passage through the reactor thermal shield. The helium inside the reactor thermal shield, being at a higher temperature than the room helium, will flow through the clearance holes in the reactor thermal insulation and consequently will add 87 Dwg. 19441 0 1200 = 7 = 1200°F = SURFACE o 20 t 1180 a AB=0.804hr / o s = 40 10A8 =~ Bhr 7 1160 S 9Af ///// .62 _8A8 N / = 60 T 1140 /// 2’ ST gop 046 — / nzo ¥ LéJ S—f A ~ " ___-———/;//_/// : % m g 100—'__'——'—_—— ey _—// / 1100 Ej - =" = 7 7 o g é j:: ah ——////// = 5 =z — 5A8 % r —-///// w x © 420 e anb - T | 4 1080 w [ 2A0 —— /—/ // w 140 —— 1060 o a6 L] < 2 L 17 _INITIAL TEMPERATURE | < — DISTRIBUTION {APPROXIMATE) x 160 = 1040 a | 5 | — 180 1020 1.24 2 3 4 5 6 7 8 9 10 15 20 30 RADIAL DISTANCE FROM CORE CENTER (in.) Fig. 66, Temperature vs. Time Relationship for Reactor Core and Pressure Shell. to the room cooling requirements and the reactor electric heater require- ments. It was assumed that the flow through the bottom clearance holes was negli- gible and that the flow through the upper clearance holes was that due to the difference in head between the helium in the clearance holes and room helium. The head available for flow 1s, then, (18) P=h('oa_pc): where P = pressure head, 1b/ft? P, = density of ambient helium, 1b/ft3 P, = density of helium in clearance hole, 1b/ft3, h = height of clearance hole, ft. To be conservative, it was assumed that the temperature of the helium in the 88 1200°F; temperature was taken as about 130°F, Thus clearance hole was the room 6.125 P = T x (0.0092 - 0.00335) = 0,00299 1b/ft? The loss in pressure head in a gas flowing through an annulus in laminar flow is 12.GL (19) p = Fr yig p where f = viscosity, lb/hr-ft, G = flow, 1lb/hr- ft? L = length = height of clearance hole, ft, y = annulus gap, ft, g, = gravitational constant, ft/hr? © = gas density, lh/ft?3 DWG. 19142 1200 26 — / - 1000 / ry 22 800 N 18 ™ ° - W 3 g St [0 Y 600 14 W s =z w O a o s w [t 400 10 200 \ 6 N 0 2 0 20 40 60 80 100 120 140 TIME (hr) Fig. 67. Summary of Temperature and Power in Entire Preheating Period. An evaluation of Eg. 19 gives 6.125 12 x 0,102 x G x T P = = 4,24 x 10°% G 1b/ft? , 0.39\? ) —EE— X 32,2 x (3600)° x (0.00335) The flow, G, 1s then evaluated by equating the available pressure head 7 3.75\2 2.97\2 to the loss 1n head because of flow: A= 6 X— || — - |- 4 12 12 G = 7.05 1b/hr-ft? , = 0.1715 fe? Since there are six 1dentical . ) Therefore the weight flow 1is clearance holes, the total flow area 1s W =0.1715 x 7,05 = 1,21 1b/hr , 89 (< 2.97in. _— 33/4 T — Fig. 68. Rod Sleeve Through Thermal Shield. and the heat loss 1s Q=MWe (T, -T,) =1.21x1.24 (1200 -130) = 1605 Btu/hr = 0.446 Btu/sec , where T = temperature in clearance hole, °F, T, =ambient temperature, °F, The heat loss through the clearance holes 1s therefore approximately 0,45 Btu/sec. SPACE COOLER PERFORMANCE The bulk of the equipment of the ARE is contained 1n three sealed pits, B4 - 14 —— —= — -14 -— OUTSIDE : QUTSIDE —— e — i o L e L bmee e B Y e 27l — 18% -3l —- NOTE: DIMENSIONS IN INCHES Fig. 69. 90 ", 6-DIA HOLES FOR CEILING SUSPENSION which are kept cool by the use of space coolers. A typical space cooler is shown in Fig. 69. Fach space cooler contains two helium blowers in parallel (total capacity 7200 cfm) and a water cooling coi1l. The entire unit was supplied by the Trane Co. The cooling coil is a Trane Co., series 93, type S coil, with a 12- by 48-in. face and four rows of tubes longitudinal to the gas flow., The heat transfer coefficient of such a coil, operating with air on one side and water on the other, 1s given 1n ref. 21, for various water and air velocities. As used 1in the ARE, these co1ls wi1ll have helium instead of air on the gas side. Since 1t was necessary to convert the performance data from those for alr-to-water operation to those for helium-to-water operation, the follow- ing equation, from which values can be obtained that are approximately the same as the actual performance data given 1in ref. 21, was used: 1 0.00374 | 0.189 (20) — = , hA ,0-8 L0 6 w a where h = over-all heat transfer coef- ficient, Btu/hr:ft?-°F, A = heat transfer area per row per square foot of coil face area, fo?, v _ water velocity, ft/sec, - air velocity, ft/min. To use Eq. 20, an equivalent air UNCLASSIFIED DWG A-3-5-224A ————— e 3 - - - - . "Mg-DIA HOLES FOR / CEILING SUSPENSION / 4% -P TAP RETURN 3t 376" ./ NEAR END L NEARE! ey Dy ; BRERS | | 25 | o = i : oxr ™ : | »x O o ! | et : i ol = i A S S—— Y . /u’ g | ALEMITE FITTING // —~ 9%~ re N kaHecpHe a, For sections 1, 3, 5, and 7 -32,300 -17,600 -9090 For sections 2, 4, and 6 -3120 -1700 -879 The helium heat transfer coefficient, hH ] formula: ¢(1%) H (37) He-m D He He He k h = 1.02 — Rel: 4% Pr°~5( .+ may be evaluated from the following 0.14 /D 0.4 /D \o.8 ) <_Hi> <_?.> Grl-05 He ! He LHe' Di 97 where D = equivalent diameter, ft, D, = outside diameter of helium annulus, ft, D. = inside diameter of helium annulus, ft, Re = Reynolds’ number, Pr = Prandtl’s number, e : . : — =ratio of viscosity at bulk Fs temperature to viscoslty at sur- face temperature, L = length of passage, ft, Gr = Grashof’s number, Having evaluated the constants 1n Eq. 36, the solution of the equation is straightforward. Once an expression for @He 1s found, Qm from Eq. 34, can be evaluated The solutions for helium velocities of 1, 3, and 10 ft/sec follow: 1. For a helium velocity of 1 ft/sec, (38) Gy, = ny g0 10% 4 n, e 8- 29% +n 6-0.9411 + K 3 and (39) & =3.39n, e>1%% _1,95n, ¢ 6:29% +0.559 e=0.941x + | | where n = arbitrary constant, K = 1070 for sections 1, 3, 5, and 7 = 104 for sections 2, 4, and 6. 2. For a helium velocity of 3 ft/sec, (40) €, =n 6.10x He 4 € * -6.87x nse +n6 6'0.3921 +K and (41) & = 6.23 n, eb.10x __ 4 9 n o~ 6.87x t0.664n, e 0-992% + g | 3. For a helium velocity of 10 ft/sec, 3 _ 7.62x -8.08x (42) Gy, = n; e tng e + n9 6'0.1371 + K and (43) & = 13.7n_ e7-62% _ 19.4 n -8.08x m 7 8 + 0,772 ng e 0. 1372 4 g | There are nine arbitrary constants in Egqs. 38 through 43. These constants have a different value in each of the 98 seven sections; there are therefore, altogether, 63 arbitrary constants. These may be evaluated by means of the following boundary conditions, which apply to all three helium velocities: (44) lim # X, — ~® 1 He is bounded. Since each section has a different origin (see definition of x, following Eq. 27}, the subscript on x refers to the number of the section being considered. Thus (45) 6 -9 , He xl=0 He x2=0 (46) g = & , n 11=0 " x,=0 d@m d@m (47) = , dx xl=0 dx x2=0 (48) 0 = g , He x,=2/3 He %, 4y=0 r =2,3,4,5,6 , (49) ¢ = g _ H - ! " xr—2/3 € Ir+1_0 r = 2’ 3’ 4, 5’ 6 r d@m dé * X, =2/3 * T4y =0 r = 2’ 3) 4, 5! 6 ) (51) lim QHe 17—'(1) 1s bounded. Equations 44 the nine arbitrary con- , to n, for each of the seven sections. The results of the evaluation are given in Table 18, through 51 were used to evaluate stants, n The values of the arbitrary con- stants and Eqs. 38 through 43 were used to calculate the temperatures of the helium and the metallic envelope for all posttions along the pipe line for the three helium velocities. The in Figs. 75, 76, and 77. The minimum helium temperature results are shown 1000 900 800 700 TEMPERATURE (°F) 600 500 100 1000 900 800 TEMPERATURE (°F) 700 600 500 Fig. 75. DWG. 19147 SECTION 4 SECTION 5 T \ / ) L\\\c HELIUM L//}r’,éf,/*r' \\r \\\\O<:::,—WALL o 94,4 2 4 6 8 2 4 8 DISTANCE ALONG PIPE LINE (in)) SECTION & SECTION 7 ’/0/_/() y >\ / ‘k\“x HELIUM Y//;f/, \ / —WALL 2 49 6 8 2 4 8 DISTANCE ALONG PIPE LINE (in) Temperature Patterns of Helium and Wall of Monitoring Annulus. Helium velocity of 1 ft/sec. 99 TEMPERATURE (°F} TEMPERATURE (°F) He l 100 DWG. 19148 1100 1000 HELIUM 900¢ ~ 1//} i 800 | / L WALL 700 | SECTION 4 SEGTION 5 600 E 2 4 6 8 2 4 6 8 DISTANGE ALONG PIPE LINE (in) 1000 900(*‘~a\\\1 HELIUM ) < /O/(/O/( WALL 700 % ~ SECTION 6 SECTION 7 600 | 2 4 6 8 2 4 6 8 DISTANGE ALONG PIPE LINE (in.}) Fig. 76. Temperature Patterns of Helium and Wall of Monitoring Annulus. ium velocity of 3 ft/sec. 101 1300 12004 1100 t000 TEMPERATURE (°F) 900 800 - 700 HELIUM E 1 I S ; ‘: | i | | | e i S— S e e : — — — | SECTION 1 ‘ SECTION 2 SECTION 3 SECTION 4 1 | | | : , : 1 : 1 i j ’ ‘ -8 -6 -4 -2 0 2 4 6 8 2 4 8 4 6 8 DISTANCE ALONG PIPE LINE (in) 1100 [ HELIUM | | __ 1000 — 5 ¢ & LwALL '—.-.. 2 900 e k}\( ~ _ - Ll ; | a | | S ! i _o-"('/{ L i i ’_— 800 1 . . | | | SECTION 5 SECTION 6 SECTION 7 700 ’ 2 a 6 8 2 4 6 8 4 8 DISTANCE ALONG PIPE LINE (in) 77. Temperature Patterns of Helium and Wall of Monitoring Annulus. Helium velocity of 10 ft/sec. Fig. DWG 19149 l i i e ] TABLE 18, VALUES OF THE ARBITRARY CONSTANTS [ SECTION NUMBER 1 2 3 4 5 6 1 n, -80.6 2.69 -2.72 2.88 ~2.70 2.38 0 n, 0 -76.1 75.5 ~76.6 15.6 =75.7 89.5 ng, 0 960 -447 722 =575 654 -637 ng -30.5 0.476 -0.459 0.467 -0.461 0.473 0 ng } 0 -27.6 27.7 -27.5 28.0 -27.6 27.9 neg | 0 965 -222 796 -354 695 -431 n. ~8.64 0.0554 -0.0537 0.0546 -0.0538 0,0548 0 ng 0 -8.20 8.19 ~7.95 8.05 -7.96 8.04 ngy 0 968 ~84.2 891 ~-155 826 -213 and the minimummetallic envelope temper- G 19150 ature have been plotted against helium 1000 velocity in Fig, 78. Since the temper- ature of the fuel 1in the pipé line 1is equal to the helium temperature and 900 since the fuel melts 1n the vicinity o ot 950°F, 1t can be seen from Fig, 78 o that the fuel will remain molten, 1in E 800 this particular case, 1f the helium & velocity exceeds about 8 ft/sec. % S 700 |- 2 = z = 600 |- 500 | o 2 4 6 8 o HELIUM VELOCITY { ft/sec) Fig. 78. Minimum Wall and Helium 102 Temperatures vs. Monitoring Annulus. Helium Flow in Chapter 7 HELIUM SUPPLY AND VENTING SYSTEM TRUE HOLDUP OF FISSION GASES IN TANKS The fission gases removed along with helium through the various gas vents 1n the fuel circuit are held up in the pipes and tanks of the off-gas system (Fig, 79) until the activity in the fission gases is reduced suf- ficiently to permit their being discharged into the stack. The holdup time of the gases in pipe lines or similar shapes of large length-to- diameter ratio 1s readily calculated as the pipe volume divided by the gas volume flow rate. All the gas is held up substantially the same amount of time. In large tanks or similar shapes of small length-to-diameter ratio, the average gas holdup time is the same as 1n a pipe line of similar volume. However, because of the mixing of the gas in the tank, not all the gas 1s held up for substantially equal periods; that 1s, some of the gas leaving the holdup tank is held up for much less than average time and some for much more than average. The true activity of the gases leaving the holdup tank (Fig. 80) of the off-gas system has been calculated and compared with the activity which would be present 1f all gases were held up for equal periods. The mixing of the gas 1n the tank 1s due to convective and diffusive forces and occurs fairly rapidly compared with the average holdup time in the tank. Thereasonably conservative assumption was made that the gas entering the tank mixes instantaneously with the gas i1n the tank. The follow- ing definitions were made for the calculations: N = flow rate of gas, V = tank volume, ft3, C(t) cfm, concentration of gases of age t, that is, C(t) dt equals the ratio of the volume of gas with age from t to t + dt compared with the total tank volume, V (age is used here to mean time measured from the time the gases enter the off- gas system), t = time, Then, min, (1) C(t + dt) dt N = C(t) dt - C(¢t) dt'jfdt , C(t + dt) - C(t) (2) P = - C(t)fif’ (3) dCCt) ey N dt y ' (4) C(t) = K e~ (N V)t where K 1s an arbitrary constant. When t = t,, where t, 1s the age of the youngest gases in the tank, N (5) C(t) dt =-—dt v and N (6) Clty) =—. V Substituting Eq. 6 in Eq. 4 and solving for K gives (7) _fi1= K e-(N/V)t0 v (8) K = W/ v N (9) C(1) =——em W/ V) Ctato) V The energy, E(t), in the fission gases xenon and krypton (bromine and iodine removed previously) at time t 1s plotted against t in Figs. 81, 82, and 83 for the separate xenon and krypton 1sotopes and for the total of these isotopes. For the determi- nation of E(t), 1t was considered that there had been 200 hr of reactor operation prior to time zero and that the fission gases had subsequently decayed time t. 103 Y01 = - 36in —L- 4ft-3in. MATERIAL AND MATERIAL SPECIFICATIONS UNCLASSIFIED aTy NAME [ SIZE | MATERIAL DWG E-A-3-8-524 P2 KINNEY VAC PUMP NO Y26166 = 1'% hp L2 DRUMS 55 gal 55 1 VAPOR TRAP, NoK " 55 gal S5 T 1 VAPOR TRAP, SUMP 55 gaf 55 . b 2 SURGE TANK VAPOR TRAP 55 gal 55 i 13 FLEXIBLE HOSE | %inx3f1-0in LG SS P 6 RESEARCH CONT. CO VALVE 4 in 1IPS 5% ! ASREQ | MANIFOLD, VAC 2in IPS SCH 40 | WS i fft-6in AS REQ | ARLINE FROM 1O cfm BLOWER | 2in. tPS SCH 40 | WS 6 SWING CHECK VALVES | 2iniPs ©58 ) = g VALVE ; G b 1 t i OIL CATCH BASIN LoGin IPS x 24in $5 4 16 4o ) 10 | CHECK VALVE 3 ss 1832 - goa = df-dnm 5 5 | SOLENOID VALVES | 1in. IPS-SCREW BRASS L - = ASREQ | VAC PUMP LINES | tin IPS SCH 40 ot N T 1 FULFLO FILTER : ol f g9 2 RADIATION MONITORS AND SHIELD , b ! 3 PACKLESS VALVE | ‘4in BAR STOCK : 58 £ ASREQ | VAC LINE ' Yin IPS SCH 40 WS o 2 MASON NEILAN VALVE 1 :/4 in {TYPE 108) 55 Ll .6 SOLENOID VALVES DY 1PS 55 Lo o DUMP TANK VAPOR TRAP FUEL SURGE TANK NOf 5 ; 2 SWING CHECK VALVE o1l in 1PS 55 ! b MONITORING SYSTEM HEATERS 1 RELIEF VALVE ¥, in 1PS | BRASS 37 TANK NO 3 FILL AND FLUSH TANKS 4 i . (SAME TYPE VALVES AND B 1805~ ~ HOSE ON EACH TANK) Jc N v ah . - 6.~ 35 2t 2 FUEL ENRICHING - o SYSTEM TFANKS TEST PIT — 2 ft-in L8075 Laoa 4ft-0in- == 3ft 4in = - 1Z2in S eri - TANK NO 4 TANK NO.S TANK NO 6 L8o2 DUMP TANK .~ FUEL SURGE TANK NO. 2 G6ft-0in A tft-6in — [ e ‘.14_1- "_:‘l’ _= ! ~ 38 10 STACK 19 in 1Q ¢fm BLOWER Fig, 79. 0ff-Gas Disposal System, 1-in. NPS TO DIMENSIONS SHOWN MATERIAL STAINLESS STEEL XB/Q—in. EXISTING PIPE COUPLING 11 ggfi%f?zzzfigfiz/ DN __/—___/ e l I I L ] LTI o et 1D UNCLASSIFIED DWG. C-A-3-8-37A N Fig. 80. 0ff-Gas Disposal System Drum. If R 1is the ratio of the true activity of the gases leaving the holdup tank to the activity which would be present i1f all the gases were held up equally, ‘s N /v f —en (N/V)Ct-t0) E(¢)dt ty V (10) R = E( +V) t ———— o N where t, 1s the age of the oldest gases 1n the tank. The total energy in all the fission gases developed may be used since the final answer desired 1s a ratio. It 1s 1mportant to note that for Eq. 10 1t is assumed that all the gases 1n the tank contain equal amounts of fission gases. This is obviously not true of the gas originally in the tank., Thus, at the beginning of operation, the value of R is actually less than 1s predicted by Eq. 10. The highest possible values of R will occur after long periods of operation, and Eq. 10 will therefore be evaluated with t, sufficiently large for the contribution to the total activity of the gases of age greater than t, to be neglected. The curve of E(t) vs. t shown in Fig. 83 for the total energy of all xenon and krypton i1sotopes was broken up into a series of M segments between t, and t_, and an equation of exponential form was fitted to each segment. | 105 e UNCLASSIFIED 3 DWG. 19302 W=0496 X £ X PXF (/) WHERE W=WATTS £ =ENERGY OF RADIATION, Mev £ =REACTOR POWER, MEGAWATTS F(r)=ACTIVITY FUNCTION i NQOTE.: ! : ALL ISOTOPES CONSIDERED AS SATURATED AFTER 200 hr OF OPERATION EXCEPT Xe'33 M o [ SUBSCRIPTS: {1=153-m HALF LIFE (2)=9.2-h HALF LIFE o xe'2266% OF SATURATION) xe135 (1) ™ o _ wn ACTIVITY FUNCTION, £ {#) (DISINTEGRATIONS /10,000 FISSIONS) M f 10 100 1000 10,000 100,000 172 hr thr fahr 24br 4 days 40 days TIME AFTER REACTOR SHUTDOWN (min) Fig. 81. Integrated Xenon Activity, F(t), vs. Time after Reactor Shutdown. Thus, for the nth segment, (11) E (t) = A e bnt, t and then o ¥ f‘n le-(N/V)(t_to) A e“bnt gt - t ) n (12) R -2 | , E + v t — ° N where ty = tp, 1 . N t (13) R = ———————”17—-223 An-TTftn 1 em LN/ tb, L et/ vy ey gy , E{t, +—) =2 n- 0 N n=1 N ¥ A — . (14) R = _ 2 "V {e-[(N/V)+bn]t+(N/V)to J , E + v N + b thoi t o = - na o Ty =1 v " _...IY.._G(N/V)tO N A R =__l/___—v Z _N—" [ e Lewsvy+enle, _ - [(N/V)+bn]tn_1] 0 N n=1 7_*_ bn 106 n o r th N o ACTIVITY FUNCTION, £ (/) (DISINTEGRATIONS /10,000 FISSIONS) o, 172 hr {hr TIME AFTER REACTOR SHUTDOWN (min) Fig. 82. The data and results of the calcu- lations for the particular problem of the first holdup tank in the off-gas system are given in Table 19, As a check on whether the intervals selected were small enough, the interval between t;, and t, was divided into two parts. Recalculation of the data for the smaller intervals is given in Table 20, The valueof 295 checks very closely with the value of 296 calculated for the original intervals, and thus the intervals selected were probably small enough. The final answer, then, is that the actual activity of the gases coming out of the tank 1s 23% greater than the activity which would be present UNCLASSIFIED DWG. 19303 W=0.496 X £ X P X F(#) WHERE W=WATTS — . £= ENERGY OF RADIATION, Mev P = REACTOR POWER IN MEGAWATTS - F{#) =ACTIVITY FUNCTION NOTE k85,1 =0.0017 SATURATED F() AT 200hr =0.04 SUBSCRIPTS: ()= 4.4-h HALF LIFE (2)=~10-y HALF LIFE 100 1000 10,000 {12hr 24 hr Integrated Krypton Activity, F(t), vs. Time after Reactor Shutdown. 1f all the gases were held up for equal periods. TEMPERATURES IN THE HELIUM VENT LINES CONTAINING FISSION GASES The off-gas system carries gases from the surge tanks, the dump tank, and the pits to the exhaust stack (Fig. 79). At times, a portion of these gases will be radioactive fission products. The gas flow rate is generally quite low, and the question arises as to what temperatures will exlist on the off-gas system with essentially stagnant radioactive gases 1n the system. The total energy ofall the fission gases produced after 200 hr of reactor operation at 3 megawatts is about 14,8 Btu/sec for a delay time of 1 1/2 minutes.(??) The 107 TABLE 19. DATA AND RESULTS FIRST HOLDUP TANK IN OF CALCULATIONS FOR THE THE OFF-GAS SYSTEM Data: t, = holdup time in off-gas system before reaching tanks = 6 hr = 360 min N = gas flow = 1/2 ¢fh = 1/120 cfm V = tank volume = 7.5 fe? vy 900 mi - = min N v E(to ' z—v> - E(1260) = 350 A Vo ) e-[(N/V)+bn]tn y N V n t, (min) E(t) A b n n Lo 1e || - e n n-—- ] t, = 360 800 t, = 1,000 | 419 | 1152 | 1.011 x 10°° 296 t, = 2,000 | 233 752 | 0.587 x 107° 106 t, = 4,000 113 480 | 0.362 x 10°° 25.7 t, = 7,000 56 288 | 0.234 x 10°° 1.5 ts = 12,000 25 173 | 0.161 x 10°° negligible t, = 20,000 10 99 | 0.115 x 1073 negligible Y- 4292 429,92 R = = 1.23 350 energy is divided among the fission gases as follows: Btu/sec Xenon 2,2 Krypton 2.0 Bromine 1,4 Iodine 9.2 This energy may be distributed over the gas volume 1n the surge tanks, which 1s about 1.3 £t3, or 1t may come out of the fuel i1n the dump tank, 1in which case 1t will be distributed over The a greater gas diluent volume. 108 maximum energy release in the off-gas which occurs 1n the release of gases from the surge tanks, 1is therefore about 11.4 Btu/sec*ft”. The fission gases on leaving the surge tanks enter a fuel vapor trap (Fig. 84) and then a 2-in. IPS pipe. The trap and the pipe are the critical system, points 1n the off-gas system, since they have the greatest volume-to- surface ratio and since the fission gases are youngest at these points. The energy dissipated per square foot of outside surface by radiation and 1000 ENERGY (watts) UNCLASSIFIED 10,000 OWG. 19304 5 NOTE: ) Xe'33 % 0.66 SATURATED Ke®® 5, » 0.0017 SATURATED 100 \ ! 10 100 1000 10,000 100,000 TIME AFTER REACTOR SHUTDOWN (min) Fig. 83. Energy Emission of Xenon and Krypton after Shutdown from Operation of 200 hr at a Power of 3 Megawatts. TABLE 20, RESULTS OF CALCULATION FOR A SMALLER TIME INTERVAL N (N/V)e, A {—[(N/V)"'bn]tn —_— -_———t e v ° N V n t (min) E(t) A b " n n -[(N/v)+qn]:n_4 - e ty = 360 800 t] = 600 600 1233 1.20 x 10°° 159 t, = 1000 419 1023 0.90 x 10-3 136 Y = 295 convection may be written 1n the where ’ familiar form Q = heat dissipated, Btu/sec-ft?, T A\ T\ € = emlssivity, . (15) o 0.173 ( s ) < e ) T, = surface temperature, °R, S — € —— — . 3600 100 100 Te = environment temperature, 'R, hc = free convection heat transfer * hc(T, - Te) ! coefficient, Btu/sec*ft?*°F, 109 UNCLASSIFIED OWG. D-A-3-8-73A He {NLET { '/, -in. SCHEDULE 4G PIPE — F { Z. ~ ’-—* 2-in. SCHEDULE 40 PIPE CAP INLET ANNULUS {2-in. SCHEDULE 40 PIPE } — 10in. -—1‘ 5 /“1 ————————— == ’d —[=TO VENT o s 5 ] o S \Wl//é < FROM SURGE |___ __________ pay TANK ? & | \ I ‘ - PAN LY " J ' N VAPOR INLET ( {-in. SCHEDULE 40 PIPE) /] # | A \\ / | J !Zfi \ VENT{ % -in. SCHEDULE 40 PIPE ) } \ ™ Y,~in. SCHEDULE 40 ELBOW 6-in. SCHEDULE 40 PIPE CAP o .4 ‘F l ‘-4! S § / 4-in. SCHEDULE 40 PIPE CAP J | | MAX. LIQUID LEVEL ON BACK SURGE \\; L I ] MAX. LiQUID LEVEL DURING | GAS DISCHARGE ———— | 7 o N=UE == V= NNER SHELL ( N = E II —— 4= ! 4-in. - — — - SCHEOULE 40 PIPE ) B o T ] N || / FILLLEVEL———Y P4 o | | f | OUTER SHELL {6-in. | c SCHEDULE 40 PIPE) —————————==N | © L/ | - 7 17 N | } v N | 2 Y N (4 ‘+ ARAAANANN N | : A V-NOTCHES TO BE APPROX. Ya=in. WIDE x Y4-in, DEEP —— " [N B / Y 6-in. SCHEDULE 40 PIPE CAP —— A - ———— 6,625 in.———-l ALL MATERIAL TYPE-316 STAINLESS STEEL Fig. 84. Surge Tank Vapor Trap. 110 The free convection heat transfer coefficient i1s determined from the data of Nusselt,(ls) McAdams, and W. J. King, ¢!'?) who correlated Nusselt’s number with Grashof’s and Prandtl’s numbers (as given by Jakob(14)), The pertinent physical dimensions and unit energies of the fuel vapor traps and the 2-in, listed in the following: IPS pipe are FUEL VAPOR 2-in TRAP ; (por trap) 1PS PIPE Gas volume, ft’ 0.13 0.0233 {per ft) Surface, fr2 2.6 0.622 (per ft) Equivalent outside 0.55 0.198 diameter, ft Total energy, Btu/sec 1.48 0.265 (per ft) Energy per ft2of sur- 0.246 0.427 face, Btu/sec‘ft2 For proper operation, the fuel vapor traps must be maintained at 1500°F, The traps are covered with electric heaters and insulated. The heater power 1is controlled by thermocouples which measure the trap temperature. The heat input required to hold a trap at 1500°F is about 0.71 Btu/sec (cf., chap. 6, section on ‘‘Heat Loss Through Insulation” ). The energy loss through the insulation would more than be balanced by the energy in the and the heaters could therefore fission gases, be shut off as the fuel vapor trap began to heat up slowly. The heat capacity of the vapor trap, including contained liquid, is about 13.2 Btu/°F. A tabulation of the energy dissipations and of the temperatures of the vapor trap at various times 1s given 1in Table 21. The vapor trap temperature would be increased by only about 40°F at the end of 20 min, and the heaters would have to be turned on again as the fission gases further decayed. The 2-in. IPS pipeis neither heated nor insulated, and therefore Eq. 15 may be used to calculate the pipe outside temperature (the inside temper- ature 1s not greatly different). For an emissivity of 0.5, the pipe outside temperature necessary to dissipate 0.265 Btu/sec*lineal ft is about 380°F, VACUUM PUMP PERFORMANCE There are two vacuum pumps in the off-gas system (Figs. 79 and 85). They serve many purposes, but their most severe requirement is that they must reduce the pressure in the fuel system sufficiently to permit the boiling off of NaK which cannot be completely drained from this system (NaK is circulated in the fuel system for precleaning and hot testing), Figures 86 and 87 give the experi- mentally determined performance of the two vacuum pumps. Figure 86 shows the variation of pressure with time 12, 3-f¢?° rate of in a pump-down test of a tank; Fig. 87 the pressure rise due to leakage after the shows TABLE 21. ENERGY DISSIPATIONS AND TEMPERATURES OF THE VAPOR TRAP AT VARIOUS TIMES HEAT IN HEAT LOSS HEAT RATE OF TIME FISSION THROUGH INTO TEMPERATURE TRAP TEMPERATURE {min) GASES INSUIATION TRAP RISE IN TRAP (°F) (Btu/sec) (Btu/sec) (Btu/sec) (°F/min) 1.5* 1.48 0.71 0.77 3.49 1500 10 0.91 0.74 0.17 0.77 1530 20 0.75 0,75 0.0 0 1538 *The gas is assumed to enter the trap after a delay of 1.5 minutes. 111 cll UNCLASSIFIED -——SQOLENCID VALVE DWG 20225 NOTE: Y%, THREE WAY COCK o) ALL DIMENSIONS FOR ALTERNATE OIL 5 T ARE IN INCHES FEED LINE 1 %6 , 7% ] \ - PLAN OF BASE 11080-29-N 16 Y5 | I o FOUR HOLES FOR Y, BOLTS - l O Y, PT R | ! 33 Ve Vo PT. FILLE 7 J_z/% P.T. DISCHARGE | 25 | | —] | 12 x18 SEPARATOR TANK | 1 1 . Y4 PT. WATER ‘ PT. SUCTION ‘ P OUTLETS Va Ya PT. WATER 37% INLET M gta | dl Y%, PT. DRAIN 1l L VALVE i @ O 1 T il - - 18‘/2 15373 B8, T TT TT th t4 +h ‘3 Lo 1y 1 1) 37 tHH || by 1! 11 11 L Fig. 85. Kinney Vacuum Pump. DWG. 131 5! 1250 1000 750 Pump 8 500 PUMP A 250 o ' 2 3 4 PRESSURE {(mm Hg) 400 \ 300 \ \\\ S \ \ @ & LIEJ \ E 200 ——— 100 o 10 20 30 40 50 PRESSURE {(mm Hg) 300 200 / 4 100 e )/ P A PUM KINNEY VACUUM PUMP 0 0 5 10 15 20 25 30 35 VACUUM {in)} Fig. 86. Vacuum Pump Performance. pumps are shut off. From these curves, curves of the variation of rate of change of pressure with pressure were drawn, as shown in Fig, 88, If a leak develops 1in the systenm, it may be desirable to remove all the NaK from the system. In order to boil off NaK at 1200°F, a pressure of about 100 mm Hg or less must be maintained. The following calculations were made to determine the maximum size of leak which might exist and still permit the vacuum pumps to maintain a pressure of 100 mm Hg. The process of evacuating gas from a tank or contalning system is 1so- thermal, and therefore (16) PV = constant = K or K 17 P =—, (17) v 113 here P = pressure, mm Hg, V = volume, fts, K = a constant. !56.15152 4 < ifiig/ 3 g ,/////,PUMPA £ o o ¥ [9p] . T 7 ? | 0 | 0 90 120 150 180 TIME (min) Fig. 87. Leakage Test. 0.00 0.0t 1000 500 200 & I £ E & T 400 w) w) V4] ot o 50 20 10 0.1 0.2 0.5 1 Fig. 88. Vacuum Pump Performance. 114 Differentiating with respect to time, t, gives (18) K dV V2 dt and dividing both sides by P gives (19) However, K (20) dP dt _ K dV P Pv2dt- = PV, and therefore dP dV dt _ dt p v Since the volume of the tank tested was 12.3 ft?, Eq. 20 becomes AP/AF (mm Hg/sec) 2 AP/AF (mm Hg/sec) Volume of test system, !!G. 19163 PRESSURE (mm Hg) 12,3 i@, dP dV dt dt dV 12.3 | 4P (21) — or | — —_ P 12.3 dt P dt The values of volumetric flow, dV/dt, as calculated from the pump-down test results, are given in Table 22, The values are for pump 1nlet conditions; that 1s, the pressure 1s equal to the system pressure and the temperature 1is approximately 560°R, since the gas is cooled before 1t reaches the vacuum pumps. The vacuum pumps are of the rotary positive displacement type, and 1t would therefore be expected that the volumetric flow would decrease slightly with decreasing pressure, since the leakage past the rotor increases. It 1s apparent from the calculated values of volumetric flow, dV/dt, that the curves of Fig. 88 are probably somewhat inaccurate., The 1naccuracy 1s not entirely unexpected because the information for Fig. 88 was obtained by measuring the slopes of the curves of Fig. 86, and the measurements were not highly accurate. The accuracy 1s of the orderof t10%, however, which 1s sufficient for the purpose of the problem. The valuesin Table 22 for volumetric flow are for pumping air. The leakage past the rotor when pumping helium may be somewhat higher than when pumping air, but 1t is probably accurate enough to assume that the volumetric flows are the same for both helium and air. The volumetric flow of helium through a leak can be approximated by considering a hypothetical “leak” in TABLE 22. CALCULATED RESULTS OF the form of a round orifice: dV (22) (———) = CAv , dt CE or1 i1ce where dV (;?) = orifice volumetric flow, orifice cfs, C= orificecoefficient =0,60, A= qrifice area, fe?, v = gas velocity 1norifice, ft/sec. The critical pressure ratio for a perfect gas 1s given by 2 Y/ (ry-1) 23 = : (23) e (5 1> : thus with », = ratio of specific heats = 1,67, It 0.487 e The throat pressure for sonic velocity is therefore (24) P, = 0.487 x 760 = 370 mm Hg. The throat temperature 1is (25) Tth = Tnmb (rC)(y‘l)/y! where T ., = ambient temperature in the helium monitoring annulus = 1660 °R, T,, = throat temperature = 1660 (0.487)(Y-1)/7 = 1235°R. For system pressures less than 370 mm Hg, the volumetric flow through the orifice will be constant. The velocity in the throat will always be THE PUMP-DOWN TEST OF A 12.3-ft® TANK P, SYSTEM dP/dt (mm Hg/sec) dV/dt (cfs) (mm He) Pump A Pump B Pump A Pump B Pumps A + B 300 5,95 5.55 0.244 0,277 0,571 150 2.56 2,28 0.210 0,187 0.397 100 1.63 1,41 0.200 0.173 0.373 50 0.86 0.70 0.211 0.172 0.383 115 sonic velocity, which 1s given by and thus (26) v = \Jg)/RT , v = 5060 ft/sec where g = 32.2 ft/sec?, Therefore v = 1.67, 4V R = gas constant = 386, (27) (d—t> = 0.60 A X 5060 = 3040 A . T = temperature = 1235°R, orifice 116 Chapter 8 DUMP AND FILL SYSTEM FUEL DUMP TANK COOLING The heat generated in the fuel after shutdown of the reactor can easily be taken up by the heat capacity of the fuel and the fuel system without overheating. However, once the fuel is in the hot fuel dump tank, 1t is desirable to keep the temperature of this tank below a reasonable level. Therefore heat is removed by allowing helium to pass through the 91 coolant tubes of the tank (Fig. 89). It 1s postulated that the maximum heat removal rate necessary is 50 Btu/sec. The problem of cooling this tank does not lend i1tself readily to analytical calculation. However, the cooling was analyzedby free-convection calculations and by chimney-effect methods., Both methods are outlined below. The equation for free convection heat transfer is (1) Q. = hAs | where ¢, = heat removed by convection, Btu/sec, h = free-convection heat transfer coefficient taken at mean helium temperature, Btu/sec:ft?-°F, A = 91 times surface area of inside of a coolant tube, ft?, f = temperature difference between the 1nside surface of tube and mean helium temperature, °F, The value of the free-convection heat transfer coefficient for each helium temperature was calculated from the Nusselt’s number. The Nusselt’s number 1s given as a function of the product of Grashof’s and Prandtl’s numbers on p. 525 of ref. 14. It 1s realized that the length-to-diameter ratio of the coolant tube 1s too great for use of these correlations; however, they were theonly correlations available, and an order of magnitude estimate could be gained by using them, The i1inside diameter of each coolant tube 1s 2.067 in. and the length is 3.1 feet. The temperature of the inside surface was taken to be 1325°F over the entire length of the tube. Mean temperature valueswere assumed for the helium 1n the coolant tube, and from these and Eq. 1, a curve was obtained of heat removed vs. mean helium temperature. The mean tempera- ature corresponding to a heat removal rate of 50 Btu/sec is 1025°F. This corresponds to an outlet temperature of 1920°F, since the inlet temperature was assumed to be 135°F. A lower outlet temperature would mean a greater heat removal rate. Thus, apparently the dump tank will be adequately cool ed. The chimney-effect method makes use of the fact that a buoyant force acts on the air in the coolant tube because of a density difference. This buoyant force 1s (2) Fe V(o —p) where "y 1 buoyant force, lb, V = volume, fts, Powp, = density of helium at room temperature, 1b/fe3, P, = density of helium at mean temperature of helium in tube, 1b/ft?. From Eq. 2, the pressure acting on the column of helium 1is (3) AP:L: A where AP = difference in upward and downward pressures, lb/ft?, A = cross-sectional area of coolant tube, ftl, The pressure can also be expressed by AP = 4 p'“ (4) P" f E 2g 1 117 NOTE ! ALL MATERIAL 1S 346 STAINLESS STEEL. ’ UNCLASSIFIED | DWG D-A-3-1-31-1A 3-in.R, 5 PIPES 6%-in. R, 12 PIPES 10%-in. R, 18 PIPES 14%-in.R, 24 PIPES 18Y%-in. R, 30 PIPES 89 COOLING PIPES, 2~in. SCHEDULE NO. _ 40x36-in LONG — \\_4_1// DOUBLE-VEE Ju.NT NELDED FROM BOTH SIDES Wil COMPLETE JOINT PENETRATION PLAN 3ft-5in. I ELBOW, 2-in. SCHEDULE | tin END PLATE NO. 40 90° SR ELL - i . \m 41-in. DIA -4'm-r J 1_/ i LA Ll A i HiH ) 3in. 4 1 | a / 1! i VENT, 1-in. SCHEDULE NO. ] N 40x4%-in LONG ! : { 14 1 '] ] 1 i / ]|} ! —~=——FILL PIPE, 2-in. ————'%-in. TANK WALL PLATE, ) 11 SCHEDULE NO. 40 128.8 x 34 in. 36in. o i 1 f 35-in. LONG 34 in. i) ' : : ; f N 1 i 1 I i N N : 4 : H N 1 1 oo ™ N 4 H i N N ' i ' /] I | ;: N ' 1 q i1 ) N | 0 1 1] D N H . 1 N N 1 nln ' N " H 4 u 4 ; H | ; N ] 1| 1 d //<' N | ! H r N 4 H H o ; L e 457 t-inEND PLATE [ / ] E a/ i ’ & 41-in.DlA7 N ] t . i { . A4 Z /.IV Ll ////////5 ELEVATION 118 Fig. 89. Fuel Dump Tank. 16 f "N R = friction factor for laminar flow, dimensionless, L = length of coolant tube, ft, D = equivalent diameter of coolant tube, ft, v = helium velocity, ft/sec, g = gravitational acceleration, 32.2 ft/sec2, Np = Reynolds’ number, dimensionless, The velocity of helium through the tube 1s, from Eq. 4, 1/2 (5) v = ( 2eD ) : 4fLp, The amount of heat removed per tube can be expressed by (6) Q = we, AT and (7) Q= hd 0 . In Eqs. 6 and 7, v = vAp k[ u 0,14 /4 \V3 h =186 — — <__mL D\u, 7Tk L ’ @ = amount of heat removed, Btu/sec, and w = weight flow rate, 1b/sec, ¢ = specific heat, Btu/lb*°F, AT = difference between inlet and outlet temperatureof helium, °F, h = heat transfer coefficient, Btu/sec'ftz'oF, A, = surface area of inside of tube, ft?, ¢ = log mean temperature difference, k = thermal conductivity of helium, Btu/sec*ft?+°F, (o = viscosity of helium at mean temperature, lb/sec-ft, t, = viscosity of helium at surface temperature of tube, lb/sec’ft. Equations 6 and 7 were solved by assuming various helium outlet temper- atures, and the values thus obtained for each equation were plotted against helium outlet temperature. From these curves, the helium outlet temperature was found to be 805°F, the heat removal rate per tube i1s 0.59 Btu/sec, and the total heat removed is 91 x 0. 59 = 53.7 Btu/sec. HEATING OF FILL TANK WITH CENTRALLY LOCATED DIP TUBE Upon heating a flush-and-fill tank containing helium, the temperature of the dip tube will lagthe temperature of the helium and metal walls of the tank during the heating process (Fig. 90). The temperature of the helium will follow very closely the temperature of the tank walls, Heat is transmitted to the dip tube by free convection of the helium and by thermal radiation from the wall, The difference in temperature between the dip tube and the wall has been determined at various wall temperatures for certain heating rates. The net heat input to the tank, excluding loss, is Q=qT+qH+qD: where dt At qr = (WCP)T E;—g (ch)fjg;" and dt At qy = (WCP)HE";'}-.‘ (WCP)HA—T- The term dt/d7 can be replaced by At/AT without much error if ATis small. The value of g, is given by qp, = hADQ 0,173 4 4 . Ae(i_i_ 3600 P 100 100 The emissivity 1is 119 UNCLASSIFIED DWG. D-A-3-1-32A 3 LUGS EQUALLY SPACED 6-in. SCHEDULE 40 PIPE ————— Z Z 1/2 in. : NY = — 210 SF —— s O 2 ft—0in ——— - k-—ain.-—w-— < N c N ™ b —2 ft—& in DIA ———— x i c N © 175 in. NOM.~s] |e— ! r o N x N 1 A X N X X JE— l—t—— 2 IN. SF Y ELEVATION MATERIAL—INCONEL Fig. 90. Fill Tank. 120 In these equations, the symbols have the following meanings and units: Q = total net heat input, Btu/sec, g = heat input of component, Btu/sec, W = weight of material, lb, c, = specific heat of material, Btu/1b* °F, At = temperature change, °F, AT = time interval, sec, h = free-convection heat transfer coefficient, Btu/sec*ft?:°F, A, = outside surface area of dip tube, ft?, f = temperature difference between helium and dip tube, °F, € = radiation emissivity, dimension- less, T = absolute temperature, °R, o f diameter, ft, and the subscripts = tank, helium, oo i dip tube. The free-convection heat transfer coefficient can be calculated from the Nusselt’s number. A curve of Nusselt’s number vs. the product of Grashof’s and Prandtl’s numbers is given on p. 525 of ref. 14, The heat input to the tank wall and the helium 1s qT+qH=Q"qD' Therefore Q"qD A'T= ; (WCP)H At + (WCP)T At the change in temperature of the dip tube 1s q DA’T D T (WCP)D and the temperature at any time 1is (19) t, = t; t At where t; 1s the temperature at the beginning of the time interval (°F). The emissivity of the tank wall was taken to be the same as that of the dip tube. The value used in making the calculation was €, =€, = 0,50 T D The dip tube was taken to be a 2-in., schedule 40 pipe that extended to the bottom of the tank. In calculating the temperature differences between the wall and the dip tube, net input heat rates of 50, 12, and 8 Btu/sec were used. The results of these calculations are shown in Fig. 91. » @ o 400 N SN N\ S - /- @=12 Btussec 160 A\\\ |5 ™ < N N~ o 80 / T~ \0\ T — “\(\{ / @=8 Btu/sec — 0 | B O 200 400 e00 800 1000 1200 DIFFERENCE IN TEMPERATURE BETWEEN TANK WALL AND DIP TUBE (°F) TANK WALL TEMPERATURE {°F) Fig. 91. Results of Fill Tank Pre- heat Calculations. 121 Chap ter 9 OTHER INVESTIGATIONS AFTERHEAT IN FISSION PRODUCTS In order to analyze many of the problems which arise 1n the ARE, 1t 1s necessary to know the decay energy of the fission products at various times after reactor shutdown. Reference 23 gives the average dis- integration energy of the fission products as a function of time after fission. This curve (ref. 23, Fig. 6a), reproduced as Fig. 92 of this report, cannot be used directly, however, because the fissions 1n the reactor occur over a considerable period of time and the fission products, conse- quently, have a wide range of ages. The decay energy of the fission products may be expressed as (1) where Q q(t) fl Q=Kf” q(t) P dt , t energy in the fission products, Btu/sec, the average disintegration energy of the fission products as a function of time after fission (Fig. 92), Mev/sec* fis- sion, fission rate 1n the reactor, fission/sec, a constant for Mev/sec to Btu/sec = X 10.16' converting 1.517 DdG. 19155 10— T T oo o j | | | | | | | / | - 1 .:}\\\//35«(”+1"m=(39d“-2+u.?d"“)1o‘b | 1 ; I = 3273 (/" %+ 20436 7% 387+ (71 ={3.8-0861/)7 ' g \ ! | ! ! i i ot : \’7 3BT (1) =0708 X #7078 o = o o @ w fO—Z a ul o )— o \ 380+ T (1) =6.425 ¢y~ 19 W o0? N w : ’ N \ = S BB(HFF(f)THEORETCAL(chef25,p1328)//;;§\\\\\\ = i N p! -4 i | ~ g 10 L . ) N\ LpLJ | ; \\ =z | 5 M - | > = T ; ; = i 5 [ ' , + & () = ENERGY OF BETA PARTICLES IN Mev per second per fission -1.0 ; & L3+ T 7 =1.00 " = 10—6 I' (F) = ENERGY OF GAMMA RADIATION IN Mev per second per fission ‘/\' @ ! =TIME AFTER FISSION | : Ve 47TER FSSION e W i | ~ N \\ 107 - - > — N N | ~ | N -B ‘ \ \\ 10 : \\ : ~ | N i N ! | \\ 0L L | S 4 -3 2 —1 3 9 10 10 1o 10 | 10 10 e 0 16° 1o 10 10 10 TIME AFTER SHUTDOWN (sec) Fig. 92. Disintegration Energy per Fission vs. Time after Shutdown. 122 t = age of fission product group under consideration, sec, t; = age of youngest fission products {(also equals time since reactor shutdown), t, = age of oldest fission products (also equals time since reactor startup), sec. sec, For these calculations, 1t was considered that the power had been constant and equal to 2850 kw, which equals 2700 Btu/sec or 1.78 x 101!° Mev/sec. If it is assumed that there is 190 Mev of energy released per fission, then the fission rate, P, 1is 9.37 x 10'® fission/sec. Substitution of these values for P and K in Eq. 1 gives (2) Q=14.22 {2 q(t) dr . t) In order to integrate Eq. 2, it 1is necessary to find a function to fit the curve of g(t) as given in Fig. 92, This was done by dividing the curve into three parts and fitting each of these parts with a different power function. The resulting equations are (3) g(t) = 0,708 ¢0%-72 (4) q(t) = 6.43 ¢~ 116 (5) gq(t) = 3.27 ¢=1-2 4+ 95, 4 ;=14 (Eq. 5 is the equation recommended in ref. 23 for old fission products). Equations 3, 4, and 5, were used for integrating Eq. 2 for various values of time after reactor shutdown (1t,) and for 100 hr of reactor operation (t, = t, + 3.60 x 10°). The results are tabulated in the following: TIME AFTER DECAY ENERGY OF THE REACTOR SHUTDOWN FISSION PRODUCTS (sec) (Btu/sec) 10° 207 103 119 10* 58.8 10° 17.7 3.16 x 10° 4.1 10° 1.4 107 0.1 These values of decay energy include the energy carried by neutrinos. The energy of the neutrinos is essentially unabsorbable and, consequently, the actual absorbable decay energy of the fission products 1is less than that tabulated above. A rough estimate of the absorbable energy can be obtained by takingone half thetotal energy, ¢ %%’ with the results shown in Fig. 93, where the absorbable decay energy in the fission products is plotted as a function of the time after reactor shutdown for the conditions of this case (2850 kw, 100hr, 190 Mev/fission). TEMPERATURE DIFFERENCE BETWEEN THERMOCOUPLE ON PIPE WALL AND BULK FLUID The bulk temperaturesof the fluids in the fuel and NaK loops of the ARE are measured by thermocouples welded to the outside of the pipe walls 1n which the fluid flows. The 1< t< 100, 100 € t < 3.16 x 10° t > 3.16 x 10° ’ difference between the measured temper- atureand the actual fluid bulk temper- ature has been calculated for the most serious case, that is, the fuel circuit (Fig. 94). For the configuration shown, the heat loss per lineal foot, as given in chap. 6, 1is: TEMPERATURE OF OUTSIDE OF PIPE WALL (°F) HEAT LOSS (Btu/sec*lineal ft) 0,23 0,31 1150 1500 The temperature drop across the fuel film 1s given by ). O hA 123 120 : o o @ o o o DISINTEGRATION ENERGY (Btu/sec) o < 20 i 102 103 104 10° 108 el 108 TIME AFTER SHUTDOWN (sec) Fig. 93. Disintegration Energy vs. Time after Shutdown. and the area i1s given by X 1. 049 T = 0,275 ft?/lineal ft, A=17 where € = temperature difference across fuel film, °F, Q =heat loss per Btu/sec*lineal ft, lineal foot, h = fuel heat transfer coefficient, Btu/sec'ftz'oF, A = heat transfer area per lineal foot, ft?/lineal ft, D = pipe diameter, ft (1l-in., IPS, schedule 40 pipe has an inside diameter of 1.049 in. and an outside diameter of 1. 315 in.). Theheat transfer coefficientis givenby K 0,14 h = 0.027 —Re0® Pr"3 : D ©, where k= fuel thermal conductivity, Btu/sec*ft? (°F/ft), Re = Reynolds’' number, Pr = Prandtl's number, #4 = viscosity at bulk temperature, 1b/hr-ft, 4, = viscosltyat surface temperature, 1b/hre ft. 124 For fuel with the properties listed 1in chap. 1, and a velocity of 6.26 ft/sec, Re, so0p = 11,700 and = 22,300 . Re 1500 °F If it 1s assumed that (#/#3)0.14 ~ 1, h = 0.918 Btu/sec*ft’*°F 1150°F ) hisoor = 1.245 Btu/sec*ft?* °F, (hA) | 150°F = 0.253 Btu/sec*°F, (hA) 5900°F = 0.342 Btu/sec* °F, B1150° = 0.91°F, 61500°p = 0.91°F. The temperature drop across the pipe wall 1s ' Q 1n D, g =— = 21k n where € = temperature difference across pipe wall, °F, D, = pipe ft, thermal conductivity of metal, Btu/sec- ft? (°F/ft), = 2.72°F, 3.67°F, outside diameter, & n,1150°F 5 = n,1500°F Since the fuel film temperature drop is small and the Reynolds’ numbers are high, the difference between the fuel bulk temperature (the so-called ‘mixing cup” tempera- ture) and the fuel maximum temperature will be very small. The total differ- ence between the fuel bulk temperature and the outside pipe wall temperature 1s (6 +6_) (6 +6.) " = 0.91 + 2.72 = 3.63°F, 4. 58 °F . 1150°F 1500°f = 0.91 + 3.67 At other thermocouple locations in the fuel circuit, the temperature drop 1n the fuel film 1s less than the drop calculated above because the above conditions i1nclude the minimum i1nsu- lation thickness and the minimum Reynolds’ number encountered in the system. The temperature drop in the filmin the NaK circuit 1s, of course, very small. The temperature drops el MUST BE GAS TIGHT FOR {1 psi PRESSURE ]—~'/4-in. SLOT IN 3-in, LENGTH ONLY TYPE-307 STAINLESS STEEL FLANGE MH 42347-3 2W INSULATION 20-GAGE OVAL x 3-in. LONG FILLET WELD ALL AROUND - — SAUEREISEN - @I PrTITn AR 06 « # O ————6 in + Yyin. THERMQCOUPLE CONNECTOR / — L'/,G in. {THERMO-ELECTRIC €O.) MH 42347-3 2W INSULATION 20-GAGE OVAL x f1-in. LONG ‘ PORCELAIN INSULATOR (FISH-SPINE) FOR 20-GAGE THERMOCOUPLE WIRE TYPE A, TYPICAL INSTALLATION AT SLEEVE TYPICAL INSTALLATION AT ELBOW PIECE 12 in.; TYPE B, 8in.; TYPE C, 3in. PORCELAIN INSULATOR (FISH-SPINE) FOR 20-GAGE THERMOCOUPLE WIRE %_ , /WEL{D GAS-TIGHT ", 4 . - 7% = i < e " /. = HELIARC WELD’ = 3 - - - —__jWELDED Fig. 94. ALREADY | MH 42347-3 2w INSULATION 20-GAGE OVAL x 1-in. LONG WELD GAS TIGHT — 70185 0D x 0135+ 1D INCONEL WELD COVER A Y, -in. LONG CHROMEL-ALUMEL THERMOCCUPLE ) Thermocouple Assembly. UNCLASSIFIED DWG. A-6—0-25A 17 () Pl P T T =] L HELIARC through the pipe wall at various other thermocouple locations are given 1in Table 23. The maximum temperature differential between the outside of a pipe and the bulk of the fluid 1is approximately 4. 6°F. It is important to note that 1f the flow rates in either the fuel or NaK circuits are reduced, during operation, for some unforseen reason, the temperature differential between the outside of the pipe wall and the bulk of the fluid will This i1ncrease 1in temperature differential, since 1t occurs only within the fluid, should not become serious so long as the flow 1s turbulent; in the laminar reglion, the temperature differential can become great enough to render the thermocouple unreliable. increase. however, TABLE 23. TEMPERATURE DROPS THROUGH THE PIPE WALL AT VARIOUS THERMOCOUPLE LOCATIONS NOMINAL PIPE PIPE WALL HEAT LOSS o (°F) DIAMETER (in.) TEMPERATURE (°F) (Btu/sec*lineal ft) " 11/2 1150 0.23 1.98 1500 0.31 2. 67 2 1150 0.21 1.53 1500 0.29 2.11 2 1/2 1150 0.23 73 1500 0.31 2.33 126 iMd& . . RER 1. J. H. Keenan and J. Kaye, Gas Tables, Wiley, New York, 1948, 2, C, D. Hodgman, Handbook of Chemistry and Phystics, 31°%' ed., Chemical Rubber Publishing Co., 1949, 3. M, C, Udy and F. W. Boulger, The Properties of Beryllium Oxide, BMI-T-18 (Dec. 15, 1949), 4, NBS-NACA Tables of Thermal Properties of Gases, U. S, Department of Commerce, National Bureau of Standards: H., W. Wooley, Table 6.10, “Helium (Ideal Gas State),” July 1950; R. L. Nuttall, Table 6.39, “Helium (Coefficient of Viscosity),"” December 1950; R. L. Nuttall, Table 6.42, “Helium (Thermal Conductivity),’” December 1950, 5. The Engineering Properties of Inconel, International Nickel Co. Tech. Bull, T-7. 6. R. N. Lyon (Editor-in-Chief), Liquid Metals Handbook, 2d ed., NAVEXOS P-733 (rev.), June 1952, 7. Stainless Steel for Elevated Temperature Service, U.S, Steel Corp. 8. D. Q. Kern, Process Heat Trans- fer, McGraw-Hill, New York, 1950. 9, J.H. Perry, Chemical Engineers’ Handbook , 3d ed., McGraw-Hill, New York, 1950, 10. H. F. Poppendiek and L. D, Palmer, Forced ConvectionHeat Transfer in Pipes with Volume Heat Sources Within the Fluid, ORNL-1395 (Dec. 2 1952). ’ )L i, 8 g v o PO +nt hiath o .jfif¥#*$i?§5? ) "fihfifiw Heade 11, W, H., McAdams, Heat Trans- mission, 2d ed. (rev.), McGraw-Hill, New York, 1942, 12. G, N, Cox and F, J. Germano, Fluid Mechanics, Van Nostrand, New York, 1941, 13, Flow of Fluids Through Valves, Fittings, and Pipe, Crane Co. Tech. Paper No. 409, May 1942, 14. M, Jakob, Heat Transfer, Vol, I, Wiley, New York, 1949, 15, E. N, Sieder and G. E, Tate, Ind. Eng. Chem. 28, 1429-1435 (1936). 16, K. A, Gardner, Trans. Am. Soc. Mech. Engrs. 67, 621-631 (1945), 17. A. Y., Gunter and W. A. Shaw, Trans. Am. Soc. Mech. Engrs. 67, 643- 660 (1945), | 18, W, Nusselt, Z. Ver. deut. Ing. 73, 1475 (1929), 19. W, J, King, Mech. Eng. 54, 347 (1932). 20, E., Schmidt, Foppls Festschrift, p. 179, Springer, Berlin, 1924; and Z. Ver. deut. Ing. 75, 969 (1931), 21, The Trane Co. Bulletin D-S 365, September 1951, 22, H. L. F. Enlund, personal communication, 1952, 23. K. Way and E. P. Wigner, Phys. Rev. 73, 1318-1330 (1948). 24, S. L. Jameson, Trans. Am. Soc. Mech, Engrs. 67, 633-642 (1945), 25. Johns-Manville Products General Catalog, DS Series 2. 26. M. W. Zemansky, Heat and Thermodynamics, 3d ed., McGraw-Hill, New York, 1951, 127