CENTRAL RESEARCH LIBRARY DOCUMENT COLLECTION E [ % (i fenctor-aseargh, s Pore 3 4456 0360964 b tagy AEG JESEAREH A, e Pt g AIRPLANE IN WHICH CIRCULATING FUEL IS PIPED DIRECTLY TO THE ENGINE AIR RADIATORS | e U R T : ONAL LABORATORY CE:;::EAL RESEARCH LIBRARY UMENT COLLECTION LIBRARY LOAN COPY DO NOT TRANSFER TO ANOCTHER PERSON If you wish someone e|se to see this document, send in nome with decument and the library wil| arrarge a T OAK RIDGE NATIONAL LABORATORY OPERATED BY CARBIDE AND CARBON CHEMICALS COMPAN A DIVISION OF UNION CARBIDE AND CARBON CORPORATION POST OFFICE BOX P OAK RIDGE. TENNESSEE @ s i ORNL-1287 This document consists of 6§ pages. Copy é-;of 170 copies. Series A. Contract No. W-T7405-eng-26 A DESIGN STUDY OF A NUCLEAR-POWERED AIRPLANE IN WHICH CIRCULATING FUEL IS PIPED DIRECTLY TO THE ENGINE AIR RADIATORS R. W. Schroeder and B, Lubarsky DATE ISSUED: MAR 31 1953 O0AK RIDGE NATIONAL LABORATORY Operated by CARBIDE AND CARBON CHEMICALS CORPORATION A Division of Union Carbide and Carbon Corporation Post Office Box P 0ak Ridge, Tennessee 3 U456 03L0ALY b e R AT R 9 ot £ L e e O R I U WA . . - * - . . - . 64-74. 75. 76-80. 81. 82-84. 85. 86-87. 88 -93. 9. POMEOEr P =P = UE00NDEIPEIMOED kORNL-1287 ReactorjFResearch and Power JERNAL DISTRIBUTION I ubarsky G. Affel . 28. B S. Bettis 29. R.N. Lyon S. Billington 30. WD, Manly F. Blankenship | 31. L. Meem P. Blizard L 32. F J. Miller C. Briant L 33. . Z. Morgan B. Briggs 1 34. . F. Poppendiek H. Buck Y 35.4P. M. Reyling W. Cardwell 1 36/ H. W. Savage E. Center : 3% E. D. Shipley H, Clewett A [ A. H. Snell E. Clifford 3§ f. F. L. Steahly B. Cottrell p 0. R. W. Stoughton D. Cowen ! 21. C. D. Susano B. Emlet (Y-12) 42. J. A. Swartout K. Ergen F 43. E. H. Taylor P, Fraas ' 44, F. C. VonderLage R. Gall 45. A. M. Weinberg R. Grimes 46. G. C. Williams Hollaender 47, C. E. Winters S. Householder 52. ANP Library B. Humes (K-25) 53. Biology Library P. Keim Central Files T. Kelley 60. Health Physics Library M. King 61. Reactor Experimental E. Larson Engineering Library S. Livingston Central Research Library EXTERN A Argonne National Lal Armed Forces Speciall Atomic Energy Commjly Battelle Memorial Brookhaven Natio Bureau of Ships % California Rese Carbide and Cajili Chicago Paten ect (Sandia) o on SR Company - (Y-12 Plant) et 1ii iv 95. 9. 97-101. 102~ 104. 105-108. 109. 110-116. 117. 118-121. 122-123. 124. 125-127. 128. 129. 130-131. 132-133. 134. 135. 136. 137. 138. 139. 140-141. 142. 143. 144-147. 148-155. 156-170. Chief o Naval Resear Departme§t of the Navfifi; Op 36 duPont C-«pany i General ERectric COuVany (ANPP) General El§ctric Cop Pany, Richland Hanford Opefations Ufflce Idaho Operan-ons 0 Iowa State C8l1leg i’ Knolls AtomicQop¥r Laboratory Los Alamos Sci *.lflc Laboratory Massachusetts gtitute of Technology (Kaufmann) Mound Laborato/ National Adv1s National Advig New York Oper North Americg -mm1ttee for Aeronautics, Cleveland _y ! =m1ttee for Aeronautics, Washington FionsQffice ¥ Aviat) fi&, Inc. Nuclear Devel§ pment Al ‘:c1ates, Inc. Patent Bran-f Washlng Rand Corpor ,1on San Francis Operatlons f1ce Savannah Rr fer Operations?y Mf1ce, Augusta Savannah ”z er Operations @fice, Wilmington University / of California Rafitation Laboratory Vitro Co ?ratlon of Americ § 3 -sg-x ) Walter Kf#de Nuclear Laborat 1es, Inc. Westingh fice Electric Corporj ffion Wright Air Development Centen\ Technig Information Servicel}§ Oak Ridge i” AP E AR BT S g i S e Ve CONTENTS INTRODUCTION AND SUMMARY . DESIGN OF AIRPLANE AND POWER PLANT FOR MACH 1.5 AT 45,000 FEET . Reactor Core . . . e e e e e e e e e e e e e e e Physical descrlptlon Power distribution . . . . & & v « ¢ 4 ¢ ¢ v v o e e e e . Engines and Accessories . . General descr1pt10n of the power plant . Main engine system . . Shield-cooling system . . . . . . . . . . . . . . Reflector-cooling system . . . . . . « ¢« « . . Accessory system . . . e et e e e e e e e e e e e Over-all power plant performance . . Physical arrangement of power plant . . . . . . . . Power plant weight . . . . . . . . . . . ¢ ¢« ¢ v+« .. Power Plant Radiators . . . . . . . . ¢« &« v v ¢ « o o Physical description . Radiator design relat10nsh1ps Fuel-to-air radiator . Auxiliary radiators . . . . . . . . i v 4 e 4 e e e e e Airplane . . . . . . . . L i i e et et e e e e e e e e e e Airplane configuration . . . Airplane lift-to-drag ratio . . « « ¢« v ¢ ¢« ¢ « « ¢ o o Airplane pitch control . Airframe weights . . . . . . . . ¢ & v ¢ v e e e e e e e SEA-LEVEL PERFORMANCE SHIELDING ANALYSIS . Assignment of Radiation Contributions . . . . . . . . . . Configuration to be Shielded . . . . . . . . . . . . Basic Data for Shield Design . . . . . . . . ¢« « ¢ « « « & Calculation of Shield Dimensions . . . . . . . . . . . . . Delayed neutrons into crew compartment rear Delayed neutrons to crew compartment sides . . . . . . . . Delayed neutrons into front . . . . . ¢« ¢« ¢ ¢ ¢ o o o @ Gamma rays from the exposed fuel e e e Gammas from radiators into rear of crew compartment . . . T W . 25 VOO e 13 16 16 17 17 19 19 21 23 25 25 28 31 32 33 35 35 35 36 37 37 37 37 37 38 Gammas from radiators to sides . Radiator gammas into front . . Specification of Reactor Shield Thickness Reactor neutrons into crew shield rear . Reactor neutrons into crew shield sides Reactor neutrons into front of crew shield . Reactor gamma rays into crew shield rear . Gamma rays from reactor to crew shield sides . Gamma rays from reactor to crew shield front . Special Shielding Considerations . Crew shield sides near the rear Slanting front wall Physical Description of Shield . STATIC CHARACTERISTICS OF THE REACTOR REACTOR CONTROL Control Features Determined by Simulator Study . vi Pressure in Fuel Tubes . 38 39 39 39 40 40 41 41 41 42 42 43 43 45 56 ST 58 AR W, © ACKNOWLEDGEMENT The authors are indebted to E, P, Blizard and F. H. Murray who prepared the section entitled “Shielding Analysis,” to W. K. Ergen and C. B, Mills for the section on “Reactor Statics,” and to E. R. Mann for the section on “Reactor Control.” The advice and assistance of J. Y. Estabrook, B. L. Greenstreet, E. L. Hutto, J. D. Jackson, and A. B. Longyear* materially contributed to the completion of the calculations and drawings contained herein. Special recog- nition is due R, C, Briant, whose criticisms and suggestions have substantially improved the technical content of this report. *On loan from Aerojet Emgineering Corp. vii A DESIGN STUDY OF A NUCLEAR-POWERED AIRPLANE IN WHICH CIRCULATING FUEL IS PIPED DIRECTLY TO THE ENGINE AIR RADIATORS R. W. Schroeder INTRODUCTION The search for a nuclear power plant capable of propelling an airplane at supersonic speeds at high altitudes has led to a close study of circulat- ing- fuel reactors, One of the ad- vantages of such a reactor is that the heat developed in the fuel may be transmitted to the air stream 1n several ways, The heat might be employed in a vapor cycle so that use of a compressor-jet engine would be possible, or the heat might be trans- ferred to a liquid coolant that would be used in a turbojet engine. In the divided-shield concept, all parts of the aircraft except the crew compartment are subjected to thoroughly uninhabitable radiation conditions. Ground handling of such an airplane imposes problems that are perhaps not even now thoroughly appreciated. How- ever, 1f 1t 1s assumed that these problems are soluble in a practical manner, then 1t 1i1s not only prudent but necessary to investigate the extreme of such a system. The inherent adaptability of the fluid fuels being developed permits the study of a high-powered system wherein the heat is transmitted directly to the air in the engine, The first asset of such an arrangement is that the liquid-to-liquid heat exchanger is eliminated., The first difficulty is, of course, shielding. In this arrange- ment, the intensely radiocactive fuel would have to be carried through a (I)On loan from Lewis Flight Propulsion Labora- tory, National Advisory Committee for Aeronautics. B. Lubarsky(1) AND SUMMARY large space between the reactor and the engine radiators. The shield would be, then, 1n some sense, the opposite extreme of a unit shield. The notion must of necessity exploit shadow shields to the utmost. Since the air- plane and the surrounding air would be subjected to more radiation than in any other scheme, theair and structure scattering are of maximum importance, as would be expected. In most nuclear airplane proposals it 1s i1mpossible, really, to separate power plant and airframe studies. In this instance, any such separation would be completely impossible; there- fore this report covers in an initial way the design of a circulating-fuel- direct-to-air tactical airplane operat- ing at Mach 1.5 and 45,000 feet. The reactor, fluid circuit, heat exchangers, shielding, and airplane studied are described and illustrated in the body of this report. However, a brief description of the entire system is presented at this point to orient the reader. The reactor investigated includes beryllium oxide as a moderator and reflector, Inconel as a structural material, and fused fluoride salts combined with uranium tetrafluoride as the fuel. The fuel, which is in the liquid state at operational tempera- tures, 1s pumped through Inconel fuel tubes that pass through the moderator. The fuel leaves the reactor at a temperature of 1500°F and i1s routed to fuel-to-air radiators located in each DESIGN STUDY of six turbojet engines. After being cooled to 1000°F in the radiators, the fuel 1s pumped back to the reactor by axial-flow pumps driven by air turbines. The system postulated is not predi- cated on any specific radiator design; however, the radiator designs studied included Inconel tubes (with Inconel fins) through which the fuel passes. The designs studied were such that the heat exchanger frontal area require- ments exceeded the engine frontal area by a large factor. Accordingly, the heat exchangers shown have been divided into rectangular banks and placed parallel to the engine longitudinal axis. Compressor-discharge air flows parallel to the engine axis, makes a right angle turn to pass through the radiator, and then 1is directed toward the turbine nozzle box. The turbojet engines employed were designed for a turbine inlet tempera- ture of 1250°F and acompressor pressure ratio of 6.1 while operating at Mach 1.5 at 45,000 feet. They are similar in principle to current turbojet engines except for deletion of the chemical burners and addition of fuel- to-air radiators, A divided shield with water sur- rounding the reactor and lead and hydrogenous plastic around the five- man crew compartment is employed. The shield has been designed for a maximum dosage of 1 r/hr within the crew compartment at design-point operation (Mach 1.5 at 45,000 ft), No mechanical control system has been shown. As discussed more fully in the body of the report, 1t 1is expected that the negative temperature coefficient of reactivity of the reactor described will cause the reactor to behave as a slave to the external heat-removal system (engines and radiators). If this premise is valid, the primary control requirements may be satisfied by a fuel-enrichment shim for start-up purposes and fuel drainage provisions for shut-down. The ANP Aircraft Reactor Experiment will, it is hoped, clarify the validity of these premises. The airframe has a delta-wing con- figuration, The empennage includes a triangular planformrudder and elevator. The center of lift and center of gravity, which coincide, are forward of the reactor and engines because of the crew-compartment moment. The bomb load has been located at the center of gravity to avoid changes in trim con- current with bomb release, The engines are located behind the reactor-shield assembly, but as close toit as possible to minimize fluid-piping length. The engines are also located as close to the airplane center line as their size permits to minimize fuselage diameter and to obtain maximum shadow shielding by the reactor shield assembly. The engine air intake 1i1s located forward of the wing leading edge and is in the form of an annulus surrounding the fuselage. ‘ The descriptions and discussions contained in the body of the report have been prepared as concisely as the complexity of the subject matter per- mits, and no attempt has been made to summarize this material. Comments regarding the ultimate feasibility of the cycle described, or comparisons between this cycle and other cycles, would be premature because much more detailed study, experimentation, and advancement of the related arts are needed, It may be said, however, that the studies made to date indicate a high performance potential and have not revealed the presence of inherent limitations or obstacles that are believed to be insurmountable. It is expected that the Aircraft Reactor Experiment and parallel research and development being conducted by the Oak BRidge National Laboratory may clarify many of the premises and suppositions included in this study, and, in addition, advance the tech- nology of high-temperature circulating- fuel reactors. Problems such as airplane operation, flight stability, ground handling, maintenance, and repair are not dis- cussed in detail. These matters re- quire exhaustive study and are regarded as being beyond the scope of this report. However, with regard to ground handling and maintenance, any nuclear- powered airplane with a so-called “divided shield’’ will require sup- plementary shielding for airplane access during ground operation or after shut-down., The amount of such supplementary shielding required will depend on the power history of the reactor, the distribution of sources of radiation within the airplane, and the amount of shielding permanently installed about these sources. The configuration discussed here will require a greater thickness of supple- mentary shielding than one in which the fuel circuit is more deeply sub- merged in the airplane shielding. The extent to which this will compli- cate the ground-handling problem would require very detailed investigations. Also, with regard to airplane operation, flight stability, and other such con- siderations, it should be recognized that only a few experimental airplanes have to date achieved supersonic speeds, and none of these approach in size the airplane discussed here. Determination of the optimumaerodynamic configuration, stability criteria, incidence angles required for take-off and landing, etc. will involve further aerodynamic research and airframe design studies. The airframe con- figuration illustrated should there- fore be regarded as highly tentative, These studies deal primarily with the power plant and the shielding. Changes in the airframe will have little effect on these studies unless the reactor-to-crew separation distance or power requirements affected significantly, The calculated performance of the system studied is summarized as follows: are NUCLEAR-POWERED AIRPLANE AT AT SEA LEVEL 45,000 FEET Speed Take-off Mach 1,5 Total net thrust (1lb) 165,600 53,850 Take-off distance (ft) 2,500 Total air flow (lb/sec) 4,137 1,751 Turbine inlet temperature (°F) 1,125 1,250 Fuel temperature (°F) reactor inmlet 1,000 1,000 Fuel temperature (°F) reactor outlet 1,500 1,500 Fuel flow (lb/sec) 3,130 1,650 Maeximum reactor tube temperature (°F) Inside surface 1,583 1,554 Outside surface 1,608 1,567 A summary of the weights of the various portions of the aircraft is given in the following: WEIGHT (1b) Airplane Wing 46,000 Tail 9,200 Fuselage 29,900 Landing gear 18,900 Controls 2,100 Total 106,100 Power Plant Engines 59,900 Auxiliary system 5,000 Inlet and exhaust ducting 10, 300 Rediators Core 17,900 Baffles, structure, headers, contained fuel, etc. 6,000 Total 99,100 Shielding Crew shield Lead 30,800 Plastic 25,900 Reactor shield assembly Reactor assembly 10, 000 Water 28,200 Structure, insulation, etc. 10,200 Total 105,100 DESIGN STUDY Payl oad Crew (5 at 250 1b) 1,250 Furnishing 850 Pressurizing and oxygen 550 Communicating equipment and jamming radar 600 Bombing and navigating equipment 1,700 Photographic equipment 50 Instruments 400 Bomb load 10,000 Firepower (tail turret and ammunition) 3,000 Contingencies peculiar to shielded cockpit 1,600 Total 20,000 Contingency 19,700 Total airplane weight 350,000 A summary of the fuel holdup in the various portions of the power plant is given below (there are 3.14 1b of U235 per cubic foot of fuel). FUEL HOLDUP (£t Reactor Core 7.96 Headers 3.65 Radiators Core 6.9 Headers 8.4 Piping between reactor and radiators Common inlet piping 2.5 Common ocutlet piping 2.3 Individual piping between lines and radiator (including pumps, etc.) 4.0 Total 35.711 DESIGN OF AIRPLANE AND POWER PLANT FOR MACH 1.5 AT 45,000 FEET REACTOR CORE A general discussion of a reactor intended to provide sufficient power to operate an airplane at Mach 1.5 and 45,000 ft is presented in this chapter. The decision to explore the po- tentialities of circulating- fuel reactors necessitated the review of several broad classes of moderators: (1) low-temperature hydrogenous liquids (such as water) used with double-wall construction or insulation between the fuel and the moderator, (2) high-temperature hydrogenous liquids used with single-wall con- struction, and (3) solid moderators, such as beryllium oxide. FEach of these possible moderator arrangements appears to offer some advantages and some disadvantages, but it is not possible to make an irrevocable decision at this time as to which one should be used. Use of the first moderator would involve the difficult problem of rejecting the moderator heat from a low-temperature source to a relatively high-temperature sink. The required air-flow rates would be large, inas- much as the permissible air tempera- ture rise would be limited and the driving temperature differences would be low. Furthermore, the double-wall construction within the reactor appears to involve serious problems because of differential expansion between the cold tubes and the hot tubes, tube sheets, headers, etc. Accordingly, it was decided to avoid this approach for the present, The second moderator appears to be attractive 1n many respects, At present, however, there are no combinations of high-temperature hydrogenous fluids and structural materials that are known to be com- patible at the operating temperatures of circulating-fuel reactors. There- fore active consideration of this possible moderator must be deferred. The third arrangement has been employed in the design studies outlined here because it appears to involve no major material uncertainties and permits a relatively simple core design. Inasmuch as the heat of the fuel is not transferred within the core, incorporation of a heat exchanger lattice within the core is not neces- sary, and relative coarseness of core geometry is permitted. As the fuel- tube surface area is diminished, how- ever, two constraints appear that influence the required tube diameter, tube surface area, and fluid velocity. First, the moderator heat inflow to the fuel stream causes a film tempera- ture drop, 6, which increases the fuel-tube temperature. Second, the lower velocities of the fuel particles adjacent to the walls lead to greater fuel residence times and higher wall temperatures. In the geometry achieved after several iterations, the first effect was found to dominate. The film drop associated with moderator heat inflow may be expressed as 0.2 ,.QL_ oDt A h A Vo8 where @ = temperature difference, °F, é%== heat flux, Btu/sec. ft?, h = heat transfer coefficient, Btu/sec*°F- ft?, D = tube diameter, ft, V = fluid velocity, ft/sec. If it is desired to achieve a maximum wall temperature of approximately 1550°F with a fluid inlet temperature of 1000°F and a fluid outlet tempera- ture of 1500°F, the permissible & will be 550°F at the inlet end and 50°F at the outlet end. The high permissible inlet & can be employed advantageously by using a two-pass arrangement in which the cold inlet fluid is passed first through the region of highest power generation - the central portion of the core. Since wall temperatures in this region were found to be readily controllable, relatively low flow velocities and large tube diameters could be used. NUCLEAR-POWERED AIRPLANE Wall temperatures near the outlet end of the reactor tended to become more critical as the fuel temperature in- creased. This tendency was alleviated by the reduction in specific power generation as the fuel approached the unreflected end of the peripheral pass. Further alleviation was provided by decreasing the tube size and increasing the number of tubes, which also in- creased the surface-to-volume ratio, and by increasing flow velocities in the second pass. After several iterations, a geometry was achieved that resulted in maximum fuel-tube wall temperatures, in each pass, of approximately 1550°F. The core (Fig. 1) consists of a series of parallel tubes, arranged in two series passes, that convey circu- lating fuel through a beryllium oxide block lattice. A beryllium oxide reflector adjacent to all core surfaces except the fluid inlet and outlet end has been provided and is to be cooled by circulation of nonuranium-bearing fused fluorides. Physical Description, The reactor, as shown in Fig., 1, can be considered as being contained in a 55-in, -dia sphere if the fuel inlet and outlet lines and reflector coolant (salt) lines are excluded., The reactor core consists of parallel tubes arranged in concentric circles and contained ina40,4 -in. ~-dia cylinder with conical and truncated -conical ends. Each core tube is surrounded by a moderator in the form of hot -pressed beryllium oxide, Specific design features are presented in the following: 1. The cylindrical core has mani- folds on the ends to provide for two- pass flow of the fuel, 2. The fuel, metal tubing, and moderator volume fractions are held constant throughout the core. The cylindrical core contains approximately 34% fuel, 2% metal tubing, and 63% moderator. 3. The fuel used for the calcu- lations of this study is a molten DESIGN STUDY DWG. 17662 PLAN REFLECTOR ~> FUEL IN SALT ouT == SALT IN, SIX PLACES VERTICAL SECTION ON ¢ Fig. 1. Beryllium Oxide-Moderated, Circulating-Fuel Reactor. b LA bt . mie 2L s e e e mixture of fluoride salts, one of which is uranium tetrafluoride in a low concentration, 4, The moderator and reflector are beryllium oxide blocks. 5., The reflector is situated about the core as shown in Fig. 1. 6. The core shell is perforated around the cylindrical section to permit the influx of reflector coolant to fill the core-moderator interstices. Six small tubes connect the core to the reflector through the crossover header to augment filling the inter - stices. The coolant will be maintained at an absolute pressure above that of the fuel circuit to prevent the accumulation of stagnant fuel in the moderator interstices in the event of an internal leak in the fuel circuit. 7. The tube sheet, at the un- reflected end of the core, is separated between the fuel inlet and outlet to permit the differential expansion that occurs because of the temperature rise in the core, 8. Minimum pressure loss and mini - mum volume (uranium holdup) were con- sidered in designing the inlet, outlet, and crossover headers. The 1inlet header is a single 9,5-in, line that feeds all core tubes in the first pass through a single header., This inlet line extends 5 ft from the reactor to a collector manifold that, in turn, receives all fuel returning from the engine radiators. The outlet is a l.5-in, annulus that receives all outgoing fuel from the second - pass core tubes and transmits the fuel to a common, annular manifold that, in turn, feeds all engine radiators. The reactor outlet annular header is concentric with the reactor inlet line. This header arrangement elimi - nates any adverse flow conditions that may arise i1f one or more engines are shut down as a result of malfunction or battle damage. 9. All metallic parts that come in contact with either the fuel or NUCLEAR-POWERED AIRPLANE the coolant are Inconel, which has been shown to have the best corrosion resistance to molten salts and also good high-temperature strength charac- teristics. Power Distribution. The six turbojet engines require a reactor power output of 321,000 Btu/sec and a fuel flow rate of 14.7 c¢fs, The freezing point of the molten salt mixture dictates a minimum, reactor -inlet, mixed-mean fluid temperature on the order of 1000°F., The strength of the materials of the reactor core and pressure shell dictates a maximum, reactor -outlet, mixed-mean fluid temperature of 1500°F, The physical properties of the molten salt mixture used in the calcu- lations of mixed-mean fluid temperature and fuel-tube wall temperatures are given in the following: 0.39 Btu/lb-°F 112 1b/fc? 0.5 Btu/hr- ft2 (°F/fv) Specific heat, Cp Density Thermal conductivity Viscosity 8.3 to 2.1 centipoises The power distribution within the core 1s determined in the section entitled “Static Characteristics of the Reactor” and is shown in Fig. 29. Five per cent of the total power generated was assumed to be generated in the moderator. This power is trans- mitted to the fuel via heat conduction through beryllium oxide, interstices filled with molten salt, and the tube wall, and then by convection to the fuel. The power distribution in the moderator was assumed to be the same as the fuel power distribution, Fuel-tube wall temperatures based on these power distributions were calculated for various tube stations in both the first and second pass, as shown in Fig. 2. A temperature profile through a typical core section 1is shown in Fig. 3, TEMPERATURE (°F) ed OWG. 17663 1600 FUEL-SIDE TUBE-WALL FUEL-SIDE TUBE-WALL TEMPERATURE TEMPERATURE 1500 1400 1300 [] MIXED-MEAN FUEL TEMPERATURE m BOUNDARY LAYER TEMPERATURE RISE DUE TO MODERATOR HEAT FLUX BOUNDARY LAYER TEMPERATURE RISE DUE TO VOLUMETRIC POWER GENERATION 1200 L= LENGTH FROM UNREFLE END 1100 1000 © [REFLECTED END REFLEGTED END o Q.2 0.4 0.6 a8 o o8 0.6 0.4 0.2 o L/L,, CORE TUBE LENGTH RATIO L/L,,CORE TUBE LENGTH RATIO FIRST PASS - ROW NO 11 SECOND PASS-ROW NO1{5 Fig. 2. Longitudinal Temperature Pattern in Fuel Tubes in Reactor Core. AQNLS N9ISHd D’! 1!564 1800 p — v Lo [ —MOLTEN SALT 1700 P OUTER ROW, FIRST PASS, / Ll o=0.576 // 1600 § "} —-MODERATOR c & (Be0) ¥ d w 1500 § C @ ¢ = E 1400 ' N r & =1 - 1300 j} 1200 ) —at b= TUBE WALL 0 0.2 0.4 0.6 0.8 1.0 DISTANCE FROM FUEL TUBE CENTERLINE (in) Fig. 3. Temperature Profile Through Fuel Tube and Moderator. ENGINES AND ACCESSORIES A turbojet cycle, in which fuel -to- air radiators are substituted for the conventional chemical burners, is employed to provide sufficient thrust for operating the design air- plane. Compressor bleed -off air is used for the reflector- and the shield- cooling systems; some of this air is then expanded through turbines to furnish power for accessories, and the remainder is expanded through adjust- able nozzles to give propulsive thrust, Once the total air-flow require - ment was established, the total com- pressor inlet area needed was deter - mined on the basis of NACA develop - mental experience., The number of engines necessary to accommodate the total air flow (or to provide the total inlet area) will depend on the size of engine that can be made very arbitrary. NUCLEAR-POWERED AIRPLANE available when an airplane of the type described is constructed. At present, any determination of the number of engines to be used will be The use of six engines has been postulated because of the convenience from the standpoint of installation. The use of a different number of engines, within reason, would have only secondary effects on the over-all airplane weight and performance. General Description of the Power Plant., Figure 4 is a schematic diagram of the main engines and accessories. The main engines are turbojets with circulating -fuel -to -air -radiators instead of the conventional combustors. Heat is generated in the circulating fuel as it passes through the reactor and is then transferred to the engine air flow in the circulating-fuel -to - air radiators. Air is bled from the compressors of the main engines to auxiliary radiators to remove heat from the reactor -shield coolant and the reflector coolant. A portion of the air passing through the reflector- coolant radiator is used to operate a number of air turbines that drive all the liquid pumps in the power plant. All the air bled from the main compressors is eventually dis- charged rearward and provides some additional thrust. With an airplane gross weight of 350,000 1b and an airplane lift-to-drag ratio of 6.5, the power plant is required to produce a total thrust of 53,850 1lb at design flight conditions. The power plant may be considered as consisting of four principal portions: the main engine system, the shield -cooling system, the reflector - cooling system, and the accessory system, Main Engine System. The air for all four of the systems enters the inlet duct of the airplane and passes through the diffuser. It is then carried in ducting around the reactor shield and into the compressors of the DESIGN STUDY o DWG. 17665 KAAAA] Lfi%’fi 9 KOO0 E OF TWO PUMPS AND AUXILIARY o = e TURBINES Tz 28 fi - ) ¥ T \23 24 > 25 == ONE OF TWO GENERATORS AND AUXILIARY = TURBINES 5 19 20 18 _”';/ ONE OF SiX AUXILIARY TURBINES ONE OF SiIX PUMPS [N —~ et 3 - ONE OF S A TOTAL TOTAL AL TOTAL TotaL | wovar LOCATION FLUID | PRESSURE | TEMPERATURE FLOW LOCATION FLUID ; PRESSURE | TEMPERATURE| "g ow (peia) °p) (1b/sec) (psia) C°F) | (1b/aec) A, Radiator Imlet Line Fuel 105 1500 1646 8. First-Stage Bleed Air 8.68 145 BS5.6 Radiator Outlet 9. Radiator Inlet Line | Air 8.46 145 85.6 Line Fuel 25 1000 1646 10, Radiator Outlet Line| Air 7.60 3c0 85.6 C. Pump Outlet Line Fuel 175 1000 1646 11. Jet Pipe Air 1.38 300 85.6 D. Reactor Inlet Line Fuel 160 1000 1646 12. Auxiliary Jet Air 2.142 85.6 E. Reactor OQutlet Line Fuel 120 1500 1646 13. Exght-Sta ¢ Bleed Air 29.0 430 110.7 F., Radiator Inlet Line | Water| 200 350 61.8 14. Radiator Inlet Line | Air 28.3 430 104.9 G. Radiator Outlet Line | Water 167 300 61.8 15. Radiator Outlet Line| Air 25.4 1000 104.9 H. Pump Outlet Line Water| 211 300 61.8 16. Auxiliary Turbine J. Shield Inlet Line Water 206 300 61,8 Inlet Line Air 24.7 1000 7.3 K. Shield OQutlet Line Water| 205 350 61.8 17. Auxlliari Turbine L. Radiator to Pump Outlet Line Air 7.24 T17 7.3 Line Salt 137 1000 195.2 18, Auxiliary Jet Air 2.142 7.3 M. Radiator Qutlet Line | Salt 137 1000 10.8 19, Jet Pipe Air 24.7 1000 97.6 N. Radiator Inlet Line | Salt 165 1200 206 20. Auxiliary Jet Air 2.142 97.6 P. Reflector Outline 21. Radiator Inlet Line | Air 28.3 430 5.8 Line Salt 170 1200 206 22, Radiator Qutlet Line| Air 25.4 1000 5.8 3. Reflector Inlet Line | Salt 175 1000 206 23. Auxiliary Turbine . Pump Outlet Line Salt 180 1000 206 Inlet Line Air 24.7 1000 5.18 0. Aircraft Ambient Air 2.142 -67 24, Auxiliary Turbine 1. Compreasor Inlet Outlet Line Air T.24 T17 5.18 ine Air T.24 108 1948 25. Auxiliary Jet Air 2.142 5.18 2. Compresaor Outlet . 26. Auxiliary Turbine ine . Air 43.5 544 1751 Inlet Line Air 24.7 1000 0.17 3. Radiator Inlet Line [ Air 42,4 544 1751 27. Auxiliary Turbine 4, Radiator OQutlet Line | Air 38.0 1250 1751 Outlet Line Air T.24 T17 0.17 5. Turbine Inlet Line Air 36.9 1250 1751 28. Auxiliary Jet Air 2.142 0.17 6. Turbine Outlet Lime | Air 10.6 824 1751 29, Jet Pipe Air 24.17 1000 0.62 1. Jet Air 2.142 1751 30, Auxiliary Jet Air 2,142 0.62 Fig. 4. Schematic Diagram of Power Plant. 10 six main engines. The air required for the shield-cooling, the reflector- cooling, and the accessory systems is bled from various stages of the main compressors, as will be described. The air for the main engine system passes through the compressors and enters the fuel -to-air radiators, where it is heated by the fuel circulating from the reactor. The air then expands through the turbines that drive the compressors and is exhausted rearward through variable -area exhaust nozzles. A thermodynamic calculation was carried out to determine the specific impulse and cycle efficiency of the turbojet engines for various values of compressor -pressure ratio, turbine NULCEAR-POWERED AIRPLANE inlet temperature, and pressure drop in the radiators and associated ducting between the radiators and the com- pressors and turbines., The following efficiencies were used for the various components: Diffuser and inlet ducting pressure recovery factor (actual total pressure per ideal total pressure) 0,92 Compressor efficiency, total - to-total adiabatic 0.85 Turbine efficiency, total- to -total adiabatic 0.90 Exhaust nozzle velocity co- efficient 0.97 Figures 5 and 6 show the specific impulse and cycle efficiency of the UNCLASSIFIED OWG. 17666 a0 —-"——___ __-‘"“‘*--\‘ 1380 "—_-___-hh“*-.‘\_‘\\\\‘\“‘!350 30 —] — = L\\ \ 1250 \ \ 1250 2 50 \\\‘\\\ 1150 s 20 . q § 4¢) - g 48 N 3 ( 2 )RAD——O 05 \ 050 & ( > )MD—O.IO 0so -4 & x B g 5 £ 10 & & — o a a E & & g 40 & ] $ g z ; _\ w "-é" "i" 30 ___———"—'-\ 1350 5 \ t350 — E — o ] e T —— \ \ ) -—-—-__-.§-“5~‘\\“ =0 fih‘"“-~. 1250 20 - 1150 T~ 150 G%q =019 \\\\\\\ A ) £y RA0 1050 ( )mo 0.20 10850 10 2 4 6 8 2 4 6 8 COMPRESSOR PRESSURE RATIO Fig. 5. Variation of Specific Impulse with Compressor Pressure Ratio for Turbojet Engines. Alticude, 45,000 ft; Mach, 1.5; diffuser efficiency, 0.92; compressor efficiency, 0.85; turbine efficiency, 0.90; nozzle efficiency, 0.95. All efficiencies are total-to-total adiabatic. 11 DESIGN STUDY UNGCLASSIFIED DWG. 17667 40 2 - [&] = 5 b T S 30 ’fl_ i & B - AP W Q—- =0.05 Ap 3 £ lanp ~p ) =0.t0 = RAD [&] 20 I TURBINE INLET TEMPERATURE (°F) 1350 —————— 1250 ——1150 ——— —1050 40 & P O = il o —_— o 30 e —— e — W S —— e ¢ —— —— — H — —— — — 0 Ap =1 T~ 6 s (7’" =045 (~A—P) =0.20 RAD | P lanp i 20 2 4 6 8 2 4 6 8 COMPRESSOR PRESSURE RATIO Fig. 6. Variation of Cycle Efficiency with Compressor Pressure Ratio for Turbojet Engines. turbojet engines for compressor - pressure ratios from 2 to 8, turbine inlet from 1050 to 1350°F, in the radiators and associated ducting of 5 to 20 per cent,('? These curves, together with the radiator data in- cluded in the ‘“Power Plant Radiators’ section, permitted selection of the following design-point conditions: temperatures and pressure drops Compressor-pressure ratio 6.0:1 Turbine inlet temperature 1250°F Pressure drop in radiator and radiator ducting 15% It will be noted that the engines alone would be favored by lower com- pression ratios, higher turbine inlet temperatures, and lower radiator (l)ln the actual power plant, the specific impulse and cycle efficiency will be reduced some- what by compreassor bleed-off. More exact specific impulses and cycle efficiencies are presented in a later gection on "Over-All Power Plant Per- formance. ' 12 Conditions and efficiencies same as in Fig. 5. pressure drops and that the radiators alone would be favored by higher com- pression ratios (greater densities), lower turbine inlet (greater driving forces), and higher pressure drops (greater velocities), Several preliminary engine and radiator design studies, in which various combinations of the controllable variables were used, indicate that the design-point conditions selected are close to optimum. temperatures With the use of the efficiencies and other factors given, thermodynamic calculations were made of the air circuit of the main engine system. Allowance was made for the guantities of bleed air needed for the other systems. Pertinent values of air pressure, temperature, and weight flow at various stations in the main engine system are given in Table 1 and e R AR S 0 0wt sl iic'a e Fig. 4. The values of weight flow are for all six engines combined. The thrust produced by the six main engines is 48,690 pounds. This is approximately 90.4% of the required thrust, the remaining 9.6% being produced by the other systems. The specific impulse of the main engine air is 27.8 1lb of thrust per pound of air per second. The amount of power that must be generated in the fuel and moderator of the reactor is 321,000 Btu/sec. The heat generated in the reactor core (fuel and moderator) is trans- ferred to the main engine radiators by the circulating fuel. The maximum fuel temperature leaving the reactor was set at 1500°F. Higher temperatures would, of course, be desirable but would make the problem of designing the various components appreciably more difficult, The temperature entering the reactor was chosen as 1000°F, This, again, 1s a compromilse between conflicting requirements, Higher reactor inlet temperatures would reduce the size of the radiators but would increase the fuel flow rate and hence the duct sizes for the same pressure drop, thus increasing the TABLE 1. NUCLEAR-POWERED AIRPLANE amount of fuel in the system. Lower values of temperature would, in addition to increasing the radiator size, increase the danger of freezing the fuel. Therefore the value of 1000°F was selected as a reasonable compromise., The total weight flow of fuel for all six engines is 1646 lb/sec., Values of fuel temperature and pressure at various stations in the main engine system are listed in Table 2 and Fig. 4. The properties used in the analysis of the circulating fuel are: 112 1b/fe? 0.39 Btu/1b*°F 0.5 Btu/hr- ft? (°F/ft) 4.84 1b/hr-ft Density Specific heat Thermal conductivity Viscosity Shield-Cooling System. A conserv- ative estimate of the rate of heat generation in the reactor shield is 1% of the core heat generation rate, (1) Therefore 3210 Btu/sec must be removed from the reactor shield, This 1is accomplished by circulating the shield (2} peport of the Shiclding Board for the Air- craft Nuclear Propulsion Program, ANP-53 (Oct. 16, 1950). AIR PRESSURES, TEMPERATURES, AND WEIGHT FLOWS AT VARIOUS STATIONS IN THE MAIN ENGINE SYSTEMS TEMPERATURE PRESSURE WEIGHT FLOW (°F) (psia) (l1b/sec) Station 0, ambient conditions -67 2.142 Station 1, compressor inlet 108 T1.24 1948 Station 2, compressor exit 544 43.5 1751* Station 3, radiator inlet 544 42.4 1751 Station 4, radiator outlet 1250 38.0 1751 Station 5, turbine inlet 1250 36.9 1751 Station 6, turbine exit 824 10,6 1751 Station 7, exhaust jet** 1751 *Air (197 1b/sec) is bled from various stages of the main engine compressors for the shield- cooling, **Velocity = 2345 {fps. the reflector-cooling, and the accessory systems. 13 DESIGN STUDY water through a radiator. The temper- ature that can be maintained in the shield without boiling the shield water 1s, of course, dependent on the pressure maintained. To keep the pressure reasonably low, a shield- water temperature of 350°F and a pressure of 200 psia were selected. The shield-water temperature is reduced 50°F in the radiator. The weight flow of shield water required 1s 61.8 1b/sec. The temperatures and pressures of the shield water at various stations in the shield-cooling system are given in Table 3 and Fig. 4. Air for the shield-water radiator is bled after the first stage of the main engine compressors, because at that point the shield water i1s at a low temperature; bleeding at a later stage would increase the temperature of the bled air., It .would be possible in flight to use ram air to feed the shield-water radiator, but it seems more desirable to design the system TABLE 2. IN THE MAIN to use air bled after the first com- pressor stage, since this will permit cooling of the shield water while stationary on the ground without the use of auxiliary equipment external to the airplane. The temperature of the air entering the shield-water radiator is 145°F, and the temperature leaving the radiator is 300°F., The weight flow of air is 85.6 lb/sec,. After the air passes through the shield-water radiator, it is exhausted through a variable—area nozzle and produces some thrust. Air temperatures and pressures at various stations in the shield-cooling system are given in Table 4 and Fig. 4. The thrust produced by the jet is 425 1b, and the specific impulse is about 4.96 1b of thrust per pound of air per second. Reflector-Cooling System. It is estimated that the rate of heat generation in the reflector will be about 3% of the core heat generation rate. Therefore 16,050 Btu/sec must FUEL TEMPERATURES AND PRESSURES AT VARIOUS STATIONS ENGINE SYSTEM , radiator inlet Station A B Station C, D E , radiator outlet pump outlet Station Station , reactor 1inlet , reactor outlet TEMPERATURE (°F) PRESSURE (psia) 1500 105 1000 25 1000 175 1000 160 1000 120 TABLE 3. WATER TEMPERATURES AND PRESSURES AT VARIOUS STATIONS IN THE SHIELD-COOLING SYSTEM TEMPERATURE (°F) PRESSURE (psia) Station F, radiator inlet 350 200 Station G, radiator outlet 300 167 Station H, pump outlet 300 211 Station J, shield inlet 300 206 Station K, shield outlet 350 205 14 g bR BPRER S BT i 17 T st § el 2 be removed from the reflector. This is accomplished by circulating a molten mixture of fluoride salts (containing no uranium tetrafluoride) through the reflector and then through a radiator, where the heat picked up by the salt in the reflector i1s re- moved. The reflector inlet temperature of the salt was set at 1000°F and the outlet temperature at 1200°F, The weight flow of salt regquired is 206 1b/sec. The temperatures and pressures of the salt at various stations in the reflector-cooling system are given in Table 5 and Fig. 4. The properties used for the circulating-fuel analysis could be used for this salt analysis because the fuel has a low uranium concentration, Air for the reflector-coolant radiator is bled after the eighth stage of the main engine compressors. NUCLEAR-POWERED AIRPLANE This bleedpoint is a compromise between the conflicting requirements of over-all engine performance (which favor bleeding at an earlier stage) and radiator and duct size (which favor bleeding at a later stage)., No attempt has been made to optimize the bleed point, but one possible com- promise was selected. The air temper- ature entering the reflector-coolant radiator is 430°F and the outlet temperature is 1000°F. A weight flow of 110.7 1lb/sec is required. After the air has passed through the re- flector-coolant radiator, a portion of it (12,48 1lb/sec) is used to operate a number of air turbines that drive the power plant accessories. The air that is not diverted to the accessory system is exhausted through a variable- area exhaust nozzle. Values of air temperatures, pressures, and weight TABLE 4. AIR TEMPERATURES AND PRESSURES AT VARIOUS STATIONS IN THE SHIELD-COOLING SYSTEMS TEMPERATURE PRE SSURE (°F) (psia) Station 8, bleed point after first compressor stage 145 8.68 Station 9, radiator inlet 145 8.46 Station 10, radiator outlet 300 7.60 Station 11, exhaust nozzle entrance 300 7.38 Station 12, exhaust jet® *Velocity = 1610 fpa. TABLE 3. SALT TEMPERATURES AND PRESSURES AT VARIOUS STATIONS IN THE REFLECTOR-COOLING SYSTEM TEMPERATURE PRESSURE (°F) (psia) Stations L and M, radiator outlet 1000 137 Station N, radiator inlet 1200 165 Station P, reflector outlet 1200 170 Station Q, reflector inlet 1000 175 Station R, pump outlet 1000 180 15 DESIGN STUDY flows at various stations in the reflector-cooling system are given 1in Table 6 and Fig. 4. The thrust produced by the jet is 4530 1lb, and the specific impulse is about 46 1b of thrust per pound of air per second. Accessory System. Power must be provided to drive the liquid pumps in the power plant and to drive the electric generators that furnish electrical power for the airplane. This is accomplished by using a portion of the air coming out of the reflector- coolant radiator to operate a number of air turbines that drive the power plant pumps and the electric generators. By assuming a pump efficiency of 80% and a total generator capacity of about 425 kw, the required pumping power for the power plant at design flight conditions has been calculated to be about 1310 horsepower. (At sea level the required pumping power is much greater, and the pumps and air turbines must be designed to handle this greater load; also, a greater portion of the reflector- cooling system air flow must be di- verted to the accessory system. This has been provided for and is described in the chapter on “Sea-Level Per - formance,” ) The weight flow of air required for the air turbines has been calculated. For the calculation, it was assumed that the turbine exit pressure was equal to the ram pressure (7.24 psia) and that the turbine efficiency was 70%, The weight flow required 1is 12,48 lb/sec. Values of air tempera- tures and pressures at various stations in the accessory system are given in Table 7 and Fig. 4. The various jets produce a thrust of about 210 1lb, and the specific impulse is about 16.8 1b of thrust per pound of air per second. Over-All Power Plant Performance. The combined thrust of the shield- cooling, the reflector -cooling, and the accessory systems is about 5160 pounds. This thrust, added to the main engine thrust of 48,690 lb, gives a total power plant thrust of 53,850 l1b, the required value, The average specific impulse of the power plant is about 27.64, and the over-all cycle efficiency (with the power generated in the reflector and shield included in the power input) is about 29.63%. TABLE 6. AIR TEMPERATURES, PRESSURES, AND WEIGHT FLOWS AT VARIOUS STATIONS IN THE REFLECTOR-COOQLING SYSTEM TEMPERATURE PRESSURE WEIGHT FLOW (°F) (psia) (lb/sec) Station 13, bleed point after eighth compressor stage 430 29.0 110.7 Stations 14 and 21, radiator inlet 430 28.3 110.7 (total) Stations 15 and 22, radiator outlet 1000 25.4 110.7 (total) Stations 19 and 29, exhaust nozzle entrance 1000 24.7 98.22 (total) Stations 20 and 30, exhaust nozzle* 98,22 (total) *Velocity = 2930 {ips. 16 TABLE 7. NUCLEAR-POWERED AIRPLANE AIR TEMPERATURES AND PRESSURES AT VARIOUS STATIONS IN THE ACCESSORY SYSTEM TEMPERATURE (°F) PRESSURE (psie) Stations 15 and 22, reflector-cooling radiator outlet Stations 16, 23, and 26, turbine inlet Stations 17, 24, and 27, turbine outlet Stations 18, 25, and 28, exhaust jet* 1000 25.4 1000 24,7 117 7.24 *Veloeity = 1990 fps. Physical Arrangement of Power Plant, One possible layout of the required power plant equipment is shown in Fig. 7. The six turbojet engines are arranged circumferentially around the cowl and as far outward as they would go. (There is space left in the bottom of the cowl where there is no engine, because it was originally thought that the main wing spar might come through at that location. It is apparent from Fig. 7 that for this particular airplane configuration the spar will not be at that location, and therefore the engines could actually be spaced differently.) The main engine fuel -to-air radiators occupy the space normally occupied by the com- bustors of the turbojet engines. The shield-coolant radiator is located Just behind the reactor in the central hole between the engines. The re- flector -coolant radiator is divided into seven parts. One part, located in the central hole, is of sufficient size that the air handled by it is adequate to operate the air turbines that drive the shield -water pumps and the electric generators., These turbines, pumps, and generators are also located in the central hole. The remainder of the reflector -coolant radiator is divided into six equal parts that are located in the triangular spaces between the engines, outboard of the engine center -line circle. A portion of the air flow from each of these reflector -radiator sections is used to operate six air turbines that drive six fuel pumps and six reflector - coolant pumps. The air turbines are located in the triangular spaces between the engines, outboard of the engine center -line circle, The fuel and reflector -coolant pumps are located in the central hole, the power being transmitted by gears and shafting from the air turbines. Space has been left in this section of the fuselage for the installation of the rear landing gear, which is shown dotted. Power Plant Weight. The turbojet engine weight was calculated by each of three methods: (1) the empirical method described in the TAB report, ¢’ (2) the method of Rand Corporation,¢*? and (3) by using the specific weight data (pounds of engine weight per pound of sea-level air flow), published by the manufacturer, for an advanced turbojet model. Since the engine is a proprietary model, its identity will not be divulged. The last method yielded the highest estimated weight and was employed in (3)Repart of the Technical Advisory Board, ANP-52 (Aug. 4, 1950). *)R. S. Schairer, R. B. Murrow, amd C. V. Sturdevant III, Bomber Capabilities - Turboprop and Turbojet Power Plants, R-143 (Aug. 1, 1949). 17 81 i DWG.17668 REFLECTOR COOLING RADIATOR (7 PARTS) / /‘MAIN ENGINE TURBINE (6} FUEL PUMP (AND PIPE) (&) MAIN ENGINE COMPARTMENT 6y - B A — — ——_ | ™ FUEL AND REFLECTOR COOLANT 7 SHIELD WATER RADIATOR (1) ~— =" PUMP AIR TURBINE (AND DRIVE SHAFT) (6) \{ —REFLECTOR COOLANT , H PUMP (6) /‘Q\.fifi ‘ > ________ : - @}g 2\ . , X 5 I COOLING RADIATOR T Tz &7 \. . { 7 PARTS) \ i REACTOR SHIELD ASSEMBLY {{) e ;g e _ - \4‘© SECTION A-B MAIN TURBOJET ENGINE (6) ELECTRIC GENERATOR AIR TURBINE (2) ELECTRIC GENERATOR (2) ____\ _ 444 1 E - S NN : 1 *__WATER PUMP AiR TURBINE (2) WATER PUMP (2} ‘ REFLECTOR MAIN ENGINE COMPARTMENT (6 SHIELD WATER RADIATOR {1} REACTOR SHI ASSEMBLY (1) MAIN ENGINE TURBINE (6} FUEL-TO-AIR RADIATORS (6) 1ELD WATER RADIATOR (1) REAR LANDING GEAR /C 1 (APPROXIMATE POSITION) . / I SECTION A-A SECTION C-C NOTE: NO. iIN PARENTHESES INDICATES NUMBER OF SIMILAR ITEMS IN POWER PLANT, Fig. 7. Power Plant Arrangement. AANLS NOISHId the weight summaries (a specific weight of 15.8 1b per pound of sea-level air flow or 33.2 1b per lb/sec design- point air flow). It was assumed that the weight increase associated with the longer shaft, which was needed because of the heat exchangers, was compensated for by omission of the combustion chambers. The air flow of the six engines of the aircraft con- sists of three parts: 1751 lb/sec passes through the entire engine; approximately 111 lb/sec is bled at the eighth compressor stage; approxi- mately 86 1lb/sec is bled at the first compressor stage. The engine weight was calculated by assuming 33.2 1b of engine per lb/sec of air flow as the flow that passes through the entire engine; 40% of this value was assumed for the air flow bled after the eighth compressor stage; and 10% was assumed for the air flow bled after the first compressor stage. The weight of the engines, less radiators, therefore is 59,900 pounds. The weights of the main engine radiators and the reflector- and shield-coolant radiators are presented and discussed in the section on ““Power Plant Radiators.” The total weight of the main radiators, including baffles, structure, headers, circu- lating fluid, etc., is 23,900 pounds. The weight of the auxiliary radi- ators, pumps, air turbines, electric generators, and liquid piping, in- cluding circulating liquid for all the radiators, is estimated at 5000 pounds. The weight of the inlet and exhaust air ducting was calculated by a method similar to that used in the TAB re- port®) and found to be 10,300 pounds. Therefore the weight of the entire power plant is 99,000 pounds, POWER PLANT RADIATORS All the nuclear powered aircraft studied to date require heat transfer equipment with surface-to-volume and surface -to-weight ratios beyond those required innormal industrial practice, NUCLEAR-POWERED AIRPLANE To achieve the ratios required, close surface -to -surface spacing and thin- walled surfaces must be used. These design criteria, coupled with the high operating temperatures and the strong incentives to minimize pressure loss, create heat exchanger design problems without precedent. Various heat exchanger lattices have been explored, and, as might be expected, an improve- ment in performance or compactness would increase fabricational diffi - culties and probably decrease dura- bility., Determination of the best compromise between these conflicting considerations will require a con- siderable amount of fabricational development and functional testing by a competent heat exchanger manu - facturer, The radiators described here are believed to be in the proper surface area, size, and weight range, but it is not intended to imply that any radiators ultimately developed for this application will resemble in detail those illustrated (Figs. 8, 9, 10). Physical Description. Figure 8 shows a representative fuel -to -air radiator; Figs. 9 and 10 show the reflector - and shield -coolant radi - tors. The three different types of radiators in the power plant are of the same general design, that is, the tube and fin type with the liquid passing through the tubes and the air across the tubes. Each tube is bent into a serpentine coil and aligned so that the air flows across the tube along the axis of the tube coil. This arrangement permits the combination of a counterflow log mean temperature differential and a crossflow heat transfer coefficient., The various serpentine coils are arranged in the over -all lattice so that the individual tubes form a conventional, triangular pattern. The over -all radiator dimensions resulting from this design are generally of the order of several inches thick, 2 to 18 in. high and 50 to 350 f¢ 19 0¢ _—— DWG, 1 7669 by SECONDARY DISCHARGE HEADER DISCHARGE HEADER SUPPLY HEADER SECONDARY SUPPLY HEADER INSIDE SHELL DEVELOPED SECTION A-A DISCHARGE HEADER TYPICAL ENGINE GENERAL ARRANGEMENT SRR SUPPLY HEADER wR N { 0 1FT ¢ SECONDARY DISCHARGE HEADER € SECONDARY SUPPLY HEADER e . == - = s 50.20 x 3.24 x 0.010-in. T4 _‘. § c e _ PLATES; SPACED ON 9= o TUBING, 0.08-in. 0D, 0.042 CENTERS. o © 0.01-in. THICK WALL. 0.4732 in. 500 TUBES PER RADIATOR SECTION B-B = 7 315 in. TYPICAL RADIATOR UNIT PLAN (fimfi INCH Fig. 8. Fuel-to-Air Engine Radiator. Ad0LS NI9ISAd RADIATOR FOR: REQ'D | DiM. “A" [ DIM. "B’ WATER PUMP AND GENERATOR 12 6% | 25k FUEL PUMP AND REFLECTOR COOLANT PUMP 2 8l | 17Y% TUBES 0125 0D » Q10 | HEADER ! 7 T3 -0010 THICK e FINS 0042 ON ¢ ~ 8 27, —————‘l Fig. 9. 1% long. Obviously, some method of dividing the radiator into sections and arranging these sections into a somewhat more compact space 1is needed. Accordingly, each fuel -to -air radiator has been divided into a number of sections of equal length and these sections grouped cylindrically like the teeth of a spur gear (Fig. 9). There are from one to three sections of radiator (stacked one above the other) to each “tooth of the gear,” and there are 12 teeth in all, The faces of the radiator sections are parallel to the normal path of the air flow, and therefore the air must be turned 90 deg to enter the radiator and then turned back 90 deg upon leaving the radiator. This 1s accom- plished by dividing the space between the “ gear teeth” into two parts with a reinforced sheet that connects the front of one “tooth” with the rear of the next., The space between two teeth therefore acts as the inlet air duct for one tooth and the outlet air duct for the other. To permit control of the turbine inlet temperature in relation to fixed reactor temperatures,. provision has been made for a control - lable by-pass in the reinforced sheet that will permit the engine air to by -pass the radiator, 1f desired. NULCEAR-POWERED AIRPLANE DWG 1!570 ALL DIMENSIONS ARE IN INCHES A — B FIN LENGTH 1% 0D x Vg WALL-TAPERED TO 3 0D Refl ector-Coolant Radiator. The fuel is brought to the radiator from the reactor in a 3 -in. pipe and distributed to the 12 teeth by a tapered ring header; short, constant- diameter lines perpendicular to the ring header lead to the radiator sections, and long, tapered tubes parallel to the “gear teeth” feed the individual serpentine coils. The outlet headers are similar to the inlet headers described above. The precise division and arrangement of the auxiliary radiatorsis different from that of the fuel -to-air radiators, but the principle is similar. Al]l radiators were designed with the tubes having both large, common, sheet fins (Figs. 8 and 9) and indi - vidual round fins (Fig. 10). Either of these alternate methods of con- struction would result in approximately the same radiator performance. The former is probably preferable from a fabricational viewpoint. Radiator Design Relationships. The following relationships for heat transfer and pressure drop were used in designing the radiators. Air-Side Heat Transfer. lation was made froma curve by Kern($) that was based on the data of Jameson, A corre- (S)D. Q. Kern, Process Heat Transfer, McGraw- Hill, New York, 1950, 21 ¢e TYPICAL OUTLET OR (NLET NOTE: CUT-AWAY SHOWN /s WITHOUT FINS. = =3, NOTE: FINS 0010 THICK AT 0.042 o= e ON §:534 FINS PER UNIT : FINS 3291 WIDE x 23,625 END VIEW — LOOKING AFT NOTE: 14 RADIATOR UNITS TYPICAL TUBE PATTERN ALTERNATE CONSTUCTION DWG.1767 63 HOLES THIS ROW 61 HOLES THIS ROW D - = = — _% % o:9?°°°°0°OOO°O°0°0°0°o°o°o°o°u°o°o°o°o°o"d°c°c°o°o°o°0° T‘ %= 0.375+ =% oF sYm, o s =l l=0375 TYPICAL HEADER DETAIL 3 —=— FORWARD AFT — - |-— 1109 INLET HEADER J’C_’f . 1 ! ' AR OV Y 0324R| -1 --—% OUTLET HEADER . L 2 - I — ::.:__‘;-_ _q’- BANK r 1 - : OUTLET HEADER 8 Tl ®© AR ‘ \ st I ‘ RADIATOR 85'% 1D g __________ 4 EE [l e 34 DIA. DISK 0010 THICK A E— i OUTER SHELL o | B 22 AT 0.042 ON € - 534 DISKS. i - T Y ) MR OUT \ N N t 1 i{r — == £ BANK ik - (- - ]{fjr = 1 L = \N | ! I’ MR bil INLET HEADER INLET OUTLET HEADER % INLET HEADER 3-in. 1D FEEDER LINE FEEDER RING ! SECTION A-A SECTION A-A 1 INCHES INCHES o914 0D OF TYPICAL RADIATOR UNIT INNER SHELL 4 8 12 0O t 2 3 - 8 w7 o8 3‘291—-L ' or 0648 & INLET HEADER &8s £ COLLECTOR RIN ! =0.324 58 LE & ol w0187 I 0,324 Io =" A ; ° SEE TYPICAL HEADER DETAIL SECTION B-B —TYPICAL TUBE PATTERN NOTE: ALL DIMENSIONS IN INCHES Fig. 10. sShield-Water Radiator. NOTE: SEE ALTERNATE CONSTRUCTION. AdNLS N9IS3a Foster-Wheeler, and Tate and Cartinhour: Nu = 0.092 Beo- 723 Pr0.33 , 2 surface of fin and tube DH= 7 projected perimeter of fin and tube ’ where Nu = Nusselt number, Re = Reynolds number, Pr = Prandtl number, and D, is used for the diameter term. Air-Side Pressure Drop. The data of Gunter and Shaw'®’ were used. Fin Efficiency. The curves of Gardner(’’ for circular fins of uniform thickness were used. Liquid-Side Heat Transfer. The calculation was made by using the following relationship: Nu = 0,023 Re® ® Pr’-* ., Liquid-Side Pressure Drop. The calculation was made by using the following equations: L v? a“) = 4F{f T » D 2g _ 0.046 Beo. 2 where AP = pressure drop, liquid density, 1b/ft?, friction factor, = equivalent length-to-diameter ratio, liquid velocity, fps, gravitational constant, ft/secz. An allowance of 75 equivalent diameters was taken for the pressure drop in an 180-deg bend. The following liquid properties were used both for the fuel and for the reflector-cooling salt. 32,2 112 1b/ft3 0.39 Btu/1b.°F 0.5 Btu/hr- ft2 (°F/ft) Density Specific heat Thermal conductivity Viscosity 2 centipoises Fuel-to-Air Radiator. A number of fuel -to -air radiators were designed and (6)A. Y. Gunter and W. A. Shaw, Trans. ASKE 67, 643 (1945). (7)K. A. Gardner, Trans. ASME 67, 621 (1945). NUCLEAR-POWERED AIRPLANE a complete tabulation of the geometry and performance of these radiators is contained in Table 8., All values listed in the table and mentioned below are for the radiator for one of the six engines. The radiator design actually used in the power plant is presented in column 1. It is designed to transfer 53,500 Btu/sec; the fuel enters at 1500°F and leaves at 1000°F; the air enters at 544°F and leaves at 1250°F; the air flow 1s 292 1b/sec and the fuel flow is 275 lb/sec; the inlet air pressure 1is 42.4 psia. The radiator geometryis as follows: The tubes are 0.06 in. ID with 0.020 in. walls., The fins are 0.25 in. in diameter, 0.010 in. thick, and spaced 24 to the inch. The tubes are arranged ina triangular pattern with a 0.25-in, center-to-center spacing. The tube material is Inconel, and the fins are type 430 stainless steel., The radiator face area is 67.2 ft?; the radiator height is 4 in, and there are 18 banks longitudinal to the flow. The radiator was designed to have an air-side pressure drop of 10% of the inlet pressure and a liquid-side pressure drop of under 75 psi. The liquid-side pressure drop for the radiator of column 1 is 23 psi. The fuel volume contained in the radiator core is 1,15 ft?, A manifold system was designed for the radiator of column 1 (but not for any of the other radiators) that contained 1.4 ft3 of fuel and caused a pressure drop of 57 psi., The radiator, 1in- cluding core, structure, headers, baffles, contained fuel, etc. weighed about 4000 pounds. Columns 2 to 15 of Table 8 indicate the effect of variations in geometry and performance of the fuel-to-air radiators. Columns 2 to 11 1llustrate changes in geometry. Columns 2 and 3 show the effect of varying the number of banks while holding the air-side pressure drop constant, Column 4 is similar to column 1, except that the 23 ¥e TABLE 8. FUEL-TO-AIR RADIATORS 1 2 3 4 H 6 7 8 9 10 11 12 13 14 15 Heat transfer, Btu/sec 53,500 53,500 53,500 53,500 53,500 53,500 53,500 53,500 53,500 53,500 53,500 57,900 49,300 56,100 55,600 Air flow,1b/sec 292 292 292 292 292 292 292 292 292 292 292 273 253 305 292 Fuel flow, lb/sec 275 275 275 215 275 275 275 275 275 275 275 297 269 288 283 Air inlet temperature, °F 544 544 544 544 544 544 544 544 544 544 544 430 544 544 544 Air outlet temperature, °F 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1350 1250 1275 Fuel inlet temperature, °F 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 Fuel outlet temperature, °F 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 Air inlet pressure, psia 42.4 42.4 42.4 42,4 42.4 42.4 42.4 42,4 42.4 42.4 42.4 28,3 42.4 42,4 42.4 Tube ID, in. 0.060 0.060 0,060 0,060 0,060 0.080 0.10 0.10 0.10 0.10 0,10 0.060 0.060 0,060 0,060 Tube wall thickneas, in. 0.020 0,020 0,020 0.010 0.0125 0,0125 0.0125 0.012§ 0,0125 0,0125 0,0125 0.010 0.010 0.0125 0.0125 Fin diameter, in. 0.25 0.25 0.2§ 0.20 0.17 0.21 0.2§ 0.286 0,3125 0.25 0,25 0.20 0.20 0,17 0,17 No, of fins per in. 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 Fin cthickness, in, 0.010 0.010 0.010 0.010 0.010 0,010 0.010 0,010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 Tube spacing, in. 0,25 0,025 0.025 0.20 0,17 0,21 0,25 0.286 0,3125 0.286 0.219 0,20 0,20 0.17 0.17 Tube material Inconel Inconel Inconel Inconel Inconel Inconel [nconel Inconel Inconel Inconel Inconel Inconel Inconel Inconel Inconel Fin material 430 S8 430 S5 430 58 Inconel Inconel Inconel Inconel Inconel Inconel Inconel Inconel Inconel Inconel Inconel Inconel No. of banks {(longitudinal to flow) 18 20 16 18 18 16 16 16, 18 18 20 10 16 26 20 20 Frontal area, ft? 67.2 71.6 63.2 57.2 [ 65.6 T0.5 36.6, 67.6 62.0 58.6 85.6 69.4 59.2 57.1 57.1 Radiator height, in. 4.0 2,52 1.6 6.0 7.2 5.0 9.0 13.8, 6.85 9.75 6.6 18 6,0 3.0 9.0 10.2 Air inlet velocity, fps 83.0 78.2 88.5 97.1 99 102 96 96, 89 91 97 102 92.7 80.7 111.6 117.6 Liquid velocity, fps 6.6 3.7 15.2 9.3 7.7 15.6 4.7 12.5, 5.0 T.6 6.8 7.3 7.0 4.9 7.4 8.4 Air-side heat transfer coefficient, Btu/sec* ft2-°F 0,0288 0,.0276 0.0303 0,0346 0.0355 0.0340 0.0311 0.0307, 0.0293 0,0290 0.0318 0.0330 0,0270 0,0307 0.0402 0, 0402 Fuel+side heat tranafer coef. ficient, Bru/sec: ft2:°F 0,60 0.38 1.12 0.82 0.47 0,99 0.40 0,78, 0.40 0.62 0,47 0.58 0.67 0,47 0.46 0.52 Air-aide pressure drop, psi 4.24 4.24 4.24 4,24 4.24 4.24 4.24 4.24, 4.24 4.24 4.24 4,24 2.83 4.24 6.36 6.36 Fuel-side pressure drop, psi Core 23 7.6 147 44 49 29 12,5 68, 12.3 35.5 16.8 17.4 34.3 18,6 42 70 Headers 57 Fuel volume, ft? Core 1.1§ 1.34 0.954 1.222 1.68 2.08 3.0 2.19, 2.75 2,15 2,712 2.54 1.32 1.82 1.59 1,59 Headers 1.4 Radiator weighe, 1b 3980 4540 3520 3040 3110 3160 3550 3570, 4110 3940 3340 3070 3220 3840 3020 3020 AdALS NOISId tube wall thickness has been changed to 0,010 in,, the fins to 0.020 in., and the fin material to Inconel. Columns 5, 6, and 7 indicate the effect of varying tube inner diameter. The tube wall thickness in columns 53, 6, and 7 is 0.0125 in., and the ratio of fin diameter to the tube outer diameter has been held constant at 2, Columns 8 and 9 are similar to column 7, except that the ratio of fin diameter to tube outer diameter has been varied. Columns 10 and 11 are also similar to column 7, except that while the fin diameter has been held constant, the tube spacing has been changed. (This is possible only if the tubes are individually finned. The large sheet fin type of construction will not permit this variation.) In the radiator described in column 11, the fins are actually interlocking. Columns 12 to 15 indicate the effect of variations in radiator performance. Since variations in radiator per- formance will cause changes 1in power plant performance, these radiators were all designed so that the thrust of the power plant remained constant. Column 12 is similar to column 4, except that is is designed for air inlet conditions that correspond to a compressor pressure ratio of 4 instead of a compressor pressure ratio of 6, as 1s found in the actual power plant, Column 13 is similar to column 4, except that the air outlet temperature has been raised from 1250 to 1350°F. Columns 14 and 15 are similar to column 5, except that the air-side pressure drop has been increased from 10 to 15% of the air inlet pressure. In column 14, the air outlet temperature was maintained at 1250°F, but in column 15 it was raised to 1275°F, This temperature was selected so that the thrust per pound of air handled by the power plant is the same in columns 5 and 15, Auxiliary Radiators. The designs of the reflector - and shield -coolant radiators are quite similar to that of NULCEAR-POWERED AIRPLANE the fuel -to-air radiators, A de- cription of their geometry and per- formance is given in Table 9. AIRPLANE In accordance with the general premises of the ‘“Introduction,” an airplane 1s presented that preliminary studies indicate will meet the re- quirements for flight at Mach 1.5 at 45,000 ft with the designed power plant. No attempt has been made to present a final design; the aim 1is, rather, to present a reasonably plausible design that may serve as a starting point for more detailed study. The general configuration of the airplane, an aerodynamic calcu- lation of the airplane lift-to-drag ratio, a brief consideration of the sea-level performance of the airplane, and an estimate of the weights of the various components of the aircraft structure are presented. Airplane Configuration. Figure 11 shows the general configuration of the airplane, and Fig. 12, a longitudinal section, shows the location of the crew, reactor, and power plant. The reasoning governing the location of the various items in Figs. 11 and 12 is presented in the following. The center of lift and center of gravity of the aircraft, which, of course, coincide, were taken as the reference point. The wing and tail were placed suitably, forward and aft of the center of lift, so that the resultant of the lift of the wing and horizontal tail surface occurred at the center of lift, and the center of lift of the horizontal tail was 85 ft from the airplane center of lift. (It may be noted in Fig. 11 that a triangular planform is used for the wing and horizontal tail surface. It 1s normal practice 1n current tri- angular-wing aircraft to have no horizontal tail surface but, rather, to use elevons in the wings to provide control in the pitch direction. The moment of inertia of this aircraft, 25 DESIGN STUDY TABLE 9. REFLECTOR- AND SHIELD-COOLANT RADIATORS REFLECTOR-COOLANT SHIELD-COOLANT RADIATOR RADIATOR Heat transfer, Btu/sec 16,050 3210 Air flow, lb/sec 113 82.6 Liquid flow, lb/sec 201 59.4 Air inlet temperature, °F 430 145 Air outlet temperature, °F 1000 300 Liquid inlet temperature, °F 1200 350 Liquid outlet temperature, °F 1000 300 Air inlet pressure, psia 29 8.44 Liquid inlet pressure, psia 200 Tube ID, in. 0.10 0.10 Tube wall, in. 0.0125 0.0125 Fin diameter, in, 0.25 0.375 No. of fins per 1in. 24 24 Fin thickness, in. 0,010 0.010 Tube material Inconel Aluminum Fin material Inconel Aluminum No. of banks longitudinal to flow 10 10 Frontal area, ft? 30.2 49,4 Radiator height, in. 7.2 23.1 Liquid-side pressure drop, psi 28 33 Air-side pressure drop, psi 2.9 0.844 Radiator weight (including baffles, headers, structure, contained liquid, etc.), 1b 1400 800 however, 1s going to be quite large In order to avoid changes in the because of the heavy crew shield in the noseof the airplane, and therefore a horizontal tail was added to secure a longer lever arm for the control forces in the pitch direction. Whether this 1s actually necessary is not known; the problem of control in the pitch direction is considered further in a subsequent paragraph.) The size, shape, and proportions of the wing and tail surfaces were determined from aerodynamic considerations and are discussed i1n the following subsection. 26 balance of the airplane when the bomb load 1s dropped, this load was located at the center of lift. The reactor and power plant were grouped suf- ficiently aft of the center of lift to balance the moment caused by the crew shieldin the nose of the aircraft and the resultant moment caused by the weights of the various components of the airplane structure., The engines were placed behind the reactor to afford some shadow shielding of the fore portion of the aircraft; and, LG 100 200 400 600 SCALE IN INCHES 800 1000 Fig. 11. Airplane Configuration. T DWG. 17672 ANVIdUIV dIdIn0d-HVATONN DESIGN STUDY OWG. 17!73 Fig. 12. furthermore, they were placed as close as possible to the reactor to minimize the fuel volume in the ducts to and from the main engine radiators. The cowl, the central portion of the fuselage, was made large enough in diameter to permit the passage of the engine air flow around the reactor shield; and it was extended rearward to the engine exhaust nozzles and forward far enough to permit the air intake to be ahead of the wing. The engines were placed as far out in the cowl as they would go. The crew and crew shield were placed in the nose ogive, forward of the cowl, which gave a separation distanceof 120 ft between the reactor and the crew compartment (center to center). The diameters and proportions of the nose ogive and tail boom were chosen to meet the spatial and structural requirements and to give low aerodynamic drag. (The nose ogive 1s located on the center line of the airplane; there 1s therefore considerable air inlet area above the ogive. Recent NACA aerodynamic studies indicate that at high angles of attack this portion of the air intake may be ““smothered” by a very thick boundary layer. This difficulty could be alleviated by raising the nose ogive with respect to the air inlet until the upper surface of the ogive was actually an extension of the cowl.) The diameter of the nose ogive and the inlet air-flow area requirements are such that they permit the cowl to be tapered in the manner shown in Fig. 11, 28 Longitudinal Section of Airplane, Airplane Lift-to-Drag Ratio: The various aerodynamic formulas in this section were taken from the following references: 1. Eugene S. Love, Investigations at Supersonic Speeds of 22 Triangular Wings Representing Two Airfoul Sections for each of Eleven Apex Angles, RM L9DO7, May 10, 1949, 2. Generalized Lift and Drag Charac- teristics at Subsonic, Transonic, and Supersonic Speeds, Consolidated Vultee Aircraft Corporation, Fort Worth, Texas, FZ AO4la, November 27, 1950, 3. NACA Conference on Aircraft Propulsion Systems Research, Lewis Flight Propulsion Laboratory, Cleveland, Ohio, January 18 and 19, 1950. 4. Notes and Tables for use in the Analysis of Supersonic Flow, NACA Technical Note 1428, December 1947 . The airplane wing is of triangular planform with a 60-deg sweep and a 3% thickness-to-chord ratio. The wing profile 1s that of a circular-arc airfoil with an elliptic leading edge. The nose ogive, tail boom, and cowl are parabolic bodies of revolution, and the nose ogive and tail boom are pointed at the ends. The following lift and drag formulas were used for the calculation of the airplane lift-to-drag ratio. enT e LSS A Wing Wave drag: CD_ = mB tan € - 0.65, (TR)? where C, = wave drag coefficient based on v exposed planform area, TR = thickness ratio = ratio of maximum thickness to chord, m= 4.9 at Mach 1.5, B =M} -1 M = flight Mach number, € = 90 deg minus the sweep angle. Induced drag: Aspect Ratio CD_/Ci 4 0.341 3 0.342 2.31 (e = 30°) 0.352 where ’ C, = induced drag coefficient based ' on exposed planform area, C, = lift coefficient based on exposed planform area. Friction drag: 0.0306 C, = , YV - 1 5/7 Re'/7 | 1 + M 4 0 where C, = friction drag coefficient f based on total wetted surface, = ratio of specific heats of air, Reynold’s number, Vicpo/pu , forward velocity, f{ps, average wing chord, ft, ambient density, 1b/ft?, = ambient viscosity, lb/sec*ft. ptimum lift coefficient: where G, = opt lift coefficient at maximum lift-to-drag ratio (based on exposed planform area), NUCLEAR-POWERED AIRPLANE AW CDo = CD' + CDf X o A= exposed planform area airplane gross weight , Gy * P Vg opt Aw = total wetted surface ™~ 24. Total wing lift: L = ( Ag , ept where L_ = total wing life, q = %pV:. Total wing drag: D v = |:CD° + CD] Aq ’ ¢ where D total wing drag. Tail The horizontal tail is geometrically similar to the wing and has an area equal to 20% of the wing area. The vertical tail has a 45-deg sweep angle, a 3% thickness ratio, and an area equal to 15% of the combined wing and horizontal tail area. The lift and drag of the tail surfaces were calculated by using the same formulas as those used for the wing. Nose Ogive and Tail Boom Wave drag: ! 10.7 D ? v (FB)2 where C; = wave drag coefficient based on maximum frontal area, fineness ratio (ratio of length to maximum diameter). Friction drag: 0.0306 C; = 1.05 X% f 7_1 /17 Re!/ 7|1+ M2 4 0 where C, = friction drag coefficient based f on total wetted surface, Re = Reynold’'s number, V,Lp/pu, L length, ft. 29 DESIGN STUDY Total nose ogive and tail boom drag: ratio of outlet station of Cowl area ratio = area to area at maximum diameter, D' = [C;' A"+ Cfif A:] q. L = length of the aft-portion of the “cowl. wh?re _ Friction drag: The friction drag D" = total‘drag of the nose ogive coefficient for the cowl may be ' and.tall boom, calculated from the formula used for A" = maximum frontal area, obtaining the fuselage friction drag A, = total wetted surface. coefficient if L is defined as the Cowl length of the cowl. Wave drag of fore-portion: A table Total cowl drag: of wave drag coefficients for the D" = {-[CB J + [CB ] }, A"q * Cp Alq v fore-portion *laft-portion f portion of the cowl forward of the jere station of maximum diameter follows: D" = total drag of cowl, COWL AREA RATIO L/D C; VM, A" = maximum cowl frontal area, . A’ = total cowl wetted surface. 0.4 10 0.0040 It is assumed that there 1s no 8 0.0065 increase in drag due to the inter- 6 0.010 ference of wing, fuselage, cowl, and 4 0.0185 tail; therefore 0.6 10 0.0020 L L, * Ly, 8 0.0025 D . D + D + D Dt + Dn 6 0.0040 airplane ht vt 4 0.0080 ‘"E%e L liteted ) = -to- 0.8 10 0.0010 airplane ::zgoane ' o-drag 8 0.0015 L,, = lift of the horizontal 6 0.0025 ¢ tail 4 0.0040 D,, = drag of the horizontal 1.0 All 0 tail, where D , = drag of the vertical C, = wave drag based on maximum tail. v frontal area, Cowl! area ratio = ratio of inlet area to area at station of maximum diameter, L = length of fore-portion of the cowl, D= maximum diameter of cowl section, Wave drag of aft-portion: The wave drag coefficient of the portion of the cowl aft of the station of maximum diameter may be taken from the same table as the fore-portion by using the following definitions: 30 Calculations made by using the above formulas for the airplane of Fig. 12 give: Wing Cp, = 0.00227 2 . CDi/C2 = 0,352 Cp = 0,00182 f CDo = 0.00591 Cy = 0.1298 opt CDs = 0.00591 A = 4620 L = 291,100 D = 26,540 Horizontal tail Cp = 0.00227 Cy /CF = 0.352 Cp = 0.00190 NUCLEAR-POWERED AIRPLANE Cowl The cowl 1s evaluated as 1f the nose ogive and tail boom were not present, since their drag has already been accounted for. The inside surface of the cowl 1s actually engine ducting and engines and its drag has already been accounted for by the efficiency of the various engine components. [CB ] = 0,0100 (approx.) YIfore f cDo = 0.00608 [cg ] = 0,0100 (approx.) Yiaft C; = 0,1315 opt CB = 0,00180 = f CD‘ - O. 00608 AII = 269 Ay, = 924 A’ = 6330 (approx.) L,, = 58,900 D" = 8150 _ The airplane lift-to-drag ratio is Dy, = 5480 therefore L 2 Lift _ 291,100 + 58,900 . 350,000 7,03 D/iiiotiame = Drag 26,540 + 5,480 + 3,350 + 6,280 + 8,150 49,000 T Vertical tail CD = 0,00435 CDf = 0,00198 CDo = 0.00831 A = 832 = 3350 vt Nose Ogive and Tail Boom The nose ogive and tail boom com- bined are assumed to be similar to a parabolic body of revolution of about 95 ft in length and about 10 ft in maximum diameter, CB' = 0.1185 Céf = 0,00181 A' = 78,5 A; = approx. 2000 D' = 6280 For the sake of conservation and be- cause of the uncertainties present in the lift-to-drag ratio calculation, a value of 6.5 was used for the lift- to-drag ratio; this leaves a con- tingency of 0.53 in the ratio. A calculation was made for a rectangular wing of 3% thickness, 25% and an aspect ratio of 3, and the lift-to-drag ratio was about 10.55, as compared with about 10.98 for the delta wing. Airplane Pitch Control. The problem of controlling the aircraft in the pitch direction may become acute be- cause of the heavy weight of the crew shield far forward in the airplane,. For this reason it was decided to have a horizontal tail surface with an 85 -ft lever arm to provide this control rather than elevons in the wings as in the normal practice. A calculation showed the mass moment of inertia of the airplane in the pitch direction to taper ratio, 31 DESIGN STUDY be about 3.8 x 107 slug ft?2., If the entire horizontal tail surface was movable, as it is 1n some recent air- craft, it would be possible to exert a torque of 3.70 x 107 ft.1b (assuming a maximum lift coefficient of 1.1 for the surface). This would provide an angular acceleration of 55.0 deg/sec? to the aircraft, which would probably be more than ample. The angular acceleration in the pitch direction required of a large airplane of this type is not known at this time. If this requirement were established, some other arrangement of control surfaces might prove more desirable, Airframe Weights. The following formulas for the weights of the various components of the airplane structure are taken from the TAB report(3) and from various Rand reports, primarily R-143, (%) Wing Weight. The wing weight was calculated in the same manner as in the TAB report. KfizSa .KEA +'(772)‘4 [W f&(AJ _lfli fa()\;k)] W, = 1.15 ’ 1+ K,n S8 £.00 (TR) A "2 where w_ = weight of wing, W = lifting force provided by wing = 291,100 1b, K, = a constant = 4.0 1b/ft?, K, = a constant = 12,5 X 10-% fe!, A = wing area = 4620 ft?, n = load factor = 4.0, TR = thickness ratio = 0,03, f, = 0.113¢%) fa = 0.064(%) fs = (8) W, = distributed weight in wings = 0, k = portion of span over which ¥, is distributed = 0, A = taper ratio = 0, S = structural span (length of span measured along the midpoints of the chords) = 136.5 ft. (S)Schairur, Murrow, and Sturdevant, op. cit.; fl' fp, and f3 plotted on p. 120. 32 By the above formula, is 46,000 pounds. Tail Weight. The weights of the horizontal and vertical tail surfaces were estimated by two methods. The method of the TAB report,(s) which assumes that the total tail weight 1is 20% of the wing weight, resulted in a total tail weight of 9200 pounds. The method of the Rand report,(*’ which gives relations for the weight of the horizontal and vertical tail surfaces similar to the wing relationship above, resulted in a total tail weight of 8100 pounds. The more conservative estimate of 9200 pounds was used. Fuselage Weight. The fuselage weight was estimated by the same method in the TAB report and in the Rand report, the wing weight 15.0 nL (W, + W, ) Wf = D L 4.0 + -1 108 D? Wf = weight of fuselage, fuselage maximum diameter, Lf length of fuselage, load factor = 4.0, ch= weight of fuselage contents. n o 3 " This equation gives a weight of 8200 1b for the nose ogive and tail boom and a weight of 21,700 1b for the cowl. The total fuselage weight 1is therefore 29,900 pounds. Landing Gear Weight. The weight of the landing gears was estimated by the method of Rand{*’ which assumes that the landing gear weight is 5.4% of the gross weight of the aircraft, This is slightly more conservative than the TAB method, ¢(3) which assumes the landing gear weight to be 5.0% of the airplane gross weight. The weight of the landing gear i1s therefore 18,900 pounds. Controls Weight. The weight of the airplane controls was estimated by the method of the TAB report,(3) which assumed the controls weight to be 0.6% of the airplane gross weight. For this airplane, the controls weight is therefore 2100 pounds. NUCLEAR-POWERED AIRPLANE Total Airframe Weight. The total weight of the airframe, including wing, tail, fuselage, landing gear, and aircraft controls is 106,100 pounds. SEA-LEVEL The optimization of engine and radiator per formance was based on design-point operation, but liquid- line sizes and pump capacities were based on the higher flow rates that would be required at sea level., 1In studying design-point performance, the engines and radiators were sized to permit the attainment of a stipulated thrust., In considering sea-level static performance therefore the design is constrained by the geometry selected to meet design-point (45,000 ft) conditions. These constraints still permit broad operational latitude, however, and additional operational constraints were established to permit solving for sea-level performance, as follows: Engine rpm: take-off engine speed was selected as equal to design-point engine speed. Engine air flow: take-off air flow was selected as equal to design- point air flow on a corrected air flow basis, that is, constant wN8/$, where w 1s the mass air flow, & varies as the compressor inlet temperature, and & is the compressor inlet pressure. Reactor inlet and outlet temperatures: take-off reactor inlet and outlet temperatures were selected as equal to those at design point. Since the mean reactor temperatures are there- fore substantially the same as at design point, there is no need for shimming. A higher reactor AT would entail exceeding the established metallurgical limits; a lower reactor AT would entail large increases in pumping power for a given power abstraction, PERFORMANCE With these specifications, aspecific solution for reactor power, fuel flow rate, turbine inlet temperature and engine thrust can be obtained. De- creasing the operational altitude in- creases the engine mass air flow, which in turn increases the radiator heat-removal capacity and therefore demands increased reactor power, Were the entire system tooperate at design- point temperatures, the power flow would increase directly with fluid flow rates, and it would be necessary for heat transfer coefficients to vary with flow rate to the first power. Actually, however, the heat transfer coefficients will vary as flow rate to some fractional power. Consequently an increase in driving temperature difference is required to permit the higher sea-level powers. This re- quirement for a higher temperature difference causes the system to stabilize at a lower turbine inlet temperature than was attained at design point (1125°F at sea level; 1250°F at design point). However, the greatly increased air flow permits a total thrust of 165,000 1b at sea level, compared with 53,850 1b at design point. This take-off thrust appears to be adequate, since it permits a calculated take-off ground roll of approximately 2500 feet. A reactor power of 640,000 kw is required, This wil] increase the crew radiation dosage but has not been considered in connection with shield design because of the presumably short duration of operation at this power level. Sea-level performance 1is summarized in Table 10. 33 DESIGN STUDY TABLE 10. SEA-LEVEL STATIC PERFORMANCE PRESSURE (psia, TEMPERATURE (°F) WEIGHT FLOW approx.) (1b/sec) Fuel Circuit Radiator inlet 292 1500 3130 Radiator outlet 25 1000 3130 Pump outlet 525 1000 3130 Reactor inlet 475 1000 3130 Reactor outlet 342 1500 3130 Air Circuit Aircraft ambient 14.7 59 Compressor in 14.7 59 4137 Compressor out 87.7 461 3720 Radiator in 85.5 461 3720 Radiator out 78.0 1125 - 3720 Turbine in 76.1 1125 3720 Turbine out 24.1 728 3720 Jet 14.7 Jet vel. = 1360 ft/sec 3720 Air flow to shield coolant radiator, 182 lb/sec Air flow to reflector coolant radiator, 235 lb/sec Portion to air turbines, 88 lb/sec Portion directly to jet, 147 lb/sec Thrust from main circuit, 155,900 1b Thrust from portion of reflector coolant airflow that goes directly to jet assuming radiator outlet air temperature = 875°F, which comes from assuming (6, /6 e, /6 9700 1b Thrust from portion of reflector cooling circuit through air turbines and from shield cooling circuit assumed = 0 f Total thrust = 165,600 1b De:)-ain rad, Des)refl. cool. rad. = Maximum reactor tube wall temperatures DESIGN POINT SEA LEVEL Inside tube 1554 1583 Outside tube 1567 1608 Take-off ground roll to 110% of stall speed stall speed = 165 mph, assuming all lift from wing Cy = 1.1 ground roll = 2480 ft 34 SHIELDING The shield design for the aircraft requires an extension of the methods described in the report of the Shielding Board(!) to take account of the delayed neutrons and fission-product gamma rays from the exposed part of the circulating fuel. The first step in the shield design was to assign fractionsof the radiation tolerance to the several radiation sources. This was done on the basis of an approximate estimate of the weight penalty for shielding each component, After careful analysis, the dose distribution can presumably be revised, with some weight reduction, but the analysis will not be made at this time. Next, the crew shield was designed to provide protection from the delayed neutrons and gamma rays from the unshielded circulating fuel. Finally, the reactor shield was chosen so that in conjunction with the crew shield the primary radiations would be approximately attenuated. Structure scattering was calculated separately and treated as aperturbation on the design determined without it, The crew shield thicknesses were then slightly increased to take account of the structure scattering. ASSIGNMENT OF RADIATION CONTRIBUTIONS A total -gamma-dose to total -neutron- dose ratio of 3 was chosen, since neutron shielding is accomplished with less weight than gamma shielding. Another reason for adhering to this ratio is that much less is known about the relative biological effectiveness of neutrons, and by keeping this contribution to a small part of the total, the over-all uncertainty is correspondingly reduced, For both neutrons and gamma rays the contributions through the crew shield rear and sides were taken to be the same. The reasoning in this case was that although the area of (1) geport of the Shielding Board for the Aircraft Nuclear Propulsion Program, ANP-53 (Oct. 16, 1950). NUCLEAR-POWERED AIRPLANE ANALYSIS the rear is much less than that of the sides, the difference is almost offset because the radiation entering the rear is mostly unscattered and hence harder than that incident on the crew shield sides. For radiation entering the front of the crew shield, an appreciably smaller contribution is assigned, since not only is the radiation scattered, and hence comparatively soft but the area of the front shield slab is small. In distributing the contributions between reactor and exposed fuel in the radiators, account was taken of the relative hardness (energy of 1 photon) of the radiations. For both neutrons and gamma rays the radiator radiations are more easily shielded and hence these are assigned a smaller contribution. The results of these deliberations are given in Table 11, In the following sections the numbers Ia, etc. refer to the contributions as listed in Table 11. The biological toleranceis specified as the maximum at any location in the crew shield; the calculation of the radiation level at all points of the interior is beyond the scope of this report. As an estimate, the maximum is takento be the sum of contributions from front, all four sides, and rear. In Table 11, ‘““sides’ means total contribution from four sides. CONFIGURATION TO BE SHIELDED The reactor is a sphere 3/5 ft in with a 6-in. beryllium oxide reflector. It releases heat at the rate of 325 megawatts. The reactor- to-crew separation distance is 120 ft, and the radiator-to-crew separation diameter, distance is 132 feet. The fuel 1s divided as follows: Radiators and headers 15.6 ft3 Pipes, etc. 10.4 ft? Reactor 8 fed Total 34 £t} 35 DESIGN STUDY TABLE 11. ALLOWED CONTRIBUTIONS TO THE TOTAL DOSE DOSE 2 COMPONENT FLUX (neutrons/cm“*-sec) rem/hr rep/hr I. Neutrons a. Radiators to rear 0.02 0.002 29,4 b. Radiators to sides 0.02 0.002 1/4 X 29,4 per side c. BRadiators to front 0.005 0.0005 7.25 d. BReactor to rear 0.10 0,010 e. Beactor to sides 0.10 0.010 f. RBReactor to front 0.005 0.0005 Total 0.25 0,025 IT. Gamma Rays a. Radiators to rear 0.250 0.250 5 X 10* (hard photons) b. BRadiators to sides 0.300 0.300 See reference 1 ¢c. Radiators to front 0.025 0.025 1,38 x 10* Mev/cm?.sec d. Reactor to rear 0.100 0,100 e. Reactor to sides 0.05 0.05 f. Reactor to front 0.025 0.025 Total 0.75 0.75 The total circulation time for fuel 1s 2.45 sec, of which 0,54 1s spent in the core, 0.25 sec in headers inside the shield, 0.05 sec in reaching the shield exterior, and 1.61 sec in the radiators and external and return pipes. the sec the BASIC DATA FOR SHIELD DESIGN Gamma ray equivalents: 1r 2 X 10° Mev/cm?, 1r/hr 5.5 X 10° Mev/cm?*sec, = 2 X 10% hard photons/cm?*sec. Neutron equivalents: 1 rep/hr = 10 rem/hr (biological dose), 1 rem/hr = 6930 fast neutrons/cmz'sec, 1l rem/hr = 14,700 delayed neu- trons/cm?* sec (from Snyder’ s BBE curves(?2)), Delayed neutrons per neutron formed in fission, 7.3 % 1073, Neutrons per fission, 2.5, Fissions per watt'sec, 3 x 10!°, (20w, S. Snyder and J. L. Powell, 4 Joint Project of the ORNL Health Physics Division and the ORNL Suamer Shielding Session, ORNL.421, 36 Mean free paths for neutrons in air ( from reactor): E = 3 Mev, A = 130 meters, E=0.5 Mev (delayed neutrons), A = 40 meters, Mean free paths for gammas in air (from reactor): E~2 to 3 Mev, A ~ 210 meters, E~0.5Mev, A\ ~ 90 meters. Beryllium oxide reflector: = 2.8 g/Cms. = 7.8 cm, 11.8 cm (for 3 Mev/photon), Density A vent My Attenuation of beryllium oxide for reactor neutrons = 1/6.8. Relaxation lengths: Prompt neutrons In water 10 cm In polyethelene 8.4 cm In lead 9 cm In iron 6 cm Delayed neutrons In water 2.7 cm In polyethelene 2.26 cm Gamma rays In water 23 cm In polyethelene 24.8 cm In lead 2.2 cm In 1ron 4 cm The values for polyethelene are based on its density of 0.93 for gamma rays and its hydrogen density of 8 X 10°%% cm~3, as compared with water. CALCULATION OF SHIELD DIMENSIONS Delayed Neutrons into Crew Com- partment Rear (Ia). The delayed- neutron source strength is obtained from the product of the power of the reactor, the fissions per sec per unit power, the total neutrons per fission, and the delayed fraction. S, = 3,25 % 108 x 3 x 10'° x 2,5 x7,3x 103 = 1.78 X 10!? neutrons/ sec. Of these, 15.6/34 are produced in the radiators, one half are intercepted by the reactor shield, and a further factor of 1/3 is introduced to take account of self-absorption in the radiators. Scattering calculations based on single collisions in the fuselage indicate that the number of delayed neutrons arriving on the crew shield rear will be increased by about 14% because of the scattering. The flux incident on the crew shield rear is thus [1.78 x 107 x (15.6/34) x 1/2 x 1/3 x 1.141/47(132 * 30.5)% = 7.6 X 107 neuntrons/cm?*sec. The allowed tolerance for this component is14,700 x%0.002 neutrons/cm?-sec=29.4 neutrons/cm?+sec. The lead in the rearwall acts primarily asa scatterer; so its attenuation is taken to be only 1/2. The water thickness for crew shield rear 1s thus t = 2.7 In[(7.6%107)/29.4] 39.8 cm of water 39.8 X (6.7/8) = 33.4 cm of plastic (polyethelene). dr 8.2 x 10!° NUCLEAR-POWERED AIRPLANE Delayed Neutrons to Crew Compartment Sides (Ib). The delayed-neutron source for scattering into the sides includes neutrons produced in the exterior piping, as well as one-third of those produced in the radiators. S,, = 1.78 x 10'7 x (15.6/3) X 34 +(10.4/34) = 8.2 x 10'° The simple isotropic scattering formula is used to obtain the flux incident on the crew shield side walls: S = 2 X 107 neutrons/cm?*sec, where d is the separation distance, 132 ft, and A is the mean free path in air, 40 meters. Scattering from the cowl into the sides increases the flux by about 14%, as determined from single- scattering calculation. The wing contributes onlya negligible fraction. The side wall thicknesses are, if only one-quarter of the dose is allowed to enter each wall, 2.7 1n [2 % 10% x (1.14/14,700) X 0.002 %X 0.25] = 46.5 cm of water = 39 cm of plastic . Delayed Neutrons into Front (Ic). The scattered neutron flux into the front face based on isotropic scattering would be (7/2) - 1 times that incident on the side. The flux on the front is thus [(m/2)- 1] x 2 x 10° = X 8 2, Thicknesseg'gie 10® neutrons/cm®-sec. tgg= 2.7 In [1.14 X (10%/14,700) x 0.0005] 44.5 cm of water = 37.3 cm of plastic. Gamma Rays from the Exposed Fuel. The time required for fuel to travel from the reactive region to the exterior is about 0.3 sec, and therefore periods shorter than 0.3 sec can be ignored. This is fortunate because no data exist for delay times less than about 0.25 sec. The available data, however, are not by any means 37 SRR A ot SRR R DESIGN STUDY adequate for the present purposes; so the numbers used represent con- servative estimates rather than well- measured values. The data include the work of Bernstein et al., (3:4) who measured the number of gammas of energy sufficient to photodisintegrate deuterium and beryllium from the fission products of U?3%, All numbers discussed will be in terms of photons per fission. Bernstein et al. obtained a value of 2.5 hard gammas per fission on the basis of deuterium disinte- gration, but the value is quite un- certain because 1.58 of this quantity is attributed to a gamma of 2.25 Mev, an energy which is so close to the threshold that it is subject to considerable cross-section uncertainty for even slight energy variation. A new determination made by Bell and Elliott,¢(5) which gives a threshold value of 2.237 Mev, further emphasizes the uncertainty. The energy de- termination for the fission-product gamma rays was not good enough to make Bernstein’s value meaningful . Accordingly, reliance must be placed on the data of Sugarman et al., (%) who report that in the in- terval 10 sec to 2 hr there are 0.8 photons of 2,2 Mev. By integration of their extrapolated curves, it is deduced that there is, at most, 3 Mev of gammas per fission in the period from 0 to 10 sec. For the present purposes, 1t will be assumed that there are 1.5 3-Mev photons per disintegration. Ergen,(’) by inde- pendent analysis, arrived at a value of 0.5 hard gammas per fission; so it appears that the value 1.5 is quite conservative. (3) (1947). (4)5. Bernstein et al., Yield of Photoneutrons from U235 Fission Products in Be, AECD-1833 (Feb. 20, 1948). S)R, E. Bell and L. G, Elliott, Phys. Rev. T4, 1552 (1948). G)N. Sugerman et al., Radiochemical Studies: The Fission Products, Book I, Paper 37, p. 371, NNES IV, 9, McGraw-Hill, New York, 1951, ¥, K. Ergen, private discussion. S. Bernstein et al., Phys. Rev. 71, 573 38 Gammas from Radiators into Rear of Crew Compartment (IXa). The total hard fission product calculation is made in nearly the same manner as was that for the delayed-neutron source. S = 3,25 X 108 x 3 x 101!'% x ].5 nr = 1.46 x 101°9 photons/sec . Of these, 15.6/34 are produced in the reactor, one half are intercepted by the reactor shield, and a factor of 1/2 is taken for self-absorption, As in the case of the neutrons, 14% is added for structure scattering. The gamma flux incident on the rear of the crew compartment shield is thus [1.46 > 10'® x (15.6/34) x 1/2 x 1/2 X 1.141/47(132 % 30.5)2 = 9.4 x 109 hard photons/cm2+sec . The rear crew shield plastic will attenuate by a factorof exp (33.4/24.8) or exp (1.35). The compressor, forward of the radiators, constitutes a shield equivalent to about 1 in. of Fe and gives an attenuation of exp (2.5/4) or exp (0.625). The lead thickness must therefore be tp, (rear) = 2.2 In [(9.4 x 10°)/(0.25 X 2 X 10%) - 1.35 ~ 0.625] = 22.4 cm of lead . Gammas from Radiators to Sides (IIb). For the radiator gammas scattered in air, the pipes are included in the source, and self-absorption is taken as 1/4. The source is then 1.46 x 10'% x (26/34) % 1/4 = 2.8 X 10'% photons/sec . In order to use the curvesin ANP.53,(8) 1t is necessary to convert this to the equivalent source for a 50-ft separation. This is 2.8 x 101 x (50/132) = 1.06 X 10'® photons/sec . Structure scattering is neglected here because of the slant penetration of the shield by the structure- scattered gammas. Slant penetration is probably more effective in the ®op. cit., aNP-53, p. 134, attenuation of gammas than neutrons because of the energy degradation accompanying turning of gammas in the shield. According to the reference,(?) 6.25 cm of lead are required to reduce the dose to 0.3 r/hr. Since some of the lead is replaced by plastic, the lead thickness 1is 6.25 - 39 x (2.2/24.8) 2.75 cm of lead. tohe u Radiator Gammas into Front (Ilc). For this calculation, gamma scattering is assumed isotropic, with a cross section equal to the average over- scattering angles from 7/2 to 7, that is, about 0.4 % 10°2% cm? per electron per steradian,(?) The electron density of air 1s approximately 0.602 x 10%* x 14.4 ¢ 22,412 = 3.87 x 102%° ¢cm-3 The effective mean free path is then 1 4m X 0.4 % 10-2% x 3,87 x 10?° = 5.1 X 10%* e¢m = 510 meters . The flux incident on the front face, obtained by using the previous source, 1s 7 2.8 x 108 C—-— l) = 2 A d 3.07 x 108, 5.1 % 10% cm , 132 X 30.5 cm . nwon It will be reasonable to assign to these gamma rays the energy for a scattering through an angle of 7, since for smaller angles of scattering the slant penetration of the shield will compensate for the higher energy. The energy is 0.24 Mev, for which the relaxation lengths of plastic and lead are 8.4 and 0.147 cm, respectively. (9)R. Latter and H. Kahn, Gamma-Ray Absorption Coefficients, R-170, p. 14 (Sept. 19, 1949), NUCLEAR-POWERED AIRPLANE The required number of relaxation lengths 1is (3.07X108xo.24 ln = 0.025%x5.5% 10% = 8.6 relaxation lengths . The lead thickness required, with some of the lead replaced by plastic, 1s In (5.36 x 10%) tppy = 8.6 X 0.147-37.3 % (0.147/8.4) = 0.62 cm of lead. SPECIFICATION OF REACTOR SHIELD THICKNESS In the following sections, a reactor shield is presented that in conjunction with the radiator-con- trolled crew shield will attenuate the reactor sources to the levels specified in Table 11, Reactor Neutromns into Crew Shield Rear (Id). For comparison with Bulk Shielding Facility (BSF) data, it is necessary to make some comparison of the relative leakages of the BSF reactor and the circulating-fuel reactor. When the mean free path is much less than the average chord length of the core, the leakage should be inversely proportional to the latter., A fair approximation for the average chord length is 4v s = 11.7 in. for the BSF reactor 28 1in. reactor, where vis the volume and s the surface of the core. The comparison factors must also include the ratio of the circulating-fuel reactor power, 3.25 x 10% watts, to the BSF reactor power, which is normalized to 1 watt, In addition, the attenuations of the beryllium oxide reflector (1/6.8) and of the iron shells (1/1.53) are included. The factor by which the BSF data must be multiplied in order to obtain the expected value in the circulating-fuel reactor configuration is thus F=3,25x 10% x (11.7/28) %X (1/6.8) x (1/1.53) = 1.3 x 107 for the circulating-fuel 39 DESIGN STUDY With the inverse square attenuation for reactor-crew separation included, the governing expression 1is 0.01 rep/hr = D{ig®™) x 1.3 x 107 X (ry/120)2 or D{reer) = 1.1 x 107°/r} rep/hr = 1,1 % 10"/r§ D units, where o 1s the outside radius of the reactor shield in ft (ro = 5). The equation is satisfied for 130 cm of water¢!?) of which 40 cm, or 1ts equivalent in plastic, are located effectively at the crew compartment. The lead at the crew compartment can be counted on for further attenuation, since the reactor neutrons are of high enough energy so that inelastic scattering will be important. On the other hand, the lead is not backed up by hydrogenous material and therefore cannot be allowed 1ts usual 9-cm relaxation length. A conservative value of 18 cm 1s chosen, which gives an attenuation of exp (22.4/18) = exp (1.2) , or 12 ¢cm of water. The resultant reactor shield thickness becomes t (reactor front) = 78 cm Reactor Neutrons into Crew Shield Sides (Ie). The ratio of flux incident on crew shield sides to that on the rear 18, according to simple first- scattering calculations, SO 87Ad ) d S, 2\ 4d? For this case, the ratio 1s (120/2) x 130 x 3,28 = 0.141 , where 3.28 is the number of feet per meter, 130 1s the mean free path of neutrons in air, and 120 is the separation distance in feet, (lo)fi. P, Blizard, Introduction to Shield Design -~ II, ORNL CF-51-10-70 (March 7, 1952). 40 The allowed dose into one side 1is one-fourth the total side dose or one-fourth of the dose in the rear, since the allowances for sides and rear are the same (Table 11). The dose to be measured 1in the BSF to correspond to the proper thickness of water for attenuating the side neutrons will thus be that which attenuates by a factor of 4 X 0.14 more than the thickness chosen for the rear. Thus , 1.1 x 10°% 1 (on sid = - DL S% ¢) = rep/hr 4 X 0,141 r2 0 (1.95 X 10'5)/r:rep/hr The thickness corresponding to this condition 1s 122 cm of water, for ro equal to 5 feet. Of this thickness, 46.5 cm of water equivalent 1s sup- plied at the crew compartment, and thus 76 cm 1s required at the reactor. The lead at the crew compartment is ignored, since it 1s not very thick and 1s not backed up by hydrogenous material. To allow for some structure scattering, a total reactor shield thickness of 78 ¢cm is specified. Since this value agrees with that for the reactor shield thickness calculated in the previous paragraph, a uniform shield thickness is chosen, Reactor Neutrons into Front of Crew Shield (If). The scattered neutron flux i1nto the front face on the basis of 1sotropic scattering is (7n/2) - 1, or 0.57, times that incident on the side. The allowed flux is one-fifth that for one side (one-twentieth of the dose from four sides) . The ratio of the attenuation required of the front shield to that of the side shield 1is 5 X 0,57 = 2.85 . On the other hand, the front shield is thinner than the side shield by about 2 cm, which corresponds to a factor of about 1.22. The over-all dose entering the front is greater than the tolerable dose by 1.22 x 2,85 = 3.5 , There are two factors that tend to minimize this excess: (1) the air scattering is not isotropic but rather strongly forward for the high-energy neutrons; and (2) the neutron beam 1s attenuated in air. This attenuation 1s certainly important for the neutrons entering the front with the present, large, reactor-to-crew separation distance. These two effects will more than compensate for the factor of 3.5. Note that the forwardness of scattering is not characteristic of the delayed neutrons, so that this saving could not be used for delayed neutrons. Reactor Gamma Rays into Crew Shield Rear (IId). For gamma rays, the relative escape probabilities in the circulating-fuel reactor and the BSF reactor are Aerr \ S/BSF 12 em 11.7 in. X x = 0.33 Nesp [4Y\ 15 cm 28 in. $ JcFR A more exact calculation, made by using the method of Murray,{!!) gives a ratio of 0.46, which will be used. The beryllium oxide reflector gives an attenuation of 3.65; so the effective factor of comparison is: f,=1(0.46/3.65) x3.25% 10%=4.1 x 107, For 78 cm of water, the BSF data show 0.25 r/hr. In addition to the water, there are 1 in. of iron, 24.4 cmof lead, and 33.4 cm of polyethelene plastic. Thus the total attenuation is exp (2.54/4) + (22.4/2.2) +t (33.4/24.8) = exp (12.2) The gamma dose contribution in the crew compartment is accordingly 0.25 r/hr x 4.1 x 107 X exp (~12.2) (-5/120)?%2 = 8.8 X 10°%? r/hr . (II)F. H, Murray, Fast Effects, Self-Absorption, Fluctuation of Ion Chanber Readings, and the Statistical Distribution of Chord Lengths in Finite Bodies, CP-2922, p, 15 (Apr. 6, 1945). NUCLEAR-POWERED AIRPLANE The allowed quantity, 0.100 r/hr is thus almost exactly correct. Gamma Rays from Reactor to Crew Shield Sides (IIe). As in the previous section, 78 cm of water corresponds to 0.25 X 4,1 %X 107 exp (-2.54/4) = 5.4 x 10% r/hr for the gamma dose measured at the shield exterior. The equivalent point source of 3-Mev gamma rays is thus 5.4 ¥ 10% r/hr X 5.5 X 10% Mev/cm?+sec/(r/hr) /(3 Mev/photon) X 4m (5 % 30.5)% em?® = 2.9 X 10'7 3-Mev photons/sec. At a separation distance of 50 ft, this would correspond to 2.9 x 10'7 x (50/120) = 1.2 X 10!'7 3-Mev photons/sec . For a dose of 0.05 r/hr, the curve in ANP-53(%) gspecifies a thickness of 6.25 cm of lead. This is the same as the basic amount calculated for the radiator gamma rays; so the sides are adequate. Gamma Rays from Reactor to Crew Shield Front (IIf). This calculation 1s carried out in a manner similar to that for IIc¢. The flux incident on the front face is thus: 29_m_ o TN S \\\ l 2 0.6 M \ Ar=2039cm i g N | © 04 \‘ { I o £ | @ 0.2 \\ ' w \ | O \\I x O Y 5 _ g CORE -— REITLECTOT 2 =z 0 2 4 6 8 10 12 14 16 8 20 22 24 26 28 30 32 34 36 38 UNITS OF Ar Fig. 18. Spatial Power pistribution for Reactor Section D - The Fuel- Reflected End Farthest from the Cylindrical Sides. 47 DESIGN STUDY S DWG. 17680 043 012 COMPOSITION IN VOLUME FRACTIONS CORE REFLECTOR FUEL - COOLANT 35.0% STRUCTURE {INCONEL) 2.76% STRUCTURE 0% MODERATOR (BeO) 57.24% MODERATOR 85% INERT SALT 5.00% INERT SALT 5% 010 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 FISSION PER UNIT LETHARGY PER % INITIAL NEUTRONS 0.0t LETHARGY () Fig. 19. Fission Spectrum vs. Lethargy for Reactor Section A - The Cy- lindrical Sides. s 013 012 COMPOSITION N VOLUME FRACTIONS 0.1 CORE REFLECTOR FUEL-COOLANT 34.07% 010 STRUGTURE (INGONEL) 1.97% STRUCTURE 5% MODERATOR (Be0) 60.76% MODERATOR 95% 0.09 INERT SALT 3.20% 0.08 0.07 0.06 0.05 0.04 0.03 0.02 FISSION PER UNIT LETHARGY PER Y. INITIAL NEUTRONS 0.01 19 118 17 16 15 14 13 12 4y 10 9 B 7 6 5 4 3 2 { o LETHARGY («) Fig. 20. Fission Spectrum vs. Lethargy for Reactor Section B - The Beryl- lium Oxide Reflected End. 48 NUCLEAR -POWERED AIRPLANE JRn DWG. 1T682 0.13 0.2 o 3 € oM COMPOSITION IN VOLUME FRACTIONS > R & o0 CORE REFLECTOR 3 FUEL - COOLANT 34.07% FUEL 84%, £ 0.09 STRUCTURE (INCONEL) 1.97% STRUCTURE 16% = MODERATOR (Be0) 60.76 % L 008 INERT SALT 3.20% & W 0.07 > & 0.06 I I & oos W o = Z 004 o & o003 z o @ 0.02 N W 0.01 0 0 19 1B 17 16 (5 14 13 12 4 40 9 B8 7 6 B 4 3 2 1 0 LETHARGY (¢} Fig. 21. Fission Spectrum vs. Lethargy for Reactor Section C - The Fuel- Reflected End Adjoining the Cylindrical Sides. SR OWG. 17683 013 ote 011 COMPOSITION IN VOLUME FRACTIONS CORE REFLECTOR 0.10 FUEL - COOLANT 34.07% FUEL 100% 0.09 STRUCTURE (INCONEL} 1.97% MCDERATOR (Be0) 60.76% 0.08 INERT SALT 3.20% 0.07 0.06 0.05 0.04 0.03 .02 FISSION PER UNIT LETHARGY PER ¥, INITIAL NEUTRONS 0.01 0 f¢ 18 17 16 15 14 13 12 W 10 9 8 T 6 5 4 3 2 1 0o LETHARGY (v} Fig. 22. Fission Spectrum vs. Lethargy for Reactor Section D - The Fuel- Reflected End Farthest from the Cylindrical Sides. 49 DESIGN STUDY LEAKAGE PER UNIT LETHARGY PER v, INITIAL NEUTRONS 0012 0.011 0.010 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 Fig. S DWG. 17684 COMPOSITION IN VOLUME FRACTIONS - CORE REFLECTOR FUEL- COOLANT 35.0 % - STRUCTURE (INCONEL) 2.76% STRUCTURE 10% MODERATOR (BeO) 57.24%, MODERATOR 85% . INERT SALT 5.00% INERT SALT 5% Y fl- ‘LL.H__ jy e 0.1305 THERMAL B ESCAPE AT v=18.6 [~ _‘ 20 18 16 14 12 10 8 6 4 2 0 LETHARGY (¢) 23. Leakage Spectrum vs. Lethargy for Reactor Section A - The Cy- lindrical Sides. 50 NUCLEAR-POWERED AIRPLANE SllRaF DWG. 17685 COMPOSITION IN VOLUME FRACTIONS 0.008 |— CORE REFLECTOR 0.007 |— __| FUEL-cOOLANT 34.07% STRUCTURE (INCONEL) 1.97 % STRUCTURE 5 % MODERATOR (BeO) 6076% - MODERATOR 95% 0.006 — — INERT SALT 3.20 % 0.005 }— 0.004 |— 0.04350 o THERMAL H_ha._ 0.003 — ESCAPE AT ¢ =18.6 ] . - : 0.001 ] l 0 20 18 16 14 12 10 8 6 4 2 0 LETHARGY (¢) LEAKAGE PER UNIT LETHARGY PER v, INITIAL NEUTRONS Fig. 24. Leakage Spectrum vs. Lethargy for Reactor Section B - The Beryl- lium Oxide Reflected End. 51 DESIGN STUDY S 0.045 . DWG. 17686 o L L 2 COMPOSITION IN VOLUME FRAGTIONS o e E 0.040— CORE REFLECTOR o FUEL- COOLANT 34.07% FUEL 84 % f STRUCTURE (INCONEL) 1.97% STRUCTURE 16 % | < 0.035— MODERATOR (BeO) 60.76 % £ INERT SALT 3.20% © 0.030— vl L T 0.025(+— » 0.00195 & THERMAL F 0020— | Eescape AT 3 U= 18.6\ - 5 0.015}— f o vl & I T 0.0i0F— W < T ¥ < 0.005[— /_r,_f - _fl 0 \t' 20 18 16 19 12 10 8 6 3 2 0 LETHARGY (u) Fig. 25. Leakage Spectrum vs. Lethargy for Reactor Section C - The Fuel- Reflected End Adjoining the Cylindrical Sides. 52 spectra, and the neutron-leakage spectra for the four sections of the reactor,. The effect of uranium self-shielding in the fuel-coolant tubes is indicated in Fig. 27. The change in effective multiplication constant with tube size and the corresponding uranium NUCLEAR-POWERED AIRPLANE weight in the reactor core are given as a function of fuel-coolant tube diameter, These were computed by the bare-reactor method for survey pur- poses. Uranium weight in the core vs. k, is given in Fig. 28. Reactivity coefficients for the reactor, which have been evaluated approximately, are given in Table 14, L. I DWG. {7687 0040 T I T ] [ 2 COMPOSITION IN VOLUME FRAGTIONS| l & CORE REFLEGTOR E 0.035 — 2 FUEL-COOLANT 34.07% FUEL 100% < STRUCTURE (INCONEL ) 1.97 % 3 0.030}— MODERATOR (BeO) 60.76 % '.-:: INERT SALT 3.20% & 0.025 19— o 0.00293 L a THERMAL rHT % 0020 lescape AT g v= 18.6\ Y 0.015 - .IJ ': PR Z 0.010 — m \ w s o w 0.005— /,r < % ig w 0 - 20 i8 16 14 12 {0 8 6 4 2 0 LETHARGY (u) Fig. 26. Leakage Spectrum vs. Lethargy for Reactor Section D -~ The Fuel- Reflected End Farthest from the Cylindrical Sides. TABLE 13. SOME RESULTS OF THE REFLECTED-REACTOR CALCULATIONS o PERCENTAGE OF REFLECTOR A A ) REACTOR SECTION keff THERMAL FISSIONS THICKNESS (cm) (Bk/k)/AT (°F) A 0.914 62.0 17.8 1.6 x 1073 B 0.972 60.9 204 ~0.13 x 10-3 c 0.949 50.9 12 ~0,03 x 10-5 D 1,103 46.6 20 ~0.45 x 10-5 *For 22.5 1b of U235 in reactor core, core is 25 pounds. kcff = 0,963 by area weighting. Critical uranium mass in 53 DESIGN STUDY The net(!) temperature reactivity coefficient due to thermal expansion and thermal base change is -0.66 x 104 pe in r °F; the critical uranium weight the core is 25 1lb; the uranium requirement for 27.7 ft? of fuel out- side the core 1is 87 1b, we The uranium ight is that of U235 in a 93.4% enriched uranium fuel. in ha The power density in watts/cm? the moderator and the fuel-coolant s been evaluated for this reactor (1) Expanaion coefficients asasumed: BeO, and is shown in Fig. 29. The values given are a first approximation, since the fuel reservoir at the blind end of the reactor 1s omitted and the effect of the 1/2-in., absorbing layer (Inconel) at the core boundary is included by addition to the reflector material, The integrated neutron flux normalized to one fission per unit volume (cm?) of core per second is 512 neutrons/cm?+sec. The average flux at full power is 8 x 10'%, with a peak value of 2 X 10'%® pneutrons/cm?*sec at at the center of the reactor. -6 -4 o 14,8 16 ; fuel- 1 , 1.47 10 F. e e . " eireoolfant " per The possibility of decreasing —— critical mass significantly by using 100 DWG. 17688 beryllium instead of beryllium oxide E because of its larger density of E 0.99 moderating nuclei has been evaluated. 8 26.31b O 0.98 |p——— 5 0.97 z DWG. 17689 £ O 2 1 , < 0 S oe6 \ _291b z £2: 00020308 ] T N z . ASSUMED REFLECTOR SAVING,15.24cm ___— 5 095 g — = \ & / w 5 09 > 0.94 2 = w W 0.93 \\\\\ g - 3 |b/"] g os ul L 0.92 ui 0 ' > 20 25 30 35 FUEL-COOLANT TUBE DIAMETER (in.} URANIUM MASS IN THE CORE (Ib) Fig. 27. Effect of Uranium Self- Fig. 28. Uranium in Core vs. Ef- shielding in the Fuel-Coolant Tubes. fective Multiplication Constant. TABLE 14. REACTIVITY COEFFICIENTS FOR THE REACTOR REACTIVITY RANGE OF COEFFICIENT VALUE Moderator (BeO) density [(Ak/k)/(Ap/p)] 0.321 99 to 100% of quoted density Coolant density [(Ak/k)/(Do/p)] 0.011 90 to 100% of quoted density Structure (Inconel) density -0.147 100 to 125% of [(Ak/E)/(Dp/p)] quoted vol. % Thermal base (reactor temperature) [(Ak/k)/ AT(°F)] -1.20x%10"8 1283 to 1672°F Uranium weight [(Ak/k)/(AM/M)] 0.348 54 NUCLEAR-POWERED AIRPLANE o, 2.2 CURVE A: NORMALIZED RADIAL AND AXIAL {REFLECTED END) 2.0 POWER DISTRIBUTIONS. TO OBTAIN POWER DENSITY — | N FUEL-COOLANT, MULTIPLY BY 2030 watts/cm3, A CURVE B: NORMALIZED, AXIAL (BARE END), POWER DISTRIBUTION. 1.8 e — TO OBTAIN POWER DENSITY IN FUEL-COOLANT B \ MULTIPLY BY 2310 watts/cm3 1.6 ~y CURVE C: RADIAL POWER DISTRIBUTION IN MODERATOR AND REFLECTOR. TO OBTAIN POWER DENSITY, MULTIPLY ~ BY 700 watts /¢cm3 FUEL TRANSPORT ADDS A e 1.4 ‘~\\\ FACTOR OF 0.76. Q S NG CORE VOLUME, 22.0 ff° w2 N 34.1 % FUEL-GOOLANT z \ 80.7 % BeO = 1.0 t.97 % INGONEL N N - 3 \\\\‘ m O-B \\ o =z — 0.6 z g \\\\ \\ 0.4 — N \-\ \ B 0.2 — \ \ . \;,_ o 10 20 30 40 50 60 70 DISTANGE FROM CORE CENTER (cm) Fig. 29. Power Density in Fuel-Coolant and Moderator of Circulating-Fuel Reactor. A net reduction of only 6.5% in increase in k of 10% will be re- critical mass would result from this change. At the present time a flat increase 1n keff of 5% by means of control apparatus is a maximum value to over-ride maximum transient xenon and other fission products and loss in delayed neutrons for the operating temperature range. The presently available data indicate that a net quired to raise the reactor from room to operating temperature, The uranium requirement per aircraft in flight will thus be a maximum of approxi- mately 75 1b in core, plumbing, and heat exchanger. This value will not be changed significantlyif some other, nonpoisoning, fuel-coolant solution is used. REACTOR CONTROL An ANP power plant electronic simulator was set up with design-point values for the various reactor param- eters. By means of this simulator, the following time variables were determined as the system response to various stepped changes in reactor excess reactivity: power level (p/p,), rate of change of power level (p/p,), mean fuel temperature (£,), and rate of change of mean fuel temperature (Qf). Figures 30 through 33 show these quantities plotted as a function of time for steps in excess reactivity (Ak/k) of 0.002, 0.004, and 0.006. The fuel temperature coefficient of 55 DESIGN STUDY P/A, L OWG, 17691 8 LN \Akaooos 1N L / /\*——Akflr:oooo.l | 3 \ ] // A K7k =0.002 1 S — 0 O 10 20 30 40 50 80 70 BO SO 100 TIME {msec) Fig. 30. Power Level After Various Step Changes in Excess Reactivity. P/P, 700 600 500 400 300 200 100 -100 -200 -300 -400 -500 -600 Fig DWG. 17692 Ak/k 20006 k/k =0004 k/k=0002 0 10 20 30 40 50 &0 70 80 90 100 YO - 31. TIME {msec) Bate of Change of Power Level After Various Step Changes in Excess Reactivity, 56 _—_— DWG. 17693 1390 1365 k= 1340 1315 1290 1265 k/k=0004 k= TEMPERATURE (°F) 0 10 20 30 40 50 sC 70 B8O 90 100 110 120 TIME (msec) Fig. 32. Mean Fuel Temperature After Various Step Changes in Reactiv- ity. o DWG. 17694 6500 6000 5500 5000 4500 4000 3500 @ 3000 2500 2000 1500 Ak/k 20004 1000 500 k/k=0002 -500 O 10 2C 30 40 50 60 70 80 90 100 TIME {msec) Fig. 33. Rate of Change of Fuel Temperature After Various Step Changes in Reactivity. reactivity, (Ak/k)/AT (°F), used in obtaining Figs. 30 through 33 is -8 X 10°%, This value was determined by taking the temperature coefficient of reactivity due to the volumetric expansion of the fuel and dividing by 2 to allow for other forseeable and un forseeable fast effects. The temperature coefficient of reactivity due to the moderator, structure, etc. was neglected as being too slow to affect the fast transients. The delayed-neutron steady-state contribution, usually designated as 6 z a;B,, for this circulating-fuel i for that is, non-circulating fuel, reactor was taken as 0.00172; a, =1 i ? 6 E a.lfi:. = (,0073. The mean neutron i=1 life-time was taken as 2.65X%10-% sec. CONTROL FEATURES DETERMINED BY SIMULATOR STUDY A few control features of signifi- cant merit are characteristic of the circulating-fuel type of reactor. When fuel expansion with temperature rise provides a negative reactivity temper- ature coefficient, the power demand signal from the turbojet engines 1is transmitted through the circulating- fuel coolant and provides an over-all power plant in which the reactor is a slave to the external loading system, that is, the engines. Since the major portion of the reactor power 1is generated in the fuel, the fuel has the fastest temperature response time of any element of the reactor, Accord- ingly, the reactor power follows the load demand more closely for the circulating fuel than for acirculating moderator, or for that matter, it follows more closely the load demand than is possible for any other type of coolant, As a consequence of the above- described feature, external coupling in the form of servo control loops with sensors, actuators, control rods, etc. are not necessary 1in a reactor such as this. In fact, studies made of this reactor by using an electronic power plant simulator indicate that only the self-stabilizing features inherent in the negative-reactivity temperature coefficient make possible control of this power plant in which NUCLEAR-POWERED AIRPLANE the power density is so high and such a large portion of the normally static fuel delayed-neutron contributions are not effective in the control. This comes about because of the severe servo system response times needed for control. These simulator studies indicate that servo frequency responses of as high as 500 cps would be required to control a similar but nonself-stabilized reactor in any manner comparable to the control provided by the negative-reactivity temperature coefficient. Furthermore, regulating rods would require acceler- ations comparable to impacts to provide comparable control. Such servo systems lie considerably beyond the presently known control art, Surge pressures derived from fluid temperature transients constitute the limiting features of ANP controlla- bility. The first and second time derivatives of the mean fuel tempera- ture were determined by using the simulator, and from these data the pressure surges were calculated and found to be tolerable. Relatively slow control of the reactor can be provided by some shimming means, either rods or enrich- ment, The shimming provided by rods takes care of the system poisoning, and either rods or enrichment would provide for fuel depletion. Essen- tially, rod motion merely changes the mean fuel temperature and does not control the load power. PRESSURE IN FUEL TUBES The increase in temperature of the fuel in the core, owing to a step change in reactivity, causes an increase in fuel volume. Inasmuch as the fuel is incompressible, the incremental fuel volume must be transferred from the reactor core to the surge tank as rapidly as it is generated, that is, in approximately 40 milliseconds. The rapid acceleration of the fuel required to transfer the generated volume results in appreciable inertial 57 forces in addition to the frictional forces involved. These inertial and frictional forces have been evaluated, both in the reactor core and in the piping to the surge tank (the surge tank is 2 ft from the reactor inlet). Figure 34 1s a plot of the variation with time of the incremental pressure at the reactor core outlet, at which peint the incremental pressure 1is at a maximum, for a step change 1in reactivity of 0.0025. Figure 35 is a plot of the maximum i1incremental pressure at the reactor core outlet for various step changes of reactivity. For a step change in reactivity of 0.006, the maximum incremental pressure at the reactor core outlet is 100 psi. For 0.65-in. -0D tubes with 0.025 -in, walls, the incremental BETess 20 @ PRESSURE PULSE (Ib/in2) H Q -4 0 0.02 0.04 0.06 TIME, (sec} Fig. 34. Pressure Pulse vs. Time (Ak/k = 0.0025). 58 pressure of 100 psi will give a hoop stress of approximately 3250 1b/in.?2. The tensile yield point of Inconel 1is about 13,000 1b/in.? at 1500°F. The maximum incremental pressure allowable, based on the tensile yield point, 1s 400 1b/in.?. The apparent factor of safety is 4, Basing the mechanism of failure on the maximum shear stress theory gives a maximum incremental pressure of 800 1b/in.?; basing the mechanism of failure on the distortion-energy theory gives a maximum incremental pressure of about 900 1b/in.?. 1In any case, the least apparent factor of safety is 4. o e 10 100 S0 80 70 60 MAXIMUM PRESSURE PULSE {Ib/in2) 50 40 // 30 ///// o /| 0.002 0.004 Fa¥ 77 4 0006 Fig. 35. Pressure Pulse at Core Outlet for Various Changes in Reactiv- ity.