THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING COMPONENT OPTIMIZATIONS FOR NUCLEAR-POWERED CLOSED-CYCLE GAS TURBINE POWER PLANTS H. A. Ohlgren Professor, Chemical Engineering Department Director, Industry Program of the College of Engineering F. G. Hammitt Associate Research Engineer, Engineering Research Institute Lecturer, Mechanical Engineering Department September, 1957 IP-245

ABSTRACT Nuclear-powered, closed-cycle gas turbine power plants with directly-cooled reactor cores for relatively small power outputs are examined. The results of preliminary economic optimizations for the various components comprising such plants are presented. The reactor core is examined, both from the nuclear and the heat exchange viewpoint, and results of regenerator and turbomachine optimizations are discussed.

1.0 INTRODUCTION Consideration is given to the possible development of a nuclear-powered, closed-cycle gas turbine employing a reactor concept into which is built the necessary heat transfer for the extraction of heat power. In a previous paper, efforts were made to evaluate power plant performance of cycles employing a thermalheterogeneous, gas-cooled reactor, as being developed by the General Atomics Division of General Dynamics Corporation, and a thermal, bismuth-uranium type when conditions are extrapolated to levels permitting effective use of closed-cycle gas turbines. The bismuthuranium, molten metal-fueled type is a development of the Brookhaven National Laboratories. Presently, the Babcock and Wilcox Company is undertaking under contract with the Atomic Energy Commission the development of a liquid metal-fueled reactor experiment termed "LMFRE.'t Some of the advantages which are given in the paper for a closed-cycle gas turbine design are: 1. Increased capacity for a given size and/or weight. 2. Wider range of loads without substantial loss of efficiency, since power may be reduced by reducing pressure level without affecting temperature, pressure ratios or speed. 3. Reduction of size tends to control difficulties resulting from differential temperature extraction. 4. In nuclear-powered, closed-cycle gas turbine systems, it is possible to contain the working fluid in a closed system so that direct extraction of heat from the reactor into a working fluid *Numbers refer to similarly numbered references in bibliography at end of paper. -1

can be achieved without release of radioactive gas to the atmosphere. The influence of working fluid characteristics on the design of closedcycle gas turbines has been discussed by the present writers,l by S. T. Robinson,2 and by Mr. S. T. Dennison.3 These authors provide a basis by which a suitable working fluid for a power plant can be selected with the necessary information and data regarding the thermodynamic and heat transfer relationships of the working fluid. This paper deals with summaries of results and calculations of a nuclearpowered gas turbine system which employs a reactor which is internally cooled in core and reflector by the working fluid which is used directly in a regenerative closed-cycle gas turbine system. Efforts have been made to consider optimum selection of the various components so that the integrated system of components can be evaluated in terms of reactor heat power, maximum temperature in reactor core and reflector, choice of working fluid, selection of pressure ratio)and maximum working fluid pressure. To illustrate the techniques employed for optimization of these parameters for a reactor coupled with a closed-cycle gas turbine, the authors have selected a reactor heat power output in the range of 5-10 megawatts from which it appears that the economically optimized electrical power outputs are in the range of 1400-2800 kilowatts. Although several possible types of molten reactor fuels can be employed in reactor designs, it appears that there are immediate possibilities for U-235 -2

or plutonium dissolved in bismuth metal, and operated at high temperatures, Such a concept is being considered by the Brookhaven National Laboratories. From those data which have been made available to the authors, programs and projects have been conducted to project these data to a practical,smallscale "burner" nuclear powerplant, the success of which is contingent upon a vast amount of additional research, development, and engineering. The results of the analyses do indicate that this type of reactor with builtin heat transfer surfaces has a potential for application in the lower reactor heat power range where light weight and high efficiencies in the consumption of nuclear fuels are extremely important.4 -3

2.0 DESCRIPTION OF THE FAST REACTOR SYSTEM COUPLED WITH A SIMPLE CLOSED-CYCLE GAS TURBINE A simplified flow system of a reactor with built-in heat transfer in core and reflector, coupled with a regenerative closed-cycle gas turbine power plant, is given in Figure 1. In general, the flow system considered can be described as follows. The working fluid, which may be helium, carbon dioxide, nitrogen or other suitable gas, enters the reactor system from a regenerator. The flow of gas from the regenerator is split between heat transfer surfaces provided in the core and heat transfer provided in the reflectoro Heat is transferred from the fissioning mass in the core by conductive and natural convective heat transfer through tubes into the working fluid. Since peak neutron fluxes occur in the reflector, and since the reflector is considered to be U-238 in which both fast fission of U-238 and fission of plutonium occurs, considerable additional power is generated in the reflector. U-235 or Pu-239 dissolved in bismuth, as developed by the Brookhaven National Laboratory,5 have been selected as possible fuels for one type of reactor~ The fuel will be in the molten state operating at from 6500C to 8000C. The power level of the reactor is sustained by the continuous addition of molten fuel to the core and the continuous removal of fuel and fission product gases from the reactor core. The core fuel is contained in a tantalum vessel into which a maximum of heat transfer tubes of the U-tube type is locatedo Surrounding the core -4

design is a eutectic of U-238 and iron in which the maximum temperature is sustained at 6000C to 6500C by the proper installation of heat transfer areas into the molten reflector. The reflector is again contained in a tantalum vessel with provisions for the continuous addition of uranium, as an iron-eutectic, and the removal of a continuous amount of reflector material as a product for plutonium recovery~ The working fluid leaves the core and reflector of the reactor unit and flows at a suitable temperature and pressure to a high pressure turbine in which it is expanded and from which useful work is dbtained to drive the high and low pressure compressor units (Compressor #1 and Compressor #2), which are directly connected shaft-wise to the high pressure turbine. The expanded gas leaves the high pressure turbine and is expanded again in the low pressure turbine to obtain useful work in the form of shaft horsepower, which can be converted to either electrical energy or to mechanical work. The gas leaving the low pressure turbine flows then through a regenerator, exchanging heat with the incoming gas from Compressor #2. The gas flowing from the regenerator enters Cooler #1, where it is cooled to the lowest temperature of the system and is also at the lowest pressure of the system. Compressor #1, driven by the high pressure turbine, compresses the gas to an intermediate pressure. The compressed gas then enters Cooler #1, where it is again cooled to ambient temperatures by a suitable coolant. Compressor #2 compresses the gas to the highest pressure of the system. The choice of suitable absolute pressure level depends upon the power output. An increase in power will demand increased pressure to obtain the requisite -5

mass flow and heat transfer coefficients. The gas at this maximum pressure flows through the regenerator, exchanging heat with the exhaust from the low pressure turbine. The gas leaving the regenerator is at the temperature where the cycle becomes complete. -6

3 0 PARAMETRIC STUDIES The coupling of a fissioning, bismuth, internally gas-cooled reactor to a closed-cycle gas turbine requires that the nuclear parameters be carefully evaluated in terms of heat transfer and heat cycle analysis. Optimum designs for the respective components will be affected by power level, temperature level, choice of working fluid, and choice of working pressure (in the case that limits external to the cycle are set upon this parameter). The optimum will also depend upon the application, since in most cases it will be desirable to optimize the cost, in others the weight and/or size. Nuclear power plants in the range of outputs from approximately 600 to 5000 shaft horsepower have been considered in such optimization studies. It is assumed that the gaseous working fluid will be used to cool the reactor core directly with possible pre-heat in the reflector. Preliminary results of such studies have been reported in a previous paper by the present authors.l As explained therein, the low pressure ratio, highly regenerative cycle was selected as most applicable. Curves were presented for such a cycle delineating the individual effect on thermal efficiencies of a change in efficiency or effectiveness of any one component, and also the effect of a change in temperature or pressure ratio. Thus, a basis was provided for ready estimation of thermal efficiency for such a cycle with any combination of component efficiencies and effectivenesses. Further, an evaluation of the effect on the attainable efficiency of the turbine and compressor components of power level., pressure

level, temperatures, and fluid selections was made. The degree of reduction in efficiency due to reduced power level or increased pressure level (i.e. reduced flow path dimensions), and the effect on efficiency and also on machine size of fluid selection was showno Using such data, it becomes desirable to consider the economic optimization of the principal heat exchanger components in the context of the overall nuclear power plant. For those cases in which minimum cost is the controlling factor, it would then become possible to select intelligently the most suitable working pressures and cycle temperatures, assuming that the reactor temperature is fixed by considerations of feasibility. Also, an intelligent choice of working fluid for any given conditions of reactor temperature and heat sink temperature at a given power level would be possible unless, of course, the choice were dictated by other factors, such as induced radioactivity. The principal heat exchanger components with which we must concern ourselves are the nuclear reactor itself and the regenerator. The controlling factors in the two cases are quite different, in that the cost of heat exchange surface within the reactor is considerably greater than the cost of the heat exchange surface for the regenerator. In either case, the general problem is complicated so that certain simplifying assumptions must be made before a practical analysis can be attempted. A preliminary analysis of this situation has been made for a nuclear power plant wherein a counterflow heat exchanger with passages of approximately 1/16 inches hydraulic diameter was assumed- Utilizing assumed costs for -8

nuclear fuel, heat exchange surface, amortization rates, etc., and the turbomachinery data developed in Reference 1, optimized regenerator effectivenesses were computed as a function of maximum cycle pressure and temperature and power level for air and helium. These results are summarized in Figures 2 through 7. It will be noted that the economically optimum regenerator effectiveness under the assumptions of this study is not primarily a function of power level. However, it is very definitely a function of pressure level, being substantially reduced in all cases for reduced pressure. This reduction is somewhat less for helium than for air. The corresponding economically optimized hot side film coefficients are shown in Figures 8 -through 13. The coefficients for the cold side are of similar magnitude. It is noted that these also increase substantially for higher pressures.* It should be mentioned that the increase of economically justified regenerator effectiveness for higher pressures more or less overcomes the reduced turbomachinery efficiency at high pressure (for a given power level) so that the overall economically justified thermal efficiency is not a strong function of pressure levelo The reactor theory of low power kinetics of circulating-fueled reactors with several groups of delayed neutrons6 has provided a basis for computing reactor periods of such reactors by finding the eigenvalues of a system of differential equations. Such evaluations are applicable to internallycooled reactor cores when natural convective heat transfer and fluid motion of fuelare similar to the circulating fuel type discussed by J. A. Fleck.6 The characteristics of liquid bismuth as a fuel solvent and a heat transport * The authors are indebted to W. J. Yang, formerly of The University of Michigan research staff, for the calculations on which these data are based. -g9

medium for nuclear reactors in terms of pumping power, metallurgical problems, heat transfer, radioactivity, chemical activity, and nuclear considerations has been evaluated at the Brookhaven National Laboratories.7 This work has indicated the qualifications of liquid bismuth as a heat transfer medium in nuclear power reactors, and shows characteristics which influence design and operation of reactor systems in which it is used. In the discussions of optimization of nuclear reactor parameters for adaptation to closed-cycle gas turbines where the size of the core should be of total minimum weight, the authors have endeavored to evaluate the operation of a bismuth-fueled system in the fast range. An internal heat exchange device as suggested by Robert J. Teitel4 has been adapted to the specific purpose of employing a gas coolant through channels located in the core. The use of plutonium dissolved in bismuth in the intermediate or fast range also offers promise of increasing specific power and plutonium concentration considerably above that which can be achieved by a liquid metal-fueled solution of uranium and bismuth. The solubilities of uranium, thorium and plutonium in bismuth as a function of temperature are shown in Figure 14. Thus, if the reactor average operating temperature is in the neighborhood of 8000C, it would be possible to vary the concentration from several hundred parts permillion to a maximum value of about 18% by weight if plutonium were the fuel. The variation of concentration provides one means of reactor control, and correlation of fuel volume to available heat transfer surface. 10

Thus, it appears possible to give consideration to a technically feasible nuclear reactor core employing fissile material dissolved in bismuth which is surrounded by a reflector comprised of U-238iron and is contained in the shell side of a standard U-tube heat exchanger~ Calculations have been made, premised upon a reactor vessel which is fabricated from tantalum, consisting of 77 U-tubes, 1/2 inch O.D. by 16 BWG on 1-1/33 inch triangular pitch with a 1-3/4 inch radius (minimum) contained in a 16 inch O.D. by 1/4 inch thick tantalum shell with a nominal tube length of 6 inches. For such a reactor, the heat transfer surface based on outside tube dimensions is 152.2 square feet. Provisions are made for addition of proper concentrations of fissile atoms dissolved in bismuth so that the power level of the reactor can be maintained constant. Tantalum tubes, tube sheets, and heat exchanger shell are provided. The maximum operating temperature of the bismuth-plutonium fuel is estimated to be 8500~C (15620F). The temperature of the working fluid, helium, entering the reflector is calculated to be 1000 F to maintain the reflector at a temperature below 7000C. The temperature of the working fluid entering the reactor is 11500F. During normal operation, the temperature of the working fluid leaving the reactor is 13500F. The economically optimized temperature calculated leaving the regenerator and entering the reactor reflector in the horsepower range from 1000 to 10,000 shaft horsepower lies in the range from 825~F to 880~F. Arrangements of heat transfer area in the reflector to maintain reflector temperatures not in excess of 700~C provide a -11

working fluid temperature entering the core between 9500F and 1050F. Under such conditions, and for a maximum fuel temperature of 8500C for the core configuration considered, the average temperature of the working fluid leaving the reactor core is calculated to be 13500F. Table I summarizes scme general characteristics of the core design. 3.1 Nuclear Parameters The reactor concept evaluated consists of an intermediate to fast bismuth-plutonium-fueled core contained in the shell side of a standard tantalum U-tube heat exchanger in which the working fluid (helium) flows through the tubes. The resolution of the nuclear parameters requires that multigroup calculations be conducted to evaluate criticality, flux and flux distribution, power level, etc. Final designs would be dependent upon trial and error machine computations so that adjustment of size and core composition is compatible to heat transfer and cycle performance as a function of flux time.8 The calculations conducted have been based upon the following assumptions:9 1. Fuel is plutonium dissolved in bismuth over range of concentrations. 2. Average reactor fuel operating temperature is 150016000F. 3. Reflector material is U-238 - Fe at M.P. of 650~C. 4. Published cross-section data have been used. -12

Table II presents results of lethargy group characteristics per megawatt of reactor power (base reactor)o Nuclear parametric studies in the intermediate and fast energy range are dependent upon establishment of the proper analytic approach with suitable boundary conditions. One approach is to use the age diffusion equations in proper energy groups.l0 The age diffusion equation is thus reduced to a finite set of coupled-ordinary differential equations in which each equation represents the average neutron behavior within a given energy group. In cases where the critical configuration and dimensions are large compared to the mean free path of neutrons, the age diffusion equation can be written as follows: VDV(n) - Za nvi- q + S(riu) = n(im) (3.1) VDTV(nvi) - aTnT + qT = n(rT) (3.2) Tt where D = 1 = 1 3ZTl...0. Z = macroscopic transparent cross-section tr 40 = average cosine of scattering angle Za = macroscopic absorption cross-section = average logarithmic energy decrement u = lethargy -13

nv = neutron flux S(r,u) = source generation term a n(r,u) = rate of change of neutron density with time The source of neutrons resulting from fission can be expressed as: UT S (r,u) = v [ f Zf nv du' + ZfT nvT]X(u)' (3.3) The source of neutrons resulting from inelastic scattering can be expressed as: u Sis(r,u) = i Zi nv (u' <-u)du' (3.4) 00 whe re v = number of neutrons per fission X(u) = normalized fission spectra X(u' - u) = fraction of neutrons which are inelastically scattered and degraded from u' to u. If Es and Ftr csan be considered constant over small spatial regions, the equation for steady state reactor operations can be expressed as: 1 2q _ Za q - +S(r,u) = O (3.5) 35Zf tr Z s The above equation can be expressed in integrated form over the limits of the logarithmic energy range, Ui, in the i-th lethargy group as follows: -14

22 0 I Ui.12. ) - UJf a -. + q. + S(r,u)du =0. \35 L tr/i(avg) 4 i(avg) Ui (3o6) 0 The term, q., is the degradation of neutrons out of the i-th group, and qcI is the degraded group entering the i-th group from the previous higher energy group. In cases where the slowing.down density and macroscopic cross-sections encounter small changes within the energy group, Equation (3.6) can be written in approximate form as products of averages, U. v2 - (Ji A\ -E qi + X + F S(r,u)du O0.S i(avg) Z i(avg) ui (3.7) Neutrons produced from fission and resulting from inelastic scattering can be written as ni \ =1 te F' (av) fi Z ( (avg) )(i (3o8) We can equate the slowing down density within the i-th group to the slowing down density of the previous group: I o qi = qi-1 -15

Solution of Equation (3.8) is possible if the relationship of qavg and qo is linear: q =w. (qi) i i( i)avg where wi = an appropriate constant for each group Normally, the coefficients, wi, will be less than unity in those groups and regions which do not contain source terms. By substitution of Equation (3.8) into Equation (3j7) and simplifying, we have: n V (q~i)avg + Cj(( )j (avg) = (3d9) j=1 where C.. = _W"_S. C 1 1 13 t avg'e j(avg) ii \ C j(avg) when 1 if j =k k 0 o if j k Xf = fraction of neutrons occurring in j-th group ij resulting from neutrons born in the i-th group. -16

X(is)ij = fraction of neutrons inelastically scattered in the j-th group which are released in the i-th group. Recalling that the homogeneous set of differential equations are of the form V 2 (q)avg B2(q)avg' (310) substitution of Equation (3.10) into Equation (3.9) gives: /(B2 C j(Ri)g = 0 (3.11) o —(~a c )(~ii avg - o This equation can be expanded in matrix form: B 2 CC ~ \ C11 -C12 C13 Cln l(avg) -C21 B2 C22 -C23.... C2n 2 -C31 -C32 B2 _ C33 C3n q3 =0 2 Cnl -Cn2 -Cn3.... B - Cnn qn(avg) (3.12) Equation (3.11) can be satisfied if the determinant of the coefficient matrix is zero. The determinant is a system of polynomialsof degree n. -17

3,2 Reactor Core Heat Transfer Parameters It is to be expected that the economic optimization of the reactor core as a heat exchanger will show optimum heat transfer coefficients differing considerably from those of the regenerator because of the interplay of the nuclear parameters —fissile material inventory, costs of the core and shielding, etc. —with the heat transfer parameters. A general investigation of the situation would be extremely difficult because of the many types of reactor cores to be considered and the unknown magnitude of many of the most significant cost factors. However, a preliminary investigation has been made for a particular configuration in order to at least determine the significant trends.* The configuration investigated is similar to that described in this paper in that heat is removed from a liquid-metal-fueled core by the passage of coolant gas through tubes in the core. This coolant gas is the working fluid for a closed-cycle gas turbine. It differs in that a graphite cylindrical core (height equal to diameter), fitted with vertical wells for the liquid metal fuel and holes for passage of the coolant gas, is considered. The nuclear calculations 8 are based upon the work of J. Chernick, and very rough corrections are made for the presence of steel coolant tube liners. While no attempt was made to work out the detailed features of the construction, it was felt prudent to include allowance for metallic liners of some sort. *The authors are indebted to Y. Hwang, of the University of Michigan research staff, for these calculations. -18

It was assumed that the temperature limitation for the overall power plant would be within the reactor rather than the turbine equipment. It then becomes a problem of determining the economically justifiable degree of approach between the working fluid temperature at turbine inlet and the inside wall temperature of the coolant tubes. A closer approach requires additional heat exchange surface area within the reactor, but increases overall thermal efficiency (for a fixed reactor temperature). It is thus a balance between capital cost and operating cost. Under the assumptions described above, calculations have been conducted for air for power outputs ranging between 600 and 60,000 horsepower and maximum cycle pressures ranging between 400 and 1000 psia. A reactor temperature limitation of 17000F for the inside wall of the coolant tubes was assumed. The gas inlet temperature to the reactor was determined from the regenerator optimizations previously described in this report. The outlet temperature was economically optimized considering amortized capital costs of the reactor, fuel inventory costs, and pumping power cost. The reactor cost estimation was necessarily very rough. Corrections for increased gas pressure were applied. To date, the reactor investigation has only considered air (or nitrogen) as the working fluid. It is hoped that it may be extended to helium also. The results for air are shown in Figures 15 through 19. The optimized turbine inlet temperature, log mean temperature difference, gas side -19

film coefficient, the temperature increase through the reactor, and the core diameter are plotted as functions of power output and pressure level~ Table III shows the economically justified pressure drop in absolute values)and al a portion of the pressure level)across the reactor for the various cases. It is noted that this is less than 3% even for 60,000 horsepower at the minimum pressure considered and becomes practically insignificant for the smaller powers and higher pressures. It is noted that the approach of the gas temperature to the coolant tube inner wall temperature is closest for the low powers and high pressureso Also, of course, the log mean temperature difference is minimized in these cases. The rather peculiar shape of these curves may be explained in the following manner. For the low power units, the size of the core, and hence, the heat transfer area available, is controlled by considerations of critical mass and uranium inventory. In other words,- the reactor as a heat exchanger is oversized so that the pressure and temperature differentials are very small. As the power level is increased or the pressure level decreased, the core size is still controlled by the nuclear parameters so that the gas pressure and temperature drops increase~ As yet, however, the cost of fissionable material burn-up (i.e., the thermal efficiency effect) is small. However, as the power is further increased, this burn-up cost begins to control, so that it becomes desirable to increase the reactor size at some capital cost to improve the overall thermal efficiency by reducing the required temperature differentials and pressure drops. -20

The results which have been listed apply directly only to a very specialized example, However, it is felt that the trends exhibited are illustrative and do have more general application. -21

4.0 RESULTS OF PARAMETRIC STUDIES AS APPLIED TO LIQUID-METAL-FUELED FAST REACTOR 4.1 General The overall thermal efficiencies with optimized turbomachinery component efficiencies at various temperature and pressure levels can be considered in the range of energy outputs equivalent to 1000 to 3000 BHPo Such curves are shown in Reference 1. Thermal efficiency versus pressure ratio at 1200~F and 1500~F are also plotted for component efficiencies varied individually. As a result of the calculations on which these curves are based, it becomes possible to evaluate the range of optimum temperatures for the working fluid entering the reactor for a fixed working fluid outlet temperature from the reactor. Figure 20 is a plot of the optimized temperature for the working fluid (helium) leaving the regenerator and entering the reactor versus horsepower output when the outlet working fluid temperature is fixed at 1500~F for various pressures. Figure 21 presents a similar plot when the working fluid (helium) leaving the reactor is 12000F. Thus, within limits of materials of construction, it is possible to establish specific temperature differences for the working fluid flowing through a reactor core wherein the heat transfer area is contained. The heat transfer problem to be considered in a molten metal-fueled core into which heat transfer area is incorporated is a complex -22

problem and warrants considerable research and development before final correlations between the source generation term, critical configuration, fluid mechanics and heat transfer can be achieved. An optimum design of a reactor configuration capable of heat-power generation in terms of heat transfer area and maximum temperature limits becomes a function of power level, flux distribution, maximum allowable temperatures, thermal stress, arrangement of coolant passages, materials of construction. A specific idealized example was described in the last section. 4o2 Heat Transfer from Molten Fuel to Working Fluid The calculations to date give results where it is possible to consider the heat transfer from a mass of molten fissioning fuel to a working fluid. The reactor engineer can select optimum conditions of temperature, pressure ratio, thermal efficiency for a nuclear power plant of a given power output. From such conditions, it becomes possible to consider the heat transfer characteristics of a surface incorporated into the core geometry of a molten metal-fueled reactor. From heat engine cycle analyses and the rapid advancements af technologies in materials for gas turbine components, it appears that the maximum temperature of the system is limited by the container material for the molten fuel. Investigations indicate that it is possible to achieve a coolant tube wall temperature of 17000F, and this value was used in the reactor optimization described in the -23

last section. Thus, a working fluid temperature for reactor outlet conditions at 15000F appears within reach. For such conditions and a reactor working fluid pressure of 1000 psig when delivering3000 BHP in output power, the optimum inlet temperature of the working fluid entering the reactor core is 8750F. If we select a Ap/p as.02, which appears reasonable for the system from the previously described calculations, the economically justified thermal efficiency expected would be 28%. Thus, the heat power level average for the reactor would be (3000)(7457) = 8,3 megawatts.27 Thus, to allow for thermal losses of heat to structural materials, shielding, etc., it would appear that a heat power generation between 8.5 and 9.0 megawatts would suffice. Premised upon multigroup calculations by Chernick, the size and geometry of reactor configuration is dependent upon heat transfer surface and arrangements in the reactor core. 4.3 Determination of Optimized Core Diameter As previously mentioned, summaries of calculations based upon Chernick's work, showing relationships of core diameter to output power, are shown in Figure 19, A maximum core diameter is obtained at 2000 horsepower. A minimum appears at about 10,000 BHP. These calculations have been premised upon air as the coolant but relation curves can be expected for other working fluids.

4.4 Selection of Maximum Turbine Temperature (Reactor Outlet Temperature) Versus Power Output Figure 15 summarizes calculations wherein the gas turbine inlet temperature is determined as a function of output horsepower. A minimum appears in the range of 20,000 to 30,000 BHP for the range of working fluid pressures from 400 to 1000 psia. 4.5 Determination of Optimum Log Mean Temperature Difference Based upon a tube wall temperature of 17000F, calculation summaries for log mean temperature difference (average) versus plant output horsepower are shown in Figure 1O. Maxima appear at the range of horsepower outputs for various pressures in the range of 20,000 to 40,000 BHP. 4.6 Determination of Film Coefficient for Working Fluid at Constant Reactor Tube Wall Temperature For an optimized core geometry at constant tube wall temperature, calculations showing the effect of gas coolant film coefficients are shown in Figure 1T7. Calculations were made for various gas flow rates for a fixed heat transfer geometry in terms of total average working fluid pressure in the reactor core. It is to be noted that at low reactor power levels, the film coefficient appears to remain constant at about 40 for all pressures. As power is increased, the film coefficient approaches a maximum of 560 at 1000 psi, 370 at 700 psi, and 300 at 400 psi. Note that these values are in the power output range of about 60,000 BHP. This fact arises from the situation wherein the uranium-bismuth inventory -25

and critical dimensions control for low power outputs but become a much less controlling factor for higher power outputs. 4.7 Temperature Rise of Working Fluid Through Reactor Summaries of calculations of the temperature rise of gas for various pressuresas a function of BHP are shown in Figure 18. When the pressure is 1000 psia, a maximum rise occurs at 7000-9000 BHP and a minimum rise occurs between 20,000 and 30,000 BHP. Although the calculations presented are premised upon air as the working fluid, similar relationships are expected for other working fluids. -26

TABLE I GENERAL CHARACTERISTICS OF BISMUTH-PLUTONIUM FUEL CORE DESIGN WITH URANIUM-IRON REFLECTOR Reactor Heat Power 8 8 14W Core Fuel Plutonium dissolved in bismuth by weight Addition of Fuel Continuous or semi-continuous Fission Product Removal Continuous removal of fission product gases, about 95 of total fission product Maximum Temperature of Reactor Fuel 8500~C Temperature of Working Fluid Entering 825~F - 880~F Reflector Temperature of Working Fluid Entering 950~F - 10500~F Core Temperature of Working Fluid Leaving 1350~F Reactor Core Reactor Construction Material Tantalum Maximum Allowable Surface Temperature 9000C Reactor Type Shell and tube unit with U2 bundle in core Fuel on Outside of Tubes Working fluid through tubes Heat Transfer Surface Available 152.2 square feet in core Reflector U238-iron eutectic, canned and pierced with tantalum tubes Core Dimensions 16" O.D. by 6" nominal tube length Reflector Dimension 8" annular thickness surrounding tantalum core,, - " I' " I "!, -, i,,.'- 2 -27

TABLE II LETHARGY GROUP CHARACTERISTICS PER MEGAWATT OF REACTOR POWER (BASE REACTOR) Lethargy Energy (ev) Space Avg. SpeAverage Space Average Space Average Group Relative Fissioning Neutron Flux Group Neutmn Swrg. Dwn. Rate per Flux per Unit Density cm3 Lethargy (Grp. Avg.) 1 1.0o - 15 x 107 1 5.04 x 109 5.96 x 1012 3.14 x 1012 2 1.5 x.15 x 106.979 4.o6 x 10o9 4.23 x 1012 1.84 x 1o12 3 1.5 ->.15 x 105.796 2.83 x 109 2.13 x 1012 9.25 x 1011 4 1.5 -.15 x 104.512 4.33 x 109 1.34 x 1011 5.83 x lo10 5 1500 ->150.224 5.83 x 1O9 5.70 x 1011 2.48 x 1011 6 150 -,24.0383 2.27 x 109 8.10 x 1010 4.39 x 1010 24 4.91 x 10o8 Note: The space average of total neutron flux within the six lethargy groups per megawatt of reactor power for a base reactor is: = 1.43 x 1013 nv -28

TABLE III PRESSURE DROP VS. PLANT OUTPUT FOR OPTIMIZED BISMUTH-URANIUM GRAPHITE MODERATED REACTOR |Pmax- 1000 psia 700 psia 400 psia Output p APpP psia P psia P psia P HP max max max 60,000 HP 12.8 0.0128 9.4 0.0134 11,4 0.0285 20,000 HP 3.8 0.0038 5022 0 0075 5.3 0,o0132 6,000 HP 0.38 0.00038 0,583 0.00083 01739 oo00185 2, 000 HP 0.059 0.00006 o.o88 0.00013 0o154 0.000385 600 HP 0.0093 0.00001 0.0131 0.00002 0.0224 0.000056 -29

BIBLIOGRAPHY 1. Hammitt, F. G. and Ohlgren, Ho A., "Nuclear-Powered Gas Turbines for Light Weight Power Plants," Paper No. 57-NESC-79, ASME, EJC Congress, February, 1957. 20 Robinson, S. T., "Influence of Working Fluid Characteristics on the Design of Closed-Cycle Gas Turbines," ASME, 1957 National Conference of the Gas Turbine Power Division, March, 1957. 3. Dennison, S. T., Discussion of Reference 2, private communication, February, 1957. 4. Teitel, R. J., "An Internally Cooled Liquid Metal-Fueled Reactor Design," ANS, Preprint 34, 1955. 5. Teitel, R. J., Gurinsky, D. H., and Bryner, J. S., "Liquid-Metal Fuels and Liquid-Metal Breeder Blankets," Chemical Engineering Progress Symposium (Series #13), Nuclear Engineering, Part III, Volume 50, 1954. 6. Fleck, J. A., "Theory of Low Power Kinetics of Circulating Fueled Reactors with Several Groups of Delayed Neutrons," BNL-334, April, 1955. 7. Dwyer, 0. E., Gurinsky, H., and Weeks, J. R., "Liquid Bismuth as a Fuel Solvent and Heat Transport Medium for Nuclear Reactors," ASME, Nuclear Engineering and Science Congress, December, 1955. 8. Chernick, J., "Small Liquid Metal-Fueled Reactor Systems," Nuclear Science and Engineering, 1, pp. 135-155 (1956). 9. Mozer, Bo, "Evaluation of the Univac Data for a Liquid Metal Fuel Reactor," BNL-2395, Brookhaven National Laboratories, July 28, 1954. 10. Ehrlich, R and Hurwitz, H., "Multigroup Methods of Neutron Diffusion Problems," Nucleonics, 12, 223 (1954). -30

POWER OUTPUT r —-.... CONTROL iI HIGH TEMP' LIMIT CONTROL HI- - 0 N cn~~~' II~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ II I Il~~ —-8-a —-8llili II-~ H.P ~~~COMPA I SHAIFT S COOECHAFT r-ITURBINE NEA [I i;I Ii U-1 ~ ~ I1 z~~~~~~~~~ LL II~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0 REFL R F G REGENERATOR II I 11111111 ~ I I i II / l I I II I IBUILT INTO CORE B REFLECTOR I I I I I I I I II I/a Il l I a ~~~~~I <3 I II ~~~~I i I i I I - I;;II l LL~~~~~~~~~~ I L~~~~~~~~~~~~~~~~~~~~~~~~ COOLECR COOLER__ C~~~~~~~~~~~~~~~~~~~~~FG EO -' ~~~~~~~~~~~~~~ATPWRRECO ~T IPECCECOE YL REATO UNT ITHHET RANFE GA TRBNE OWR P:E BUILT INT~~~~O CREGB ENERATOR

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e,j ao o):D:D a0 (,o oO o( -,III~llI,,l,'ilI~lill~lIIllll I A 111 -Wll- M AIf1 1 f! 1 1 1 I I 11Iuiiiil I iL I I II UII 11111 I 11 oil I1 I 111111 T I 114 I I _11 rF001 t IT1i1 -Rt W a. I It MMX: LL-j II~~~~~~~~~~~~~~~~~~~~~~~~~I a. --- W ]III I -"I I It tratU t i1wAIIILt ~tt M l V~t m1l l | m Iz m I ila- r~ll 1lll-a Dx 1w T~ Ul~mT1Lt 1 CO Lil I IfiI " -- (J'~p)~1b)(;bs(J)/n iG ep!S &oH uo lue!o!jjao 3 Wrl!J 11- e L~l 1111 1I nlql l 11H 11 1lliLG II II L 11 i 1 rll iI IH I N F N ~l II IltrlllT II IHIIM11I1I I II rI E T ill~llll |1lq~Idinliiil|ii 111 iiiiif -l- 1 llI I I I11rI II oiil~Tl1IH 1 lTI_ =e JaI ~~~~~~~~~~~~~~~~~~~~~~~~~11- lL lFTF laAL~llIIII4 11F~glm lillLl~ I+ T- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I a L 00 [ g X E I I ~~~~~~4 1111I1lr1 Wt Hll 1 LlllIII 11.1 llLI I I IIIII111111 ~ll tllt lIlIil11_~l~ll~IIIII111ll'< TT~~~~~~~~~~~~~~~~~~~ I -IIt11I~k~iiII1111111IILI~l11II11111III HI I I I1 11lilllIIII1iII t~I (.3 b BP (41lllllllrll Ibs J4) I is 1 1111 10 u|1111 091.3.n1118l IwI1 1 -4 llIIrtTTIlllrrT~ll -

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201 FIG. 14 URANIUM, PLUTONIUM, AND THORIUM SOLUBILITY IN BISMUTH 18 16LU PTNIUM 16 14 l w~~~ ~ TEP RTR -__ I tlRANIJM 21 I 0 -t —~I 400 600 800 1000 1200 1400 1600 1800 2000 TEMPERATURE F0

1700 1690 1680 0 U-~~~~~~~-! 1660 a. Ui~~~~~~~~~~~~~~~~~~ I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I -'1640 Z' C —-_Optimized Turbine Inlet Tem pera- - I -I ——. -— I- __ t -.~o Assumed Average Reactor Temp. t- 1620 ~(Coolant Tube Inner Surface 16zD Temp.) - 1700 F ture, vs. Plant Output ~FIG. 1. 1600 2X102 3 4 5 6 7 9 103 2 3 4 5 6 7 8a9104 2 3 4 5 6 789105 PLANT output HP

240 230 Optimized Log Mean Temperature Difference vs. Plant Output 00 F_ _ 220 Assumed Average Temp. of Coolant Tube Inner Surface - 1700 F ~ g- 210 Working Fluid- Air w z 200 w 200~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0 u"- 190 w ir 18C I-~~~~~~/ D ce U 170 w 160 z w 150 (..,-3 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~401) P;IA 0..J 140 FIG. 16 130 120 1010 3PLANT oUTPUT HP PLANT OUTPUT, HP

L_ o0 Optimized Gas Side Heat Transfer C_ 600 Coefficients' vs. Plant Output w a. 0 SI Assumed Average Coolant Tube z Surface Temp. - 1700 F w W Working Fluid - Air. 50 0 -I —_ CL z w IalX: 40 0 LU t,-X cr H I 200 I Z w __ _ _ _ _____I I I I ~ XFI. 1 0 300 ur_ w O G) 2X 102 10 O P P OUTPUT, H P

590 460 PSIA 580 - 570 U' o 560 X' o _ _ _ _ _ _ _ _ _ _ _ _ _ _ __-_ _ _ _ 7 0 P IA 550 w I3 530 IC 0X 520 YE 510 w C, < 500 50 0 I I The Raise in Temp. of Gas Stream Z - Through the Reactor (for Optimized w 490 Condition) 0) w - Assumed Average Coolant Tube Surface X 480 -= Temp. - 1700 F z 450 L I I I I I I11 - - Working Fluid - Air w N470 a. 0 460 FIG. 18 450 I03 I04 I0s PLANT OUTPUT, HP

;. i 11i!1! I I - Optimized Core Diameter vs. Plant Output 7.0O _ Assumed Average Temp. of Coolant Tube Surface- 1700 F ji ~ ~ - w!Working Fluid - Air ~~i~ ~ _ -— 4 PIA I~~~~~~~~~~ 60 7 41A U-~~~~PIA 0 I_ W 4.0 0 w 0 2 x 10' 3 4 5 67 89 103 2 3 456 677a9 904 4 5 6 7 910 PLANT output HP' o i o ~ ~ ~ ~ ~ ~ ~ ~ ~~. - ~ o ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~L, r-::.0ii z0.... ~ ~~~~~~~~~~~~~~FIG. 19l 2 xI0' 3 4 5 6? 8 9 103 2;s 4- 5 6 7 8 9 104 3 4 5 6 7 8 9105 PLAbiT output HP'

F0 900.. 850 -.. Irl w ~ ~ ~~~~~ I'"' ~ —<4 o i j ~ 71 (9 w JJ i5P ll! z Lii 800'< w ~~~~~~~~~~~~~~~~~~~~~~~I 750 Temperature Leaving Optimized Regenerator! FIG. 20 700 1500 F turbine inlet temp.j _102 103 HP output 104 10 2 103 HP output 1 015

F0o 700 I'~~~~~~~~~~~(-o 650 H w z w ul 600 __ _ 45 PSI 0 550 0. a.Gas Temperature Leaving 2 W Optimized Regenerator Turbinfe Inlet Temperature 500 1200 F 600 " Working Fluid - Helium FIG.21 102 103 output HP 1O

.38.36 Plant Thermal Efficiency vs..34 P reactor.32 x —1000 to 3000 BHP n ~~45t PSl~ -X ______ _____~ ___ ___ ___v_770 P IA 41 A PAPSIA 790 PS.31 1 I I I I ~~~~~~~~~~~~~~t ~ ~ I ~ ~ ~ 0? PSIA.288.26 ~ ~i ~,,I~~ i I -T~~~S~~L I I I I 150 F'URBIN t~.24I IN T THMP..22 X.2.I 6 I200 F TURBIIE INLET TEMP..14 FIG. 22.12 0.01.02.03.04 05.06.07 08.09.10.11.12.13.14.15.16.17 ]8 Ap/p -- REACTOR