ORNL m FAES Wl OAK RIDGE SCHOOL OF REACTOR TECHNOLOGY 5 g / F. C, Vonderlage, Director ’ [_—’ "This document consists of &5 —_pages, No..":..;."":i__ ofgfi._l_Zchcpies, Series,*fi.;..‘_" Reactor Deasign and Feasibility Problem ¥ A REFLECTOR MODERATED, CIRCULATING FUEL, AIRCRAFT REACTOR" Prepared by: J. H. MacMillan, Group Chairman C. B. Anthony K. Guttmann C. P, Martin J. L. Munier R. D. Worley August 1k, 1953 # A REFIECTOR MDIERATE Digtribution: 1. J. 3. MacMillian 2. B, Anthony 3. Futitmann b, P, ¥artin 50 L. Munler 6o D. Worley Mo Fox 8. Mills 9. Mann 10, . Welnberg 11. Zmola 12, ., Blizard 13. . Briggs s < b B R e b Qi B Ry O B o by w2 G » Q kg ? D o0 [ =4 o 1k, . A. Charpi= 15, M. C. EBdiand .1 6 " w & o Jfii’d,flfl Ly > Laos . Breazeale 17. 15, 19. . B. Larson 20. . N. Lyon 21. . C. Briant 22, . ¥, Frasas 23. . A, Swartoub = il OoHEER P E QR WO W riters Poppendisk Cole Livingston Rickover Bussard Yonderlags Boyis Covayou E{f';? e R Marakle Mpghreblian Alexander ey 2k, 25, 20, 21, 28. 29. 30. 31. 32. 33, 3h. 3%. 36. 37. 3 38-39 & e . s 4 3 -3 » o 6@ s, e 4 o o .2 B a . Mg EN g g™ e e O fidmww%fififlmww 9 = = ) ;;‘x: = fi F;)o ”3 neth Xasgchau wh AR WARE abpiediad D REACTOR" hO-41 DLViSlO Raactor Development, AEC, Washingion L2-45 Central Reseavch Idbravy h6-51 CRSORT Files 52-132 Laroratory Racords PREFACE The program which has evolved at the Jak Ridge School of Reactor Technoiogy consiste of two eemesteré of formal course instruc- tion, followed by ten weeks given to reactor design studies. These gtudies provide each student an opportunity of applying to a specific but representative problem the principles and technfilogy which the school attempts to impart. Individual student groups are chosen so as to include men of the various engineering professions and scientific fields in much the same pattern found in a typical reactor project. This report is based on the study made by its authors while they were studente in the 1952-53 session of QRSQRT@ It was made and the report prepared in ten weeks. Obviocusly those weeks wvere diligently spent. Even so 1t would be unreasonable to expect that the study reported here is either definitive or free of defect in judgement. The faculty and meny, perhaps all of the studente are convinced that the project well served its pedagogical purpose. The report is published for the value 1t has to those who are professionally engeged in the field, Ag the authors have noted, several members of the Oak Ridge National Laboratory gave generougly of their time and,knmwledgé” The faculty Joins with the authors iu appreciation of that help. Most particularly is acknowledged the adwvice and inspiration which the group recelved from ite consultant, E. R. Mamn. ~ F. C, Vonderlage e ‘ flgk‘for - ACKNOWLEDGEMENT S This group wishes to express its appreciation to the members of the CRSCRT faculty who presented the information which served as the technical background for this study. Thanks are also extended to all members of the Oak Ridge ANP group for their invaluable assistance, patient consultation and cordial hospitality. For his guidance and assistance. this group expresses its appreciation to the group advisor, E. R, Mann, Particular thanks are also extended to H. F. Poppendiek who made the flow experiment possible and to A. H. Fox for his guidance on the nuclear aspecte of the reactor, ;nf!ca Acknowledgements Tible AT Contents List of Figures Section 1 Section 11 hol b3 A L section V 5.1 o R W 5.3 Introduction Summary General Plent Design Greneral Descriplion t‘:j esilgn Philosophy T Materis €3 - Yot ffuel Reflector Moderator Intermediate Heat Transfer Mediumr Fabrication Reactor Physics Cross Sections Sell-snielding One Group, Two Regilon, Critiecslity Calculation Two Group, Three flegion Calculation Temperature Ceefficilent of Heactivity Fission Product Handling Excess Pael Reguirements Einetics 4 o N0 s 3 12 5 9 - Controls 5,10 ~ Btart Up 5.11 « Shut Down Section VI - Reactor Englnesring 6.1 60 6. Section VII 2 3 - Optimization - Heat Transfer 6.2.1 = Germa Heating 6.2.2 - Internal Heat Transfer 6,2.3 - Reflector Cooling 6.2.4 - Primary Heat Exchanger 6.2.5 - NaOD Heat Exchanger -~ Fuel Flow Experiment - Shielding Section VIII ~ Conclusions end Recommendations Sectlion I - Section X - om0 W 10 References Appendices - Design Data - One Group, Two Reglion Data Two Group Cross Section Weighting Two Group, Three Region Data Optimization (ramma Heating Core Heal Transfer Primary Hesat Exchanger NaCD Heat Exchangsr Nomenciature 38 39 39 40 Lo 40 40 Ly k9 53 5k 25 o7 29 61 63 63 67 10 n 73 76 71 78 Figure Number 1 2 O 10 11 12 13 14 LI15T OF FIGURES Title General Plant Layout Schematic Drawing of the Fuel Tubes Typical kgpe vs. Uranium Mass Curve Characteristic Self-shielding Factors Thermal Utilization Curves for Cylindrical Fuel Tubes Nuclear Approximation of the Screwball Gamma Heating Distrifiution Over-all Heat Transfer Coeffiecient vs, NeOD Velocity N20D lieat Transfer Coefficient vs, NaQD Velocity Temperature Variations Through the Core Reflector Power Absorption Curve Photograph of the Flow Experiment Apparatus Shield Weight Curve Ciyitical Determinant oo 25 45 L7 48 50 52 56 58 30 I INTRODUGTION The objective of this project was to apply the theoretical information presented at ORSORT to the design of a reflector- moderated, circulating fuel, aircraft reactor. The scope of the investigation was limited primarily to an analytical evaluation, although a minor flow experimeni was performed . This design study has been limited to the reactor; the propulsion system has not been considered. IT SUMMARY A preliminary feasibility study of a 200 MW reflector moderated, circulating fuel, aircraft reactor is presented. The Screwballm core configuration as presently conceived consists of: 1) A spherical shell beryllium reflector 2) ARE tybe fluoride fuel in helical tubes arranged in annular form 3) NaOD moderator and reflector coolant In an attempt to justify the use of fuel tubes, an experimental investigation of the flow in a model helical tube was conducted. The reactor analysis was conducted on a two group, three region basis. The nuclear cross sections were appropriaztely weighted and judiciously applied so that the results compared favorably with the multi-group machine calculations. The reactor presented is believed to be conservative and appears to be feasible, The fundamental limitation is the 1250°F maximum wall temperature tor prevent excessive NaOD corrosion. Large NaOD flow rates and ample flow guidance are required to minimize corrosion. If the corrosion limit can be raised, the use of NaQOD as moderator and coolant has greater potential. Helical fuel tubes ares recommended to reduce the uncertainties of unstable flow in high power-=density reactors. The engilneering complexities introduced by their use are justified for controlled flow. * The resctor described in this report will be called the "Screwball® (the Fireball with = new twist). . ITIT GENEBAL PLANT DESIGN 3.1 General Description The Screwball is a spherical, reflector moderated, eirculating fuel reactor. The fuel enters the gore at the north pole and flows downward through six 3.5 inch I.D. inconel tubes. Five of these tubes are wrapped in a variable pitch helix to form a spherical annulus of fuel and the sixth tube passes through the center of the sphere forming a helix of smaller diameter, See Figures 1 and 2. In returning the fuel flows over NsK cooled tubes in the primary heat exchanger which is wrapped in a spherical annulus surrounding the beryllium reflector. The beryliium reflector has the form of a spherical shell with holes at the north and south poles for entry of the fuel tubes. Sodium deuteroxide flows downward through the spherical cavity in the beryllium and surrounds the fuel tubes, hence functioning as a moderator "island". The NaQOD returns to the top through 0.23 inch diemeter holes drilled in the reflector and through a spherical cavity outside the reflector thereby removing the heat preduced in the reflector., The NaOD then passes through & heat exchanger and is pumped back through the core, The intermediate heat transfer medium, NaK, returning from the propulsion system passes through the sodium deuteroxide heat exchanger and then through the primary heat exchanger. This system uses only one intermediate heat transfer medium and eliminates the necessity of additional radiators for subcooling a portion of the NaK as proposed for the Fireball. However, a control system is required which will keep the return NaK temperature constant., If the temperature rises, the NaOD will be insufficlently cooled and excessive corrcsion may result. At return FUEL TUBES - GUIDE YANES | = == GAS CPESSURE ? I{g DEUTERIUM L_jl_— ;.\i\ MAK INLET O : i 1 ’L EXCHANGER FIGURE | SCREWBALL GENERAL LAYOUT APBPROKIMATE SCALE ~ 4 SIRE 30~ /o NaQD HEAT __/ - AA L~ BB BORON LAYERS ~_ 7 ’_KPRESSUEE SHELL ( =—FUEL DRAIN - NaOD DENN Dwm'n, Hamre - 0 UNCLASSIEIED DW7.#2—3M"7 FUEL IN FUEL OQUT OWG, BY C.PM. SCHEMATIC DRAWING OF FUEL TUBES -11- temperatures below 200°F,, the fuel will freeze in the primary heat exchanger, With its inherent simplicity, the use of a single transfer medium warrants further investigation. Figure 1 is & drawing of the Screwball system, and a tabulation of design dasta is contained in the Appendix 1., 3.2 Desipn FPhilosophy A brief survey of NEPA, ANP, H, K. Ferguson, and Technical Advisory Board reports indicated that homogeneous reactors held the greatest potential for efficient nuclear propelled flight. Since little information is available on a combined hydroxide of lithium and sodium (the most obvious candidate for a high temperature homogeneous reactor fuel)} the circulating fuel type reactor was chosen as an intermediate step between fixed fuel elements and the homogeneous type fuel. The large heal tranzfer surface required in fixed fuel reactors is removed from the core in circulating fuel reactors and the potential simplicity of homogeneous reactors is retained., The moderating propertlies of the uranium bearing, fused salts are generally poor, but employing thick, . efficient reflectors enables the construction of a small high power reactor. Having chosen a reflector moderated, circulating fuel type reactor, a nore detailed investigation was initiated on the Fireball as described in Referenca 2, Investigation of the Fireball design parameters yielded the following five problems which appeared to warrant basic design changes or modifications: 1. Eigh power density 2. Questionable fuel flow patterns 3. VPossibility of pressure surges 12 L. Cooling the Be "igland" 5. Self-shielding in the fuel The Screwball eliminates or reduces the magnitude of each of these problems except pressure surges. To achieve these ends compromises in simplicity and resctor size have been medes however, the increase in shield weight over the 22.5 inch core is less tham 10%. It is believed that this reactor has a real potential for alreraft application, and as such warrants further investigation. The controllability of a high power density reactor has been neither proven nor disproven. E. R, Mann states that controlling a reactor in which the fuel temperature rise in the core exceeds 2000°F. per second will be difficult and somewhat doubiful. To be more conservative, a power density of 2.5 K¥/cc (1070°F. per second) has been chosen for this reactor. With such rapid increases in fuel temperature only short lived flow instabilities or eddies can be tolerated in the fuel., The use of fuel tubes in the Screwball has greatly reduceé the uncertainty of sustained instabilities in the fuel region. Aabrief gqualitive experiment varifying stable flow through helical pipes is described in Section 6.3. Pressure surges result from rapid density changes due to temperature variations which occur in eddies of lengthy duration, or from the instentaneous introduction of a cold slug of fuel. A step decrease in temperature is difficult to visualize in a cireculating fuel reactoer, Pressure surge calculations have been made on the Fireball assuming stagnant fuel in the core and a step increase in k of 1% throughout the core. These assumptions are both conservative since neither condition is likely to oceur in the reactor. Based on these assumptions the resulting pressure -] 3w surge is not expected to exceed 150 psi.. As a result of the more tortuous expansion path out of the core, pressure surges in the Screwball are expected to be larger. However, the fuel tubes in the Serewball will withstand pressures of 200 psi and no difficulty from this phenomenon is antieipated., The beryllium central "island" in the Fireball reactor requires ccoling to remove the heat generated by neutron moderation and gamma ray attenuation. The density of heat generation is 100 to 200 watts/cc, and its removal will require a large number of coolant tubes. The beryllium hes been replaced in the Screwball by a circulating "island® of NaOD, However, the problem of NaOD corrosion has been introduced. As indicated in Section 6.2.2, no stagnant or low velocity layers in NaOD can be tolerated next to the hot fuel tubes or containing shell. The self-shielding effect, as described in Section 5.2, for the 3.5 inch diameter tubes of the Screwball should be less severe than for the spherical fuel annulus in the Fireball. ] Lo IV MATERIALS 4.1 Fuel The proposed fuel for the Screwball is a fused salt containing 50 mole percent NaF, A7 mole percent ZrFA, and 3 mole percent enriched UF&. This fuel is similar to that prqposed for the ARE and was chosen because considerable information is availsble on its physical and chemical properties. To relax the limitation on the temperature of the returning NaK (Section 3.1}, a fuel with a lower melting point would be desirable. Inconel will be used as the fuel containing material. 4.2 Reflector The reflector has two functions; moderation and shielding., Be is a good moderator. Its moderating ratio is 159 compared to 170 for carbon, In addition, it serves as an excellent shield due to its high atomic density and small age. The fast neutron leakage for a given reflector thickness is much smaller for beryllium than for sybstances. such as NaOD, BeC, graphite and BeO apgregate. (Reference 2, Figure 7). Hence, beryllium has been chosen for the Screwball reflector. 4.3 Moderator A fluid moderator with 2 low vapor pressure al elevated temperature was desired., Their high wapor pressures eliminated the possibility of using light or heavy water. Hydroxides were then considered, The diffusion length of a hydroxide is very small relative to its age. Hencé, a hydroxide in the core of the Screwball would serve &s a sink for fast neutrons rather than as a moderator, Deuteroxides do not have this undesirable nuclear property and should exhibit similar physical -] 5 and corrosive properties. Therefore, 110D ; NaOD and combinations of both were considered., The double isotopic separation eliminated LiOD from serious considerationi NaOD was chosen for the core moderstor, Na0D also serves as the coolant for the reflector., It is a better moderator than sodium (the proposed Fireball reflector coolant) so that the Screwball reflector should be a more effective shield. However, the macroscopic cross section for thermal neutrons is larger for NaOD than for godium, The slight difference in absorption does not warrant cohsidering the additional complexity of a separate sodium system for the Serewball, BMI has made a survey of containing materials for NaOH at elevated temperatures (Reference 23). Graphite, silver and nickel were the most salisfactory of the materials tested, Nickel was chosen for the Screwball on the basis of ease of cladding and electroplating and tolerable neutron cross section. The corrosion mechanism of NeOH on nickel is reported in Reference 4. 2 NaOH + Ni = NephiOp H, N&2O @Ni() The reaction equilibrium is temperature sensitive resulting in mass transfer of nickel from hot regions to adjacent colder surfaces, The corrosion can be suppressed by hydrogen pressure over the NaOH, The corrosion mechanism for NaOD is expected to be gimilar to that for NaOH, but the degree and temperature dependance of the corrosion are unknown, For this study, the temperature Ilimitation for NaOb corrosion of nickel is assumed the same as for NaOH, According to Reference 3, corrosion of nickel by stagnant NaCH is, ~16~ 1) not néticable at 1000°F 2) small at 1250°F and would be tolerable for alireraft applications 3) excessive at 1500°F A 1imiting wall temperature of 1250°F and a deuterium gas pressure in the NaOD expansion tank of two to three atmospheres are proposed for this reactor. 4oL Intermediate Heat Transfer Medium A near eutectic alloy of sodium and potassium, 56 weight percent Na and 44 weight percent K, has been chosen as the intermediate heat transfer medium. As is typical of liquid metals, this alloy has excellent heat transfer properties and also has a low melting point (66°F), The main disadvantage of NaK is the induced radiation resulting from neutron bombardment in the primary heat exchanger. 4.5 Fabrication The proposed methods for fabricating the primary heat exchanger, punps and beryllium reflector are the same as those described in Reference 2, Ni will be substituted for chromium in the reflector. Bending the fuel tubes is possible (Reference 5), with the use of a cermet internal mandrel. The NaOD heat exchanger is standard, welded shell and tube construction. The entire system will be welded, Reference 6 states that welds in nickel for 1000°F NaOH corrosion tests were made with no unusual difficulty. Inconel welding presents no major e¢omplications. The fabrication sequence has not been fully considered in the layout of Pigure 1. Modifications may be required to facilitate assembly of parts. =17 V REACIOR PHYSICS 5.1 Cross Sections The cross sections used for nuclear calculations in this report are based on current ANP data. 5.2 3elf-shielding The application of diffusion theory in Reactor design, yields at best only a reasonable gpproximetion of the nuclear characteristics of homogeneous systems. The Screwball is a heterogeneous rezctor which has been homogenized for the purpose of expediting the nuclear calculations. This fact makes it necessary to correct the diffusion eguations by lntroducing a parameter commonly referred tc as the self-shielding factor, F. This factor accounts for the local depression of the neutron flux within the fuel region, which in turn results in decreased thermal utilization of the fuel Two major disadvanbtages result from self-shielding. First, more fuel is required than for a homogeneous reactor of the same proportions: and second, the negative temperature coefficient is not as large. As seen in Filgure 3, a smaller change in k pe results from the removal of an equal mass of uranium for a reactor with a greater uranium investment. Figure /4 depicts estimated values of F vs. fuel tube diameter at various reactor operating temperatures., The calculations were based on the method set forth in Reference 7. To apply the method one must know 2 and % of each constituent, the atomic densities in the fuel tube and its diameter, and the variation of f with 2By as shown in Figure5~ From these data calculate, 18- _fi:’—"rc;r LEH s U atim Maoss Cloeve fo _ANP Coocunring _VFoee| £xg cries Y i N L S e 3 / 8 / g 3 / M / ¥ S g / b / g U‘H ;WAJ,F 2319w g, 2 # 20 F= % opp = momt PR R W a Tt as a function of lethargy, which i1s then used as a multiplying constant on the macroscopic cross section of uranium, The self-shielding factors which were incorporated in the Screwball configuration were Ffast = 0.8, and Fgp = 0.5. It is believed that these figures resulted in a conservative value for the critical mass. 5.3 Oneg Group, Two Begion, Criticality Calculation As & basis for advanced engineering and nuclear calculations, an estimate of the Screwhall criticsgl mass was necessary. For this purpose a one group, two reglon calculation was made of the proposed configuration. The general method of caleulation is discussed in Reference 8, equation 8,31.1 1 Pt P 1 7 Bo R (1m %_ag] - or o coth L. © DC BC ' Ly Bc = -.;l:-m & DC = 1 ) },'{ _ ~} 3 Zir, TS r, core radius Ly =| f-2- s T = Reflector Thickness : 5 & r Note: Edquation €.31.1 is im error in the first edition of Reference 8 The item K}m Eg should read 1o 2; Dy De The effective reflector thickness was computed for ANP Reactor 121 for which the critical mass had been calculated by the 32 group IEM technique. Assuming the same effective reflector thickness, the critical mass was detgrmined for the proposed Screwball, DD For the purpose of cross section weighting both reactors were assumed 50% fast and the fast fraction to be equally distributed among the lethargy groups. A salif-ghielding factor of 0.7 was applied to the resulting one group crose saction. Thermal base 92 was used., Dats used in the calculation are contained in Appendix 2. A critical mass of 36.4 pounds was obtained for an effective reflector thickness of 4,04 ¢m. This corresponds to 3.05 mole percent UFh in the fuel. 5.4 Twe Group, Three Region Calculation The problem of calculating the critical mass and flux distribution of intermediate reactors is wmore difficult than for thermal reactors. The ong group approximation is unsatisfactory because of the wide variation in epithermal cross secticns, Furthermore, the comparatively small size of intermediate reactors increases the lmportance of the reflector. This fact holds particularly in connection with reflector moderated reactors as axemplified by the Fireball and the Screwball, In these reactors the nuclear aharact@riatjcé are strongly 1nfluenced by reflector composition and its thickness. Because of the uncertainties in cross sections in the intermediate energy range, it is not anticipated that calculations willl lsad te accurate prediction regarding the critical mass and flux distributions., It appesars that these calculations willl at beat be a reassonsble approximation of the nuslear characteristics of the reactor. In order to conduct the reactor analysis expsditiously, the two groups, thres region method was used. -23w is schematically depicted in Figure 6. sphere 1T and region are:s Region Region Region The avproximation of the Screwball used for nuclear calculation Ry is the radius of the inner (I), with Rp and R3 representing the radii of spherical shells IIT. As applied to this rsactor, region 1 is the moderator, II the fuel bearing medium and region 11l the reflector. The diffusion equations which were used in the reactor analysis I -szlvz,GIl + zfill fr, 0 » nd -DI, <7< 5 = 5 > =D, + 2 = Ix -Dyp V%) + R f1ny arr Prr, ” zfllzfillz R , end D1y VoI, * Yaqpfir, - Zfinlfilxl e Dror 2 . Iz -Dryp, ¥*rin * 2Riin, 4111, and o Do 2 v 111, V%111, + 2 S fri, — i 0 R #. IIII 1111 * VZgn gIIl where subscripts I1 indicates fast group region I and where subscripts I2 indicates thermal group region I, etc. In the sbove Zfi = 3’2% fi&l 0 in b The above equations arc¢ founded »n the following assumptions: (1) (2) (3) There are no fast absorptions in the reflector There are no scattering collisions with the uranium in the fuel A1l fast absorption in the fuel region is due to uranium -2 f 3191 Drawmg ;{::'/ F7 s Cl 8 25~ o T (1) The use of 'f Z% in place of ¥ Zj is a valid approximation providing 24 j I" - S\nh' (H?) I : ~ COSIn (h.‘?ij-}’ ‘_S‘Y\h :{KffLL\ C - [ ~ T /. _ Ns n X {té R \ i—'DnJ_'Eg?)cas(?sz) iDH\LKQES‘“{g)EZL\) Pt [h cosh | r'Ef\ 5 L? %“5“"}‘\‘”?}’ T ka\___l___m_li o O : . ~ - ’ i o E’l — S (?)EIZ).: + CoS (8??.5:1 —_ SW\}\; (W‘E2_>l “ - COS‘T\ '\I"l \Z}J [ O : ~ SPT"‘L ( ,_I[;‘ )_l r % - i £. RN I 5 T - o ' Y ‘S %z B2\ |-y | o2, ~ R\ "" DizgztEggfor (f)'?l% DIL.;Sl I.EJ;Z) 5w (@ :?\/:.”'DI;H-Sg L?zh Cosh (;\22\1 Dizsa l‘th Sian '{\’\?z E Dflnl.:fi CO‘SKL > ) J*J;LL_ cosh ! L Lmn. 0 B ¢ | _owh (R 0 o RBem R\ — Swm {(Z\EZ\}J + oS (Z]R’z)j sk (nE’zll —cash \h? '{ +smh | L meifii i +Smk’( L )E UVCLAS S/FrED Tieoee |4 - 30 - TOTLE # Buimsag The value of the determinant veries radically with small change in uranium mass, The determinent for the Serewball was zero for two assuned uranium masses, 3/.8 pounds and 49 pounds. The curve of determinant velue versus uranium mass 'is similar to reactor 129 for messes around 3.8 pounds, Hence, the mess of thé screwball is approximately 34.8 pounds of U235a This results in the following fluoride fuel'compositicn: 2.9 mole percent UFA 47,1 mole percent ZrF& 50.0 mole percent NaF Several efforts to calculate the spatial distribution of the flux yielded results of questionable validity. Very small changes in the nuclear constants produce major changes in the flux distribution. With such a sensitive relationship no significant conclusions have been obtalined. " Based on the results of the ANP 32 group calculations, it is anticipated that the 3crewball will be approximately 50 percent thermal. If so, the flux level réquired to produce LQDO\MH.is 1019 neutrons per square centimeter per second, 5.5 Temperature Coefficient of feactivity The Screwball has been conceived for possible use in aircraft applications. It is therefore important that its contreol system te as simple as possible. Since the use of control rods is not anticipated and the delayed neutron contributions to the flux are attenuated when the fuel is circulating, the control of this reactor cén be assumed to e satisfaetery'ohly if it is provided with a strong negative temperature w3l coefficient of reactivity. This coefficient is a function of numerous nuclear and physical parameters, a few of the more important ones being: (1) liquid fuel expansion (2) fuel tube wall expansion (3) Doppler effect in fuel (4) moderator expansion (5) thermal base changes with temperature There are several reasons why keff is temperature dependent, the most important one being the thermal expansion of the core materials. This effect usually resulfs in reactivity decreases with temperature increase, 1f the over-all temperature coefficient is positive, the continuous increase 1in temperature relegates the reactor to a short nonuseful life. The reactor then contains a built-in suicide complex. A negative coefficient is obtained from the thermal expansion of the fuel and its loss from the active volume, Moderator expansion, resulting in increased neutron leakage, is also a large contributor toward a negative coefficient. The Doppler broadening, which for enriched fuel could provide a positive component of the temperature coefficient, has not been consldered in this report. In this connection, it is believed that addition of U238 «0 the enriched fuel may possibly cancel or overcome the Doppler effect; the price is a greater fuel investment. The calculations were conducted on the basis of a two group thermal reactor. Although the Screwbsll has been estimated to be 50 percent thermsl, it is believed thalt a reasonable estimate of the temperature coefficient was obtained. It was also assumed that the product of the resonance escape probability and the fast fission factor rere equal to unity. ~-32~ The effective multiplication factor based on two group, thermal reactor theory is: = e X . (1+ Cn B2) (1s IPBR) eif This steady state equation is temperatufe dependent as a result of temperature variation of core geometry, material densities and energy distribution of the neutrons, The fractian&l change in keff which accompanies a unit temperature rise 1s the temperature coefficient of reactivity. This quantity must be negative for stable reactor operation; it is obtained by taking the logarithmic derivative of the above equation with respect to the temperature, Gl R [ L) B [ W The solution of this equation based on the mean operating tempersture of approximately 1300°F and including cross sectionsappropriately weighted by the self-zhislding fuctor, yielded the following results: (S‘k/k | = 2.1 x 1070y $T Jtotal S?/& = -0,7 x 1074/op | (?Ei& = =1.4 x 10™4/op 8T | fuel ? 8T } moderator The ratio of the moderator to fuel coefficient is two to one. This ratio has important bearing on the kinetic behavior of the reactor because of the relaticnship between the temperature response time congtants for fuel and moderator regions., For the Screwball these time constants are approximately 1.3 and 9 seconds Tor the fuel and moderator respectively; the ratic of moderator to fuel constants is: approximeiely m33- seven., The combination of the above ratios becomes most important when the powver increases unless the mean moderator temperature is kept constant the fuel may freeze. The explanation of this phenomenon is as followse an increased moderator temperature reduces the reactivity and causes the fuel temperature to decrease since its negative temperature coefficient compensates for this reduction in reactivity and maintains the reactor critical. Since the reactor is without servo=type control rods, it may be possible to forestall this possibility by maintaining a constant mean moderator temperature. 5.6 Fission Product Handling The two major fission products which absorb neutrons parasitically ere Xe1?? and sml49. m important advantage of circulating fuel reactors is the possibility of continuwously purging Xe and other fission product gases from the system, thereby appreciably reducing the fuel inventory required. Reference 22 proposes bypassing a fraction of the primary fuel sitream through a turbo-diffuser unlt in which the Xe is purged with helium., It has been estimated that for an assumed equilibrium ¥e concentration condition of 8k . g 3% , about 6 percent of the K > primary flow must be continucusly passed through the separator. Additional fuel will be added "o account for the reduction of keff due to absorption by the equilibrium Xe. Samarium poisoning under s equilibrium conditions is expected to have 2 8k _ 4 64 o Fuel will k have to be added to take care of the equilibrium Sm absorption. 33J+m 5,7 Bxeess Fuel Requirements In accordance with Reference 2, the change in uranium mass required for a given change in kgpp (for ANP circulating fluoride fuel reactore iz given by the relation: | jiEZEM o 0,22 It was estimated that a kgpe of 1.021 will be required if the reactor is to operate at 100 MW for 100 hours., Background information for caleulating this figure was obteined from various ANP, ARE and HEF reports. A breakdown of the component k,pe is: Critical 1,000 Equilibrium Xe override 0.003 Equilibrium Sm override 0.006 Fuel depletion ' 0.006 Excess for delayed neutron attemuation 0.005 Excess for instrumentation in the reflector 0,001 kopp = 1.021 The excess reactivity required is obltained by increasing the critical mass by 3.3 poundsi of this, approximately one pound will be used to shim the system during operstion. 5.8 Kinetics The question of inherent stability is extremely important with high powered, mobile, circulating fuel reactors. Since high power at high thermodynamic efficiency is required, a reactor temperature approach- jng the upper permissible 1imit is desirable. The extremely rapid power =35~ fluctuation possible in reactors of high power density deems manual or even servo-type conirol impractical. As a result control rods for use during normal reactor operation were nol considered feasible. The transit time of the fuel through the rezctor is a fraction of a second. As a result, the delayed neutron contributions to the flux are attemuated when the fuel is circulated, Normally, the delayed neutrons play an important role in conventional reactors; their attenuation ralses a legitimate worry regarding the stability of the Secrewball. There are two aspects to inherent stability, (1) statiec, which means that an increase in reactor temperature causes the reactivity Lo decrease, and (2), dynsmic, which means that the oscillations in reactor power are inherently damped. As indicated under Section 5.5 the Screwball has been calculated to have a strong negative temperature coefficient, Current data and theoretical studies indicate that the rapid circulation of the fuel itself provides a powerful damping factor for‘power oscillations with periods comparable to the transit time of the fuel through the reactor. This damping factor is presumed te compensale for the delayed ncutron attenuation. Evidence supporiing this statement 3s ‘et forth under References 10, 11, and 123 it 18 dindicated that the circulating fuel reactor equation (without reliance on delayed neutrons or control rods; hes no antidariped solutions for the following, not entirely realistic conditionss (1) constant power extraction (2) large temperature and power excursions where the steady state power 1s four times design power for all times -36- (2) sudden positive excursions of the power to ten times design power, It would seem that a properly designed circulsting fuel reactor is no worse with respect to dauping oscillations than one in which none of the delayed neutrons are attenuated, 5.9 Controls The underlying control philesophy for this reactor is the "master~slave" relationship, where the power plant is the master and the reactor the slave. In other words, the power extracted from the reactor is determined solely by the demand of the propulsion system. The Screwball econtrol system is basicelly dependent upon its large negative fuel temperature chbefficient. As stated in Section 5.7, shim control is obtained by addition of enriched fuel; a possible basic écheme to zeccomplish this is set forth in Reference 13, There are not expected to be control rods in the reactor fuel and moderator regions. Ceonsideration should be given to the possibility of a variable bypass on the Xe separator to provide fine adjustments in reactivity between batch additions of enriched fuel. fn dmportant advantage of the circulating fuel reactor powerplant combinstion, is that preliminary analysis of controlability of a loosely coupled system can betpredicted for each separsate ccmpofiento Reactornand engine stability problems can, therefore, be attacked independently since surges in either component are admitted to the other after considerable delay. 4&s indicated in Reference 14, it appears that the mgster-sliave idea can probably be satisfactorily reduced to practice. e 5.10 Start Up A possible procedure for starting the reactor is as follows: (1) Heat the fluorides, to a mean temperature of 1300°F in an external system and add the enric:hed fuel. (2) Using an external heat source, heat the NaK and NaOD. (3) Bring the fuel, at correct concentration, to 1500CF, (A) Instsll a strong polonium-beryllium source in the reflector (perhaps by mixing molten polonium with the beryllium in a separate reflector tube). (5) Transfer the fuel into the heated reactor system. (6) Allow the subceritical fuel to cool. At about 1300°F, with the moderator temperature closely controlled by the NaK, the core should be critical, The reactor should now be ready to supply heat to the propulsion system. In the event that the temperature of the moderator can not be precisely controlled, it may be possible to wvary the height of the moderator level in the core and thereby effect a reasonable degree of control for start up, 5.11 Shut Down Driving a reactor suberitical when at idle power without the use of safety rods may not be a practical possibility. The practicability of draining the fuel from the core was given lengthy consideration, This was eliminated on the grounds that the additional weisht, higher radistion levels and manifold engineecring complexities would be associated with this systemn. =38- To drive the reactor subcritical a shut down rod in the reflector appears to be necessary. This rod will be completely withdrawn from the reactor during normal operation; to drive the reactor subcritical it will be inserted in the reflector either manually or antomaticelly. This rod is not expected to unduly penalize the shield or reactor design. VI. REACTOR ENGINEERING 6;1 Optimization Folliowing the decision to contain the fuel in tubes, a study was undertaken to ascertain the combinatlon of fuel tube diameters and number of tubes which would yleld optlmum pe;formance. The factors considered in the study are described in Appendix 5. The ultimate cholce was = nompromise between fih@ excessive self-shielding of large diameter tubes and the large core diameter and pressure drop associated with small dismeter tubes., Six 3.5 inch diameter tubes were chosen., 6.2 Heat Transfer 6.2.1 Gamma Heatlng The heating produced by gamwa radiatlon must be known for the deslgn of cooling passags to prevent overheatlng of ths reactor etructure. This heating superimposed on that due to heat transfer determinss the gsource ussd to calculate cocling holerdistribution, per Reference 15. For the purpose of this calculation the reactor was resclved as followss 1. Island ~ NaOD and central fuel tube homogenlzed. 2. OSource Beglon - Rewmalaning fuel tubss and NalCD in the interstices - Annulus. 3. NalDh sphericsl shell., O~ L. Hickel inconel shell 5. Be reflector and an estimated quantity of NaOD and Hi for cooling. W. 8. Fammer's method (Reference 16) was used with modifications suggested by F. H. Abernsthy snd A. H, Fox, Assumptions inherent in the method are: ..o .. a. The "straizht shead" theory of gamma absorption applies, i.e,, compton scattering degrades the photen in energy but does not change its direction. b. Mo refraction takes place at boundaries. c. The source power density is uniform over the equivalent source annulus. d., The fission rate is uniform. Assfimptions used for the Serewball: a, The Yannulus™ of fuel tubes may be replaced by a homogeneous annulus of the same thickness. b. The gammapspgctrum may be idealized as a source consisting of 1 Mev gammas only. (4 more accurate treatment would be to use scources of 1, 2, and 3 Mev gammas with the source strengths adjusted according to the rmamber of gammas between 0 and 1.5, 1.5 and 2.5, and 2.5 and infinite Mev energy. ) c. The use of T for both energy deposition probability and attenmuation factors, rather than uszing p and & buildwup: factor for attenuation, will not result in serious errors. (The proper hde build~up factors for the Screwball configuration are net known. This assumption will cause an error such that the cooling tubes will be placed closer than necessary. Accurate results can only be obtained through the use of critical experiments or actual mockups. ) d. For calculations in the source region, gemma's which traverse the island must be considered. Therefore; for these ealculations, the T for the island (0.117 inches’l) was assumed equal to that for the source region ( 0.152 inches ™). In the gource region { a spherical annulus) where the source and absorber have the same 't', R = Ro @ =7 P(r) = Po I ! 27 B2 sin © e‘”‘tfi R = 6 =o jmp2 d¢edRr (1) € } Eliminating @ with 2:R2+ rzuzrflcosg < _ po®® (R =Ro =R + T ~T R = Ri Q:Rwr Q Integsrating b arts snd usinpg Reference 1°7. [w] p oD P(r) = poT Rg’ - R [El | T (B - f)\ -BE1] T (Ro + 1) ‘] o . fiedfi (2) 2 2 - 337 = r [El | T®R -0)] -8 [T (R +r)|] ) {Mfio ! Pm"] > Tfi%’;z@ + [T r)+1] - T';RZ”P) 2 + [’E(Romr)fl_] 8“:%};:3)% [f(fli\ml”)fli'l] a” f;fi; + I‘) (3) s j’;e_2'm Close to the source region, an infinite slab source 1s assumed, 1,e., P = Po T(r) Y= B " ) ""é“’f‘c"”{E FH T Y tfi)} 2 1 3 (4) o0 where 52 (x) = J o FE | ;2 subseriptsy 1 refers to layer(s) of the slab %f (Reference 18) g refers to the source Farther from the source region, a surface source is used to calculate the sttenuation r R1 P(xW\." i P(+Yy = (....i—l.)“ L DBy e w51t e @l B v el 2 r 7 »Ro P(r) = i_f-éfil ro T () , S Ro {El | () (x - Ro) |~ B {(r)(r + Ro) l} (6) 2 r In the "igland®, the slab source should be used for atienuation near the fuel amnulus, and the surface system at greater distnace., At the center of the island, spherical symmeiry reduces the formula toz r =0 P(o) = [E('Z'l] T (o) o~ TR ; Ry A fictitious surface source which ylelds reasonable heating results in the "island" is obtained by matching the power absorption at 1/2 Ay from the source. In the reflector region, the slab source is used for about 1/2 »g3 then it is matched to a surface source on the outside of the nickel - inconel shell. FEquation (6) may be modified by replacing the Eq functions by g, functions, thus correcting the non-isotropic emission from the surface source. The second term in the parenthesis is always negligible and may be deleted, Equation (&) thus becomes: r » Ro P(x) = [E%‘l] TG R g, |t (r-m) | (@) _—SeBe r 2