CENTRAL RESEA RCH 11 " DOCUMENT cpi L LIBRARY S (T & - “PkLECTION IVRURANER | 49555 4 e 2 ) S e 3 ORNL 1517 ey .44 3 .I 456 F EE Reactors-Research and Power @ ftas | ¢ ¥ AHEH ¥ neups L' Q\\! | : N\ = NS | !w' % 5 :'3 ‘?{'}JI THE MODERATOR COOLIN s ' 8N R —— ke EL‘)P‘%‘ THE REFLECTOR-MODERATED REACTOR 6') R. W. Bussard ' W. S. Farmer o H. P A, Fox A, P. Fraas By Av br CLASSIRICA TN cn“zi To: te o 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, OAK RIDGE NATIONAL LABORATORY OPERATED BY CARBIDE AND CARBON CHEMICALS COMPANY A DIVISION OF UNION CARBIDE AND CARBON CORPORATION (4 oy > POST OFFICE BOX P OAK RIDGE. TENNESSEE » ¥ ORNL 1517 % £ ’ » This documeht consists of 45 pages. Copy4 of 165 copies. Series A. Contract No. W-T405-eng-26 THE MODERATOR COOLING SYSTEM FOR THE REFLECTOR-MODERATED REACTOR R. W. Bussard A. H. Fox W. S. Farmer A, P. Fraas September 1953 DATE ISSUED JAN 22 1954 OAK RIDGE NATIONAL LABORATORY Operated by CARBTIDE AND CARBON CHEMICALS COMPANY A Division of Union Carbide and Carbon Corporation Post Office Box P ‘r . - LCRTRIGY AR Osk Ridge, Tennessee o ' 3 4455 D349555 4 - i1 - 3 ORNL 1517 Reactors-Research and Power INTERNAL DISTRIBUTION #4i7 26o Mo Ta Key l. C. E. Center 2. Biology Library 27. G. H.g¥lewett 3. Health Physics Lilgary 28. K. o Morgan 4-5. Central Research LiVary 29« gL, Frye, Jr. 6. Reactor ExperimentalN Z0MPC. P. Keim Engineering Library ° £PY. R. S. Livingston T-11, Laboratory Records Depatment 2. T. A. Lincoln 12. Laboratory Records, ORNLWR.C. 42" 33, A. S. Householder 13. C. E. Larson e’ 3. C. S, Harrill 1k, J. P. Murray (Y-12) _ 35. C. E, Winters 15. L. B. Emlet (K-25) 36, D. W, Cardwell 16. A. M. Weinberg 37. E. M. King 17. E. H. Taylor 38. A. J. Miller 18, E, D. Shipley 9. D. D. Cowen 19. R, C. Briant 4 ;y‘ 0., R. A. Charpie 20. F. C. Vonderigiec? M. J. A. Lane 21, J. A. Swariie LSRR, W. Bussard 220 So Co ":' 1|'3o A. P, Fraas 23 F. L ”~” Ealer h‘h‘o C. B. Mills o, A, H.HEEL1 L5-49, ANP Reports Office 25. A. Hollaender EXTERGAL DISTRIBUTIOES 50. AF Plant Representat@ve, Burba Aéfi 51. AF Plant Representatie, Seatt] 52. AF Plant Representatifge Woo-_ dge 53. ANP ProJject 0ffice, F4q t Wor 54-64. Argonne National Laborftoryj ,m 65. Armed Forces Special Welipod@Project (Sandia) 66. Armed Forces Special We¥polE? Project, Washington 67-T1l. Atomic Energy Commissiorfgfeshington T2. Battelle Memorial Institge 73-75. Brookhaven National Labditory 76. Bureau of Ships s T7-78. California Research ajl¥ T79-84. Carbide and Carbon 85. Chicago Patent Grougl 86. Chief of Naval Resgifch 87. Commonwealth EdisglCompany 88. Department of t vy - Op- 89. Detroit Edison gfipany 90-94. duPont Companyjiugusta D@relopment Company g i -; 5 Company (Y-l2 Plant) 2 95. duPont Company fWilmington 96. Foster Wheeler Corporation 97-100. 101-104. 105. 106. 107-110. 111-112. 113. 11k, 1150 116. 117. 118. 119-120. 121-122. 123. 124, 125-131. 132. 133-13k, 135. 136. 137. 138. 139, 140-141. 142-143, 14k, 145-150. 151-165. - 1ii - GeneRal Electric Company (ANPP) Gener§l Electric Company, Richiiénd Hanfor®Operations Office Towa StaWg College Knolls AtdR§c Power Laborat, Los Alamos Wientific Laboghtory MaesachusettqInstitute off Technology (Kaufmann) Monsento ChemiWel Compang Mound Lsborator) National AdvisorjqComrfttee for Aeronautics, Cleveland National Advisory Qomffittee for Aeronautics, Washington Naval Research Labojdtory New York Operationsgffice North American Avigtisk., Inc. Nuclear Developmef Asfpciates, Inc. - Patent Branch, WgEhingtdy Phillips Petrol#fim Comparl) Powerplant Labfratory (WAD Pratt & Whitn@fy Aircraft Digision (Fox Project) (1 copy to W. S. Farmey Rand Corpopftion San Francifco Operations Office Sylvaniagflectric Products, Inc. USAF Heg¥quarters U. S. J¥val Radiological Defense LMyoratory UnivegEity of California Radiation IRporatory, Berkeley Unigrsity of California Radiation LaBgratory, Livermore Wal@er Kidde Nuclear Laboratories, Inc. Weg¥tinghouse Electric Corporation T&hnical Informetion Service, Ozk Ridge THE MODERATOR COOLING SYSTEM FOR THE REFLECTOR-MODERATED REACTOR R. W. Bussard A. H. Fox W. S. Farmer A. P. Fraas INTRODUCTION Cooling the reflector region of the reflector-moderated circulating fuel reactor presents an important set of problems. While reflector mate- rials and coolants can be chosen independently of shielding considerations for most types of reactor, this 1s not the case for an aircraft reactor because the shield and i1ts weight are of such great importance. Not only mist the reactor core be as small as possible but the reflector material mist be chosen to give both a minimum fast neutron leakage from the reflec- tor and a minimum production of hard secondary gammas in the reflector. A number of reflector materials were considered on the basis of fast neutron leakage per unit of thickness to get some notion of their influence on shield design. (See Fig. 4.11 in ORNL-1515)1. This study showed that beryllium was far superior to any of the other common reflector materials such as beryllium oxide, carbon, or sodium deuteroxide, and 1t is somewhat superior to Dp0. Although a fluid reflector might simplify the heat remov- al problem, none of the fluid reflector materials that can be used at temperatures of the order of 1000°F were comparable with beryllium for neutron moderation and reflection. The reflector cooling problem was there- fore studied using beryllium in order to evaluate the sources of heat generation and the magnitude of their effects. The design chosen for this study employed a fuel region in the form of a thick-walled spherical shell of fuel with a beryllium reflector surrounding 1t and a beryllium "island” filling the interior. The power was taken as 200 megawatts and the core diameter as 18 in. giving a power density 1in the fuel region of 5 kw/cm3 (see ORNL-15151, page 65). This gave a source of radiation next to the reflector greater than that in any existing reactor. (The MTR has a power density of 0.291 kw/cm3 in the fuel region.) SOURCES OF HEAT GENERATION Heat wi1ll be generated in the reflector by the absorption of gamma rays coming from the fuel and heat exchanger regions, and by the slowing 1. "ANP Quarterly Progress Report for Period Ending March 10, 1953," ORNL-1515. down of fast fission neutrons. Approximately 12 Mev per fission was taken as the total energy of the gamma rays generated in the fuel region. Of this T.35 Mev was taken as representing fission fragment decay gammas with an average photon energy of 1.5 Mev while 4.60 Mev was taken as coming from prompt fission gammas with an average energy of(é°5 Mey.2 This choice of gamma ray energy per fission has the effect of lumping all the fission product decay gammas in the core. The distribution of decay gamma energy between the core and heat exchanger regions depends upon the relative fuel volumes of the regions, which varies with the detail design. As a first approximetion all of the decay gamma energy was "lumped" in the core. For such an assumption the estimate of the power density distribution in the reflector will be somewhat higher and require more cooling close to the fuel region than would be the case had the fission product decay gamma energy been balanced between the core and heat exchanger regions. At the same time "lumping" the decay gammas in the fuel region will yield an underestimate of power density in the outer region of the reflector. It is easy to correct for these effects later as will be shown (Appendix F). Neutron capture results in the emission of a photon of approximately 9 Mev energy in the case of nickel and 6.8 Mev energy in the case of beryl- lium.3 The kinetic energy of the neutrons amounts to approximately 5 Mev per fission. CALCULATION OF HEAT GENERATION The ratio of peak to average power density appears to be fairly close to unity i1n the three-region beryllium-reflected sodium-cooled reflector- moderated reactor design. (See Table 4.1 - ORNL-1515)1. Therefore a uniform power density and hence a uniform gamma source was assumed for the fuel region in the first calculations. A later check using a non- uniform power distribution from a multigroup calculation gave essentially the same results. In order to evaluate the self-absorption of gammas i1n the fuel region, a typical fuel of sodium fluoride, potassium fluoride and UF) was chosen for evaluating the absorption coefficient. (This does not mean that the above fuel would necessarily be that specified finally for thas reactor.) Gemma rays emtted in the fuel region cover a fairly wide spectrum of energies with the mean value somewhere between 1 and 2.5 Mev. Since heat generation was of principle concern, the mean energy was taken 2. "Estimested Heat Production in the NRU Reflector," CRT-50L. 3. E. P. Blizard, "Introduction to Shield Design," CF 51-10-70, Part 1. rI -‘ -6 ‘ as 1 Mev i1n determining the absorption coefficient in the Inconel and beryllium. This served to maximize the heat generation rate and gives a limiting value. The absorption coefficient in the fuel region was also evaluated at 1 Mev. Since the elements in the reflector and fuel are principally of low atomic number, Compton scattering 1s the principle mechanism for degrada- tion of the gammas in the above energy range. The gamma rays were assumed to be attenuated exponentially in calculating the heat generation. A build-up factor was not employed since core diameter and reflector thick- ness were small enough (of the order of one mean free path for 1 Mev gammas) to make the need for a scattering correction questionable. It was assumed that scattering would be straight ahead in direction and that Compton collisions merely degrade the photon in energy. This method over- estimates the gamma ray intensity for large distances. An 18 in. diameter spherical fluoride fuel region surrounding a 9 in. diameter central beryllium island and enclosed by a 12 in. thick beryllium reflector were chosen as a typical geometry for calculation. The fuel region was separated from the island and outer reflector by a shell of 3/16 in. thick Inconel. The reactor power output was taken as 200 mega- watts 1n determining the total energy release. The neutron flux for computing neutron capture gammas was taken from the spatial flux plot for reactor calculation number 129 (see Table 4.1 ORNL-1515)1. The specific heat generation rate was computed at points spaced about one inch apart along the radius from the center of the 1sland to the outside of the reflector. The heat generation rate in the reflector arising from atfenuation of the gamma rays emitted from the fuel region was computed by several methods. In the first method (Appendix A) the attenuation was computed taking into account numerical differences in the value of the absorption coefficient of both fuel coolant, Inconel and beryllium. In Case A using this method, the absorption coefficients employed were 0.09, 0.16, and 0.30 em-1, respectively, for the fuel, beryllium and Inconel regions. In Case B values of 0.06 and 0.13 em-1 were used for the fuel and beryllium regions, respectively, in order to evaluate the effect of the absorption coefficient on the heat generation rate. The equation for exponential attenuation using the above absorption coefficients was numerically integrated to arrive at an answer for the heat generation rate at the various space points. (Appendix A.) The results of this calculation were checked by a method of graphical integration using Pappus' theorem. (Appendix B.) Another approach to the evaluation of the heat generation rate was made by means of analytical solutions for exponential attenuation in terms . ¥ £ ot =l of exponential integrals. A solution which would not involve graphical or numerical integration could be obtained for two particular cases. By assuming a uniform absorption coefficient throughout both the fuel and the reflector regions, 1t is possible to solve the exponential integrals directly. (Appendix C.) In the second case, the absorption coefficients in the fuel region and reflector region were assumed to be different. An approximaete solution can be obtained by solving the the problem in two steps. The flux of gamma rays from the surface of the fuel region was obtained using the uniform absorption coefficient solution method. The attenuation through the Inconel was obtained by a slab source approxima- tion. The resulting flux was then assumed to be spread over the surface of the Inconel and the absorption in the reflector was determined for a surface source. The results of this calculation are tabulated as Case C, using the same absorption coefficients as in Case A. The power density resulting from neutron moderation within the beryl- lium of the island and reflector was obtained dire¢tly from multigroup results by using the flux distribution §(r, M) or (¥nl)x C.F. (Correction Factor)*. The energy loss for each lethargy group Nn/is the average energy loss per collision times the number of collisions in that group at a given radius or space point. The spatial distribution _uli -u21 tn 7 W t —'}_ e - 10 1Z=1 _%_xC,F,, x f% ( e ) (1) 1s normalized to the total power lost by moderation (2 1/2% of reactor power) by the use of the integration operator (1 (see ANP-58). Gamma rays also result from parasitic capture of neutrons in struc- tural materials and coolant. One particularly strong source of hard gamma, rays is the Inconel shell separating the fuel annulus from the outer reflector. These gammas are captured over an appreciable volume rather than locally since the photon energy 1s high and the attenuation length large. A minor amount of heating also results from the genera- tion of gamma rays by neutron capture in the beryllium. The extent of the captures in both beryllium and Inconel can be obtained directly from the multigroup calculations or by using the integrated spatial neutron flux distrabution weighted by the absorption probability. The latter method was employed here. (Appendix D.) REFLECTOR HEATING The power density in the various regions of the reactor owing to absorption of gamma rays from the core and reflector regions i1s tabulated 4. D. K. Holmes, "The Multigroup Method as Used by the ANP Physics Group," ANP-58. in Table I. The rate of heat generation is shown for Case A, Case B, and Case C for the capture of gamms rays emitted in the fuel region. The last column includes the heat generation rate caused by the capture of gamma rays generated by parasitic neutron capture in beryllium plus those from parasitic capture of neutrons in Inconel. Gamma rays will also result from neutron captures in the coolant. These were not computed owing to the uncertainty regarding the final coolant to be employed and the volume fraction of the reflector that might be occupied by this coolant. Their effect should be small, however. The power density resulting from the slowing down of neutrons and gamma heating for Case A are plotted in Fig. 1. The total integrated power in various regions from heating by gamma ray absorption for Case A and Case B 1s shown in Table II. Region 6 el TABLE I POWER DENSITY IN VARIOUS REGIONS Island Beryllium Island Inconel Fuel Reflector Inconel Reflector Beryllium Neutron Radial Position Gamma. Heat Generation Capture T Case A Case B Case C (n,d) Cm. Watts/cm Watts/cm3 0 47.5 61.9 30 2.3 5.08 60 65 36 2.5 7.62 80 Th 6k 3.4 10.16 101 93 152 3.4 10.95 120 142 176 3.3 10.95 223 330 330 14,4 11.4 354 Lo7 koo 144 11.4 106 99 146 12.7 167 137 14 186 148 15.2 182 152 17.1 184 151 20.3 157 132 21.6 141 116 22.9 73 65 100 22.9 215 325 333 69.2 23.3 150 227 199 69.2 23.3 80 98 106 13.5 2k.1 23.7 27 25.4 37.7 4h .6 414.8 7.4 26.7 25.4 31.9 27.9 19.0 o4 L 17.4 5.0 30.5 10.3 1%.0 33.0 5.4 8.3 3.9 3.3 35.6 2.9 4.9 38.1 1.67 3.0 1.1 2.6 53.3 0.066 0.19 POWER DENSITY (watts /em®) 450 400 350 300 250 200 150 100 50 ISLAND INCONEL SHELL Na ANNULUS INCONEL CAN T ATING TOTAL HE TOTAL HEATING Y HEATING NEUTRON HEATING Y HEATING NEUTRON HEATING 2 4 6 8 RADIAL DISTANCE FROM REACTOR CENTER LINE, » (1n) Fig. 1. Radial Power Density from Neutron and Gamma Heating. REFLECTOR TOTAL HEATING NEUTRON HEATING y HEATING 10 12 14 16 18 DWG 187!! 20 i « AR * - £ kY TOTAL INTEGRATED POWER IN VARIOUS REGIONS Region Island Beryllium Island Inconel Fuel Reflector Inconel Reflector Beryllium — = TABLE TI Total Power Megawatts Case A 0.46 0.24 6.71 0.57 3.14 Case B 0.51 0.29 5.58 0.85 3.44 The peak heat generation rate occurs in the Inconel shell separating the 1sland beryllium from the fuel annulus. High heat generation rates also occur in both the reflector and the i1sland immediately adjacent to the fuel annulus. In cooling the Inconel core shells 1t 1s necessary to take 1nto account not only the heat generation rate given in Table I, but also the heat flowing through the Inconel from the fuel annulus when the moderator region is designed to be operated at a lower temperature than the fuel region. This can be computed readily by conventional methods. COOLING SYSTEM The heat generated in the Inconel and beryllium can be removed by any one of several coolant passage arrangements. A liquid metal 1s the most desirable coolant 1f the resulting heat is to be employed usefully 1n the engine air radiator circuit, since this gives the least sensitive and highest heat transfer coefficient. Lead, bismuth or L1l might be used 1n place of sodium because their effect on neutron moderation might offer a certain nuclear advantage. The coolant chosen should not have too high a neutron absorption cross-section (05.41_0.5b) and, what 1s just as important, must be compatible with the materials of construction. Lead, bismuth, non-uranium bearing fluorides, NaOH, sodium, and NaK were all given serious consideration as coolants for the beryllium moderator. Metallurgists consulted on the problem felt that lead or bismuth would be likely to pose serious mass transfer difficulties. The relatively high neutron absorption cross section of the potassium in the NaK made 1t quite undesirable from the critical mass standpoint. Rubidium might be used 1in place of potassium but because of little demand 1t 1is currently very expensive. Thus sodium seemed to be the best choice for the moderator coolant. Since corrosion and mass transfer might occur in a beryllium and sodium system, 1t seemed desirable that the beryllium be clad in some fashion. Work at Battelle5 indicates that beryllium can be chrome plated electrolytically to give satisfactory resistance to sodium attack at 932°F. Chemical plating 1s also possible with beryllium. However, the formation of brittle intermetallic compounds and the difficulty of elim- inating pinholes with either chemical or electrical plating methods makes the stability of any plating rather questionable under thermal cycling and high temperature conditions. An alternate possibility 1s to can the beryllium in thin-walled Inconel cans and to fill the small interstices between the beryllium and the can with stagnant sodium to provide a thermal bond. This arrangement appears to be the more promising of the two, but both possibilities are being investigated. The reflector could be constructed of two large hemispheres of beryllium if the canning technique were used. Cooling passages could be rifle-drilled through the beryllium and lined with thin-walled tubes, which could be welded 1nto headers at the ends. The Brush Beryllium Company has indicated that 5. J. G. Beach and C. L. Faust, "Electroplating on Beryllium," BMI-T732. -] el the fabrication of these large hemispherical shells would probably be no more difficult than the fabrication of large flat slabs. Personnel of the Y-12 beryllium shop state that 1t would not be difficult to rifle drill holes 3/16 to 1/4 in. in diemeter as much as 40 1n. deep, with the hole diameter held to within 0.001 in. and the hole center location held to within 0.010 in. These holes could be drilled at a rate of 2 1n./m1n. This estimate was based on the experience gained in machining the beryl- lium of the MIR reactor and in drilling small diameter holes in the beryllium reflector of the SIR. In addation to the holes in the beryl- lium reflector, channels could be provided between the Inconel core shells and the canned beryllium reflector in order to remove the heat generated in this region. An slternate construction for the reflector region involves the use of a large number of wedge-shaped segments shaped much like the sections of an orange. These sections could be made with shallow grooves in their surfaces to form passages for cooling streams of sodium. This would be a relatively expensive arrangement since a great deal of machine work would be required because the beryllium can be hot-pressed to uniformly high densities only in flat slabs or spherical shells. A design study was made using the rifle-drilled hole arrangement to investigate the detail problems of cooling the beryllium regions. The beryllium was assumed to be canned in Inconel and cooled by sodium flow- 1ing through Inconel tubes in rifle-drilled holes. Stagnant sodium would be allowed to fill the interstices between the beryllium and the can to facilitate heat flow across that boundary. In order to achieve a well- balanced design, & number of factors must be considered. The volume of both the sodium and, especially, the Inconel must be minimized to keep parasitic neutron absorptions within reasonable limits. It 1s also nec- essary to operate the reflector regions at a relatively high temperature to keep from penalizing the engine-radiator system. Large thermal stresses are likely to result from the high rates of heat generation to be found in these regions. Because beryllium becomes quite ductile at temperatures sbove LOOPF cracking ought not be a problem. It was felt that thermal stresses should be kept within reasonable limits to reduce distortion, however, as this might become a problem after a number of thermal and/or povwer cycles of the system. For this reason, the temperature variation 1n the beryllium between adjacent coolant passages was held to 50°F in this first design. The pressure drop through the various coolant passages was limited to 4O psi to keep pressure-induced stresses low. The maximum beryllium-sodium interface temperature was held below 1200°F to minimize the possibility of mass transfer in the beryllium-stagnant sodium-Inconel systen. smeliiiny Several detail designs were investigated that favored first one and then another of the various requirements, that 1s, minimum poison, minimum variation in beryllium temperature, minimum beryllium-sodium interface temperature variation, minimum sodium system pressure drop, etc. Fig. 2 shows the hole pattern in the beryllium for a promising arrangement. The temperature distribution for this hole pattern i1s shown in Fig. 3. ALTERNATE COOLING SYSTEMS A careful examination of alternate cooling systems was made 1n an effort to avoid the problems involved in cooling a solid beryllium island. The sodium-cooled, solid beryllium outer reflector was assumed 1n every casge. The use of a semi-fluid beryllium powder mixture with a liquid metal in the interstices was considered. A mln%mum porosity or liquid metal volume fraction of 12% may be attainable. This would necessitate the use of a liquid metal with a low neutron capture cross-section and good "moderating" properties such as lead or bismuth. These are difficult to contain, however, owing to corrosion and mass transfer. If a satisfactory container material could be found, a semi-fluid moderator with a reasonably small neutron age, [, would be attractive on the basis of ease of removal for beryllium recovery and also as a safety measure. Replacing the fuel annulus and i1sland by a graphite block containing perhaps 40 unlined fuel passages about 1.5 in. in diameter has been proposed as another possibility. The success of this system would depend largely on whether the fuel could be kept from diffusing or penetrating into the graphite as a result of permeation and/or cracking. If this were to occur, severe overheating would result and self-destruction of the graphite would take place. The destruction would be abetted by the large decrease in thermal conductivity that accofipanles a temperature increase in graphite. Actual testing of graphite in fused-fluoride, uranium-bearing salts under conditions of thermal and mechanical shock will have to be made to evaluate this problem. In addition, multigroup calculations will be necessary to determine the critical mass and power dastribution. This latter item 1s expected to be poor. Should Inconel tubes be required to protect the graphite, a secondary cooling system would be required for cooling the Inconel tube wall to 1500°F owing to the volumetric heat source effect. If this were required the major advantage expected of graphite would be lost. A non-viscous fluid moderator for the i1sland with desirable heat trans- fer properties would simplify the heat removal and the fabrication problems 6. M. Muskat, The Flow of Homogeneous Fluids Through Porous Media, J. W. Edwards Company. el 3 N Nl ISLAND Y . O ) NS DWG 18744 PASSAGE FOR INLET Na TO REFLECTOR (2 REQ'D) 026-in -DIA HOLES IN Be, CONTAINING 025-in ~0OD TUBES FOR Na COOLANT FLOW INCONEL SHELLS AND Na ANNULUS Fig. 2. Cooling Hole Distribution 1n Reflector-Moderator. ® i Lo oyt -SI- TEMPERATURE (°F) 1600 1400 1200 1000 800 600 400 200 DWG 18742 ISLAND FUEL REFLECTOR r ZAPPROXIMATE AW NN/ TEMPERATURE U U DISTRIBUTION , U N N | 7 X r Na COOLANT vp HOLES Na COOLANT HOLES e by = INCONEL SHELL—=— L | Na ANNULUS %:?;, v e — INCONEL CAN o b 5 flf:w? o 2 6 8 10 12 14 16 18 20 RADIAL DISTANCE FROM REACTOR CENTER LINE (in) Fig 3 Temperature Distribution Across Midplane of 200-Megawatt Reflector- Moderated Reactor Sodium inlet, 1000°F, sodium outlet, 1150°F. in this region. A non-fuel bearing fluoride or sodium deuteroxide has been suggested for this purpose. However, the heat transfer properties of these fluids are generally poor so that cooling the Inconel shell sufficiently that there would be no serious hot spots becomes a severe problem. For example, 1f in the case 1n the preceding section sodium deuteroxide were to flow through the 9 in. diameter” island with a mass velocity giving a 100FF axial coolant temperature rise, a heat transfer coefficient of only 312 Btu/hr f£2 OF would be obtained. In the design cited having a 3/16 in. Inconel shell, there would be a heat flux of 1,000,000 Btu/hr ft2 from the shell, and thus a radial temperature drop through the hydroxide boundary layer of 3200°F. A major improvement in the sodium deuteroxide heat transfer coefficient could be obtained only by i1ncreasing its velocity. To increase the velocity enough to give satisfactory cooling would entail an excessive pressure drop, and even then minor vagaries in velocity distribution would make occasional hot spots rather likely. The same problem presents 1tself if a design involving an i1sland filled with a fluoride is considered. Only the liquid metals appear to have the necessary thermal properties for this purpose. Lead, bismuth, or L7 appear to be the only possibilities. In order to use these latter fluids successfully the mass transfer and corrosion difficulties currently common to them must first be solved. Nickel and 1ts alloys which are usually the best container materials for fused fluoride salt fuels exhibit generally poor corrosion resistance to these liquaids. CONCLUSIONS The heat generation rate or power density was computed for a reactor using a fuel annulus with a beryllium reflector and island. The heat generated in the reflector can be removed by sodium-cooling a canned beryllium reflector-moderator. Further, the Inconel shell containing the fuel annulus can be satisfactorily cooled by the same sodium system. Differential thermal expansion does not appear to be a problem since the volumetric coefficient of expansion of both the Inconel and the beryllium are approximately the same -- (5.5 x 10~ 1nches/inch OC). Furthermore, samples of extruded beryllium have shown negli%ible dimensional change and warping after thermal cycling up to 930°F. At the time of writing the sodium cooled, beryllium i1sland and reflector arrangement 1s felt to be the best proposal. No new technological problems appear to be 1nvolved 1in the detailed mechanical design of this system. A number of alternate cooling systems are available which may have some advantages over the solid beryllium system above. However, all of these involve problems that will have to be solved by experimental investigation. 7. The Reactor Handbook, Vol. 3, Materials, USAEC. > 4~ -15- —“ . APPENDIX A Gamme.-Ray Absorption Inside and Outside A Spherical Annular Source The heat generation rate due to absorption in a region within and out- side a spherical annular source can be obtained by means of numerical or graphical integration of the integrals defining the dastribution of gamma rays. Several approximations were used to set up the integrals. The first approximation used involved the straight ahead theory of gamma absorption. Here 1t can be assumed that Compton collisions merely degrade the gamms energy, but do not scatter the photons. Only exponential attenuation with a coefficient characteristic of the material through which the photons pass need be considered. When a photon passes from one medium to another, no refraction is considered. A uniform fission rate in the: source region was assumed. Thus a uniform power density for the core was determined by divading the total reactor power output by the volume of the fuel region of the fuel annulus. \ The attenuated intensity at @, distance r from a point source of density Pos 18 glven by the formula _Mr MPo € P = “— dv A-1 By vhere podV represents the source intensity, e'/4r the aflsorptlon effect, 1/hsr2 the spreading effect from the point source, and A the probability of absorption at the point Q. Then the total intensity at Q due to a source extended over a region R 1s given by b/(‘ 2 S P = MPo Tz W A-2 R For the reactor in question, the source was taken as an annulus be- tween an inside sphere of reflector material and an outside spherical shell of the same material. Because of the spherical symmetry, the distribution of heating power along any diameter of the spherical system was considered a sufficient answer to the problem. Consider a point F in the fuel spece of the reactor as 1llustrated. I M~% e If the power density at thais point 1is Py 1n an element of volume 4V, then the power at a point Q a distance h from the center of the reactor may be obtained by integration, using spherical coordinates centered at Q. Be- cause of the symmetry sbout the axis along which h is measured, the element of volume dV = 2xre sin 6d6dr includes the volume around all points F with the given spherical coordinates r and 6. Since r may pass through both reflector and fuel spaces, 1t 1s broken 1nto r = ry + ro, where the sub- script 1 refers to the fuel and 2 refers to the reflector. Separate reciprocal attenuation lengths, 47 and 4o must be determined for these materials. For convenlence the fuel space may be divided 1nto three regions (I, II, and III) bounded by cones tangent to the inner and outer spheres. 1In section the figure 1s as follows The total power generation P due to absorption at Q is given by summing the contribution from the three source regions I, IT, and III. M-l(No//L) '2\ 1 9—/0-1 e/ T /171 2 P= £y /. AN A o 8.4 A6 R 0 Lmfi—bi A~ i (r LR ) Aeri @ + b ’ t -/ a("’ A+‘2'q"i) "/""1("3_ - a ’“‘3) 4 + @o/fij X 0 Lm5+o-_1 1~ I pYRIR) fhkn 4b, e"‘/’";f"a, - 2 A-3 + f’a/“:-{ ifl‘n. s & 4(4. ffi(—é > a8 i, A T where, for simplicaity, g =Y ey~ A8 o ' bl = Ra "'j'. Al 9 It 15 possible to represent ro as a function of © by the equation: ro = h cos © -YR® - h® sin® © A-b and 1 /n® - ®° ‘ cos 6 = —-'I':é——+r2, A-5 and then ry=Tr-Tp . A-6 !.‘ ! - . P _18- el The total power generation P at Q, on eliminating ry 1s then given by the expression* M‘J (No/,l. ) A ara B — oty P:/Po/"'&f J e—w&#d/‘&fiimflx’wéfi,dfi 0 A X.Mfi“bi pion 8 A A8 1 R @VKKJ ‘&A#L5i+b L 4"0/‘-;[ ’ [ 16‘(/“'.1‘/“'13('“&*2"'1)"/"1"' A 0 ng-hfl-g_ o4 A - L = /'va__—/u._.l/‘u + e Q”a /1) M-l(fi/j\.) s 6 +by f i B A e . A-T ‘“"""-1 ("’o/'&) Aowoa 8 ~by Integrating this equation with respect to r yields: /MM-:L("’D/’L)\ ; & g -1 A (R/A) : ey TV - +{ e &11—63&’%1)%«9%9 A8 4 Arasa (ngfi&) -y Let s = h cos ©. Then A P io_fi’; e—/“;(fl-*fq) [l _ e-—/"-i("‘i “Ai)jl s g A YAE - A2 X 2 -n, . e-fla@""'i) |: _ ‘4/:1‘1] / , A-9 A2 - R where /Ci = VR& _J\.:L'l'fl& /FE-I :-]/Nj‘-'/e\. + ’ This 1ntegral can be evaluated by numerical or graphical means for the heat generation at any point Q. In several special cases the above equation can be 1ntegrated. For h = 0, the complete spherical symmetry of the system gives the power at the center as: R - - - 2 P = Po/ae f e Agro e /Ml(r ro) t_z'%g s _ PoMa S HM2To [1 - e'fll(R'rO)] . A-10 A Another point of special interest 1s the point at the interface of fuel and island reflector. Here h = r, and the fuel region can be broken -20- & - up into two regions as follows: ™~ . }PL_ (.]/" 2 \ }pL Qo »‘ /2 v AL +b Fo s g et = o = Ay ) P = 2 c R 8 A E 0 alvomé A 1/2. ~ o IT T/ _ ’f’o/"';_ f -ol/a-&/vomél: _ _/,.,1(6 —namfi):, ,04»9,4(.9 - 1/a3 : H 4‘ - (b + A mfi) _ +ao/"‘.1j [1-—6/_13‘ 2 ]Mé’,fiéfi A-12 /1 /2 Let s = ro cos®. Then ds = ry sin 646 and " F‘ o9 e"%/"‘a’a‘ [1 _ e-/“i("'a'/")] Ao 2y 1 0 I'\./o ) - (tg—a + [l - e.’Ahi : ] Ao 0 —S g Yy 400/«72 _1 - e f T ——— Ze— o —— + A, ——— 1/'-_1“"0 Q/";\ e T leama) - Ca= - s _ e/“‘i:."(eé,/“';. +1)/& , A-13 0 where /C»&: R&_%a "l'/cla=L . The last integral can easily be determined by graphical or numerical integration. For a point at the surface of the outer reflector adjacent to the fuel space, the fuel space can be broken into three regions as before. The heat generation or power density P is given by the sum of the contributions from each of the three regions. o b porn (00 /R) f R et 6=, 0 - M P= A - f [ T i b de 0 - I i o Yoy IR) 2R 22 6 * /5 f + X : Rm@*‘AL - IT / T/ AR o b ""”’*f f " pin b ds| , A A e na (R) Jy 0 —pg (R ) ety e )7 ® i 6.4 s IT where R ) e R Or on integrating with respect tor , Po - 22 f - - e B + f 0 Sy O [e 4 (K era 2 ¢ I:l _ e-/"-.L(Rma"""&)] Ry a8 ol6 e—/fiiaflmé -;lza-;\i‘l A-15 Let s = Rcos®. The above integrals then become: JRE R _ a e"a/kl B P _ 1 N A [ gy gl s + e e -1l-e ]Ao A-/6 R —n Where /v‘e-a': f"oa.""‘ fia‘ +A‘=L The last term above can be integrated numerically or graphically. -2~ APPENDIX B Mechanical-Graphical Gamma-Ray Heating Computation A method of graphical integration was used to check the- approximate values of power density obtained by numerical integration using the method of Appendix A. In this method lines were scribed on an aluminum sheet to simulate the fuel space boundaries. From a point P i1n the diagram below curves were drawn showing lines of constant values of e-MT, fThese curves, when rotated about the X-axis, form surfaces of revolution enclosing regions of a given total power. | / Ao} - . —te——— \ ) | By choosing radii so that each of these shells encloses the same fraction, say 10%, of the total power, 1t is possible to keep errors uniform through- out the computations. When more than one material is involved, the radius has to be divided into r) and rp, so that e-(H1r1 + M2r2) has the required value. After the curves are drawn, the areas of the irregularly shaped regions bounded by these curves may be obtained with a planimeter. Then the volumes of the corresponding solids of revolution may be computed from Pappus' theorem in the form V = A(2ny) B-1 where ¥ is the distance from the axis of rotation to the centroid of the area. This centroid may be located by cutting the aluminum sheet along the bounding curves, and balancing the irregular pieces on a knife edge. A point Q 1s then chosen 1n the volume and the average power 1is considered as generated at this point. Then the value of the integrand (e~MT/hxr2) 1s evaluated at this point. The product of this value and the volume of the region gives the power density contributed by this . . > - ’ 1 .‘\ region to the point P. Repeated computations for all the areas in the fuel region give the total power density as observed at P. The arbitrary choice of a point for evaluating the integrand does not seriously affect the result as long as points are chosen near the geometric center of the area. Accuracy 1s limited to two significant figures by the precision of cutting the sheet, and of locating the cen- troids. This method, however, can be applied to very irregular geometries in which axial symmetry allows the use of Pappus' theorem. «26- mllleny T APPENDIX C Solutions 1in Terms of Exponential Integral Functions for Radiation Heating due to a Spherical Annular Source The power density at any point within or outside of a fuel bearing source region can be evaluated by approximation without recourse to numer- ical or graphical integration. As in Appendix A the straight ahead collision theory of Compton Scattering was assumed. The gamma rays may be attenuated exponentially without considering a "buildup factor.” The source was assumed to be an isotropic emitter. The power density at a point within a spherical annular source 1is given by the following expression for the case of the same asbsorption coefficient 1n both source and absorber region: R=Ro e=fl AS Pg = Po Mg 2xR° s1n6 WE— dodr C-1 R=Ri 8=0 where Ry - 1nner radius of the source annulus Ro - outer radius of the source annulus r - the distance from the center of the spherical coordinates to the absorber Po - source power density /qa - absorption coefficient of the absorber o - distance from particular source point in any given gesma source shell to the absorber The resulting expression can be reduced to a double integral in terms ofJP and R by eliminating the angle & through the cosine law. f.2 = R2 + r2 - 2r R cos® c-2 This gives the following equation: R=Ry f = R+tr Af Py = I’_g}./'& R 7?'—dfd3 c-3 R=R, f = R-r By integration by parts and using the exponential integrals tabulsted in the WPA Tables of Sine, Cosine and Exponential integrals it is possible to evaluate the above integral completely. - Pa, = %{‘E Roe-r [El| /\' (Ro—r) - El' I‘“(Ro"’r) J RiE_rE = ) (® ) iy l‘ M (Ry-r - E3] M(Ri+r - M(Ro-r) =2 -(MRo+1+Mr) E%IE 0 (MRi+1+pM 1) #M(Ri ¥} +(MRBo+l-Mr) -2‘“"—';' ) (MRi+1l-Mr) ;H: KEL v C-4 o ber is located a.t a radi&l m point r (r ZR,) out- side the source annulus , the absorption or power density for the same absorption coefficient in both source and sbsorber region is given by the following double integral. -r+R R=R, PoM P, = 3528 f f R—-—dfrm c-5 R=Rj -I‘-R -28- — Integrating by parts and using exponential integrals again this becomes 2 2 P, = Po Aa Ro-r [ Ell/u(r-Ro)! - E]_’ (I‘+Ro)l] 2r e | 312~r2 - AT [ ElI/L{(r—Ri)I - Ell ,U(r+R1)U | ~-M(r-Ro) ~-M(r-Ri) + (MRg-l+Mur) 2—%?- - (MRy-1+pmr) _2___}(9_2 i - M(Ro+T) - M (Ry+r) + (MBoHl-Mr) 5z - URL-MT) o c-6 When the source region has an absorption coefficient that i1s dif- ferent from that of the absorber (M #A445), or in the present case the reflector region, the previous solutions are not exact outside the boundaries of the source region. It 1s necessary then to use the above solutions 1n the case of a thick annulus to compute the flux Pa//t( g at the boundaries of the source region, r= R; and r= Ro. For velues of r much greater than Ry or much less than R, the resulting power density at r can be obtained by treating the flux (Fg/Mg) computed from our previous expression as the source term of an isotropic spherical surface emitter. The power density for values of réRi due to an isotropic spherical surface emitter would then be given by: Py = ‘;%)Rifla g.": Ell/,{(Rl—r)l - El} M(Rl+r)I} C-T 2 At the center of the sphere where r=o0 this becomes: P - M. R: P, = [2 Ma e Ta fi c-8 s andk A‘% The power density for values of r > R, due to an i1sotropic spherical surface emitter would then be given by: PB. Py = ‘/‘7521230#& fi_% { Ell,u(r-Ro)l - El’ M(r+Ro)’} C-9 For values of r just outside the boundaries of the source region but close to R; or Ry, the power density in the case of U ,#Ag cen be obtained by treating the source as a slab and introducing a radius ratio correction. Thus for r = Ry but near Rg,: 2 Py = (13%) PZ:Z: {C/Q(RO—R:L) + Mg (r - Rofl EljflS(Ro-Rl) + Hg(r-Ro)| + e“/aa(r-Ro) [1 _ e'/'/S(Ro'R:L)J - U, (r-Ro) Ell /Ia(r-Ro)l} c-10 A similar result can be obtained for r < R; but near R;. By Judiciously solving the spherical annulus, infinite slab, and spherical shell absorption equations in series, it 1s possible to obtain a good approximation of the true” absorption in a compdsite solid system such as the reflector-moderated reactor. The flux from the surface of the spherical annulus source 1s used as the boundary condition in solving the slab source case for the attenuation through the thin Inconel shell on either side of the source annulus. The flux leaving the face of the Inconel 1s corrected for angular distraibution and i1s used as the boundary condition in the spherical surface source solution. APPENDIX D Gamma Heating from Parasitic Capture of Neutrons Gamms rays would be emitted as a result of neutron capture in the beryllium reflector, beryllium island, Inconel shells and sodium coolant. The source term can be evaluated approximately by using the spatial flux plot (1n ORNL-1515,l page 54) for Reactor Calculation Number 129, The reactor power was taken as 200 megawatts and a fuel space of 43,700 cm3 was computed for an annular fuel space bounded by spheres of 22.9 and 11.4 cm radius. Thus the thermal neutron flux at the outer Inconel shell is approximately 5 neutrons/cm2 sec per f1351on/sec em3 of core volume. Since there are 6.2 x 1018 fissions per second for opera- tion at 200 megawatts, the thermal flux is given as 7.1l x 101k neutrons/cm? per second in this region. The resulting source of gamma rays 1s treated as a slab source in computing the heat generation in the external reflector. Thus P, = P08 ) (MgtgrMgty) Ep(MgtgiMgts) 2 Mg + o Meata [1 - e stsj -MgtgE] (M ata)} D-1 The absorption was corrected in turn by the radius ratio squared. The heat generation in the beryllium reflector and island due to gamma absorption from neutron capture by beryllium was assumed to be uniform. The magnitude of the heating was assumed to be equal therefore to the source term. 1 "ANP Quarterly Progress Report for Period Ending March 10, 1953." ORNL-1515 APPENDIX E A Possible Cooling System Based on Sodium Cooling of a Beryllium Reflector-Moderator In order to demonstrate the feasibility of cooling a reflector- moderator of solid beryllium, a study based on cooling with a liquid sodium coolant flowing through a number of holes was made. The heat removed from the moderator was to be transferred to liquid NaK in the reactor intermediate heat exchanger-air radiator circuit. In order to avoid compromising the air radiator operation it is desirable to operate the moderator coolant system at temperatures comparsble to those in the external NaK systems (~~ 1400°F). Consideration must also be given in setting a temperature to corrosion and mass transfer in the coolant system and to the strength of the structural materials. The chosen maximum allow- able Be-Na interface temperature was approximstely 1200CF. At this temperature thermal stresses are no longer controlling since the beryllium w1lll be stress relieved by plastic flow, The number of cooling holes of & given size required at any section of the moderator will depend on the power density and allowasble temperature difference within the beryllium. The hole size 1s dependent upon the allow- able maximum pressure drop in the coolant system, the alloweble neutron poison fraction within the moderator, and the heat transfer characterisites of the system. Coolant flow rates are determined by the allowable pressure drops, coolant temperature rise, and system heat transfer characteristics. Sodium was chosen as a coolant because 1t has excellent heat transfer properties combined with reasonably low neutron capture cross-section and can be contained without excessive corrosion in acceptable materials of construction. In view of the present lack of information on mass transfer and corrosion of beryllium by sodium at high temperatures, the present system was designed based on canning the beryllium with Inconel. The cooling holes were to be lined with Inconel tubes which could be welded to the moderator can. To insure good thermal contact between the beryllium and the can, stagnant sodium would be introduced into the can along with the beryllium. The reflector-moderator can be constructed in two canned hemispheres, accurately aligned by tapered positioning pins. The coolant tube holes would be rifle-drilled through each hemisphere in a conical pattern con- forming with the shape of the fuel passage. i{“n ey hY g . » - . - - ~ Equations describing the power density dastribution in the Be of the i1sland and reflector were fitted within 10% to the curves in Fig. 2. These were found to be (see Nomenclature, p. 38) - -7.06 Pp (r) = 180 (2) watts/ce E-1 and P; (r) = 100 e0'907(r/r1) watts/ce E-2 The total power generated within the reflector beryllium was determined to be 6.46 megawatts by Piot, = f Pp (r) av \Y The 1sland 1s not physically spherical, but for purposes of analysis 1t is closely approximated by a Be sphere symmetrically located on the axis of a Be cylinder. In order to determine the power generated within the cooled 1sland structure 1t was necessary to determine the total power generated within the cylindrical "end caps" as well as 1n the central sphere. For the cylindrical end caps 1t was assumed that the average power density was one-half of that in the central sphere. Thus the power could be calculated from Eq. E-2 for any given value of (r/r ), where r1 for the central sphere was taken as 4.2 inches and for the cylindrical end caps as 2.7 1nches. The over-all cooled cylindrical length was assumed to be 12 inches. The total i1sland power generation was then determined to be 1.42 megawatts by: 1 Piot. =fi1(r) dVsphere E[PI(I') WVoyl. The total power to be removed from the beryllium is thus 7.88 megawatts or 3.9% of the total reactor power (200 megawatts). The peak heating occurs in the Inconel shells containing the fuel in the core region. The total power to be removed was determined from the average power density within the Inconel and the shell thicknesses and sizes. It was found to be 0.21 megawatts for the island outer shell and O0.73 megawatts for the reflector inner shell. The total power to be removed from the island and reflector, including the Inconel core shells thus becomes 8.82 megawatts or 4.4% of the total reactor power. a A The power generated in the reflector beryllium was broken up into eight spherical shells of equal total power in order to facilitate the numerical calculations for the coolant system design. Similarly, the total power in the island exclusive of that absorbed by the annular sodium layer was divided into three equal power spherical (i1sland sphere) and 2 equal power cylindrical (i1sland end caps) shells. In order to remove the heat generated in the Inconel shell and that transferred from the fuel region, sodium mist flow in an annulus between the Inconel shell surrounding the fuel region and the Inconel can containing the beryllium reflector. The number, length and diameter of the passages for cooling the system can be defined by the following relationships and specifications. (a) Tube surface area heat transfer requirements- U 3 = 3500 Atot L6 where A 8y pax, & 100CF E-3 (b) TFlow heat capacity: Wiot. Cp ATyg = 9 b where llTNa mnex. 200°F E-4 (c) Flow pressure drop: L fv2 = )-I- = T m— AP f D 2g, where AP, = 2880 psf. (20 psi) E-5 (d) Temperature difference within the berylllum:8 2 2 2 ATg, = 6.68 x 103 E:—e L—ln (]—}%—e) + 0.908 (ESBE - o.9ozj E-6 where A Tge max = 50°F 8, W. S. Farmer, "Cooling Hole Distribution for Some Reactor Reflectors," CF 52-9-201. e ol X (e) Auxaliary relations: Weot, = N DPPv E-T f = 0.046/Re® 2 where Re = ?::P Atot . = NnDL Material properties were taken at 1100°F for sodium snd at 1200°F for beryllium and Inconel. e (1b/1t3) pa(1b/sec £t) Cp(Btu/1b OF) k[Btu/hr ££2(OF /1)) Sodium 50.4 1.4 x ]_O'lL 0.30 37 Inconel -- - -- 12 Beryllium -—- -- -- 50 In determining a tube diameter, consideration was given to the poison volume fraction. _The poison volume fraction is defined as the ratio of the total tube hole cross-sectional area, in any given moderator shell, to-the total moderator cross-sectional ares of the same shell. The poison fraction 1s thus proportional to ND2. For a fixed tube length L and fixed beryllium to sodium coolant temperature drop, A 6y, N will be inversely proportional to D. Hence the poison fraction is directly proportional to tube diameter. The total thermal resistance for heat transfer from the beryllium to the sodium 1s the sum of the thermasl resistances across the stagnant sodium layer within the Inconel tube, the tube wall, and the sodium coolant film. Due to the low conductivity of the Inconel, the tube wall is the controlling resistance and variations in the sodium film resistance owing to varying velocities have only a small effect on the over-all heat transfer coefficient U. The value of U used throughout the calculations for heat transfer to coolant flowing in the cooling holes was 8,000 Btu/hr £t OF. This value 18 within 10% of .the values obtained by evaluation of the heat transfer coefficients for the various different coolant velocities existing in dif- ferent tubes. The heat transfer coefficients for heat transfer from the Inconel shells to coolant flowing in the annulii around the fuel region depend almost entirely on the coolant velocity, hence i1t was necessary to evalugte U for the actual coolant velocities expected in the annulii. The number of holes and the mass flow rate per hole was adjusted to satisfy not only the thermal specifications but also the pressure drop D requirements. Repetitive trial and error calculations were performed in order to determine a satisfactory, specific coolant system design. The results of these calculations show that a satisfactory balance between poison fraction, pressure drop, heat transfer requirements, and beryl- lium temperature drop can be achieved with the use of 0.250 in. 0.D. tubes with 0.010 in. thick walls, separated from the beryllium by a 0.005 in. annular gap filled with stagnant sodium. The Inconel modersator can was taken to be 0.025 in. thick with a 0.025 1in. thick sodium-filled gap between the can and the beryllium. The results of these calculations are summarized in Table III. The resultant moderator poison fractions are shown in Fig. k. Aeaps TABLE III Reflector Moderator q per Region r,/rg region L N S ATge 1 9.3/9.75 765 1.4 69 0.67 50°F 2 9.75/10.3 765 1.6 69 0.76 50 3 10.3/10.85 765 1.8 65 0.81 50 L 10.85/11.5 765 2.0 65 0.90 50 5 11.5/12.4 765 2.2 76 1.01 50 6 12.4/13.9 765 2.6 76 1.35 50 7 13 9/16.2 765 3.1 69 1.93 32 8 16.2/21.3 765 3.5 65 3.27 LW1°F Sodium Annulus Around Spherical Core Thickness q A ey Wya, 0.070/0.100 930 280F 22.6 Totals for reflector system q = 7050 Btu/sec N Over-all AP = 810 psf ATy, Island Moderator q per Region r,/rp region L N S ATpe 1 2.8/4.2 450 (ave)0.6 88 0.58 500F 2 2.0/2.8 450 1.7 38 0.61 50 3 0.5/2.0 450 1.7 35 0.62 36CF Sodium Annulus Around Island Region Thickness q per region A8y Wy End caps 0.300" 200 520F 40. Central Sphere 0.300/0.185 170 106°F 30. Totals for island system q = 1720 Btu/sec N Over-all AP = 1685 psf ATy, Aby 56°F 51 L6 Lo 28 28 25 24 Op 295 554 150°F A6y, a 6 6 ‘ ‘_ 99°F 920F A 161 150CF WNa A PTube A TNa 17.0 295 150°F 17.0 322 150 17.0 423 150 17.0 463 150 20.1 532 150 19.5 570 150 17.0 650 150 17.0 810 1500F A TNa. 137OF Wy, = 164.2 1b/sec WNg APpppe ATy, 10.0 30 150°F 21.2 1485 71 19.4 1485 96°F P ATy 170 16%F 30 1.9°F Wy, = 40.6 1b/sec st DWG 22520 0 24 S 020 AL 5 ZE g o i z Ll = 016 v 2\; - L I > - - - wl ! w wl a - z 012 % 3 T O [ 3 = o '; i O O 1?@12 = © L3 < 008 = » 2 Q \ 1os @ @ \ 0 04 \ 0 0 2 4 6 8 10 12 14 16 18 20 Fig 4. Volume Fraction of Sodium and Inconel at the Reactor Mid-plane as a Function of Radius. The Volume RADIAL DISTANCE FROM REACTOR CENTERLI NE (in) of Inconel 1n any Region is 4149, of the "Sodium plus Inconel” Volume. Symbol Atot. NOMENCLATURE FOR APPENDIX E Meaning Heat transfer surface area inside tubes Coolant specific heat Coolant tube 1inside diameter Coolant hole diameter through the moderator Flow fraiction factor Thermal conductivity Coolant tube length Number of coolant holes Power density at any point in the moderator Power density in the reflector moderator Power density in the island moderator Total power Coolant flow pressure drop Heat transfer rate Radial distance from reactor centerline to any point in the moderator Outer radius of i1sland moderator Inner radius of reflector moderator Inner radius of an arbitrary moderator shell Outer radius of an arbitrary moderator shell Reynolds number mliienny Units Btu/1b OF ft ft Btu/hr £t° OF/ft ft Watts/cm3 Watts/cm3 Watts/cm3 Megawatts 1b/fte Btu/sec in. in. in. in. in. Symbol ATNa iésTBe Meaning Coolant hole center to center spacing holes in triangular array Temperature rise in the coolant fluid Temperature difference within the moderator material Over-all heat transfer coefficient Coolant velocity within the cooling passages Coolant weaight flow rate Mean temperature drop from internally heated material to coolant stream Coolant weight density Coolant viscosity Units ft OF OF Btu/hr f£t2 OF ft/sec lb/sec OF 1b/ft3 lb/sec ft «40- *fi APPENDIX F The primary effect on the moderator coolant system of the existence of fission products in the heat exchanger region will be heating of the outer regions of the Be reflector by decay gammas. For a 200 MW reactor the heat exchanger thickness will be approx- imetely 6 inches. The volume of the heat exchanger shell region, for a reactor core diameter of 18 in., is thus sbout 25 cubic feet. Of this, only some T0% is occupied by the heat exchanger, the rest being void space or pump and flow channel locations. Since only 40% of the heat exchanger volume 1s occupied by fuel the volume of the fuel is approx- imately (25) (0.7) (0.4) = 7 cubic feet. The fuel volume within the 18 1n. core 1s asbout 1 1/2 cubic feet, thus the amount of uranium in the heat exchanger region will be about 0.82 of the total system investment, while that in the core will be 0.18 of the total. It can be shown that heating due to absorption of garmmas from a plane source of finite thickness (bj) and bulk power demsity (Sp) will be given by T, - zzjo [ Bo(Mrx) - Bo(Meby +prx)] s T . = attenuation coefficient for heating in the heated region (cm-1) A = attenuation coefficient for total interaction in the source region (cm-1) by = thickness of source (cm) x = dastance from source into heated region S, = source power density (watts/cc) P, = power density produced at point x in region watts/cm3 and oo e's¢ Eo(f) = J//’ o ds iy 41— iy By use of the foregoing equation the reflector heeting due to absorp- tion of decay gammas from the heat exchanger region of a 200 MW reactor was computed and 1s shown in Fig. 5. This computation was based upon an assumed average decay gamms energy of 1.5 Mev and assumed attenuation coefficients of 0.16 em-1 and 0.30 cm-1 for beryllium and Inconel, respec- tively, as used previously in the body of this report. The attenuation coefficient in the source (heat exchanger) region was teken as 0.13 cm*l, and the coefficients for heating and total interaction were assumed to be the same. It is readily sapparent that this heating is small compared to that to be expected from the core gammas and from moderation of fast neutrons. The local power density in the outer four inches of the beryl- lium reflector 1s shown to be approximately 2.5 watts/cc, as compared with 1.0 watts/cc shown 1n Fig. I. This increase necessitates a reduction 1in the cooling tube spacing in this region from 3.27 in. on centers as 1in the design presented in Appendix E to 2.42 1in. on centers for the higher power density, if the allowable AT within the beryllium 1s to be held to 50°F or less. This corresponds to an increase of the number of tubes in region 8 of the design in Appendix E from 65 to 120 tubes. The total power to be removed from this region i1s higher by a factor of about 2.5, thus the temperature drop from the beryllium to the coolant sodium will become 33° and, for a coolant temperature rise of 150°F, as previously, the over-all pressure drop will be 1430 psf. oF It should be obvious from the foregoing that the effect of decay gamma heating of the reflector on reflector-moderator cooling system design wi1ll be minor and in any event will be well within the uncer- tainties of the neutron and gamma heating and cooling system design calculations. DWG 22672 {00 — @ o - HEATING FROM CORE ONLY o o — N 5 O / POWER DENSITY (watts/cm3) \ N 20 < N HEATING FROM CORE PLUS HEAT EXCHANGER\ ~|— ) e — e O i e Eseash e 10 12 14 16 18 20 DISTANCE FROM REACTOR CENTERLINE (in) Fig 5 Effect of Heat Exchanger Decay Gammas on Power Generation in the Reflector — 42— -~ o