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Iterative Procedure for Enrichment Zoning of Nuclear Thermal Rockets


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ITERATIVE PROCEDURE FOR ENRICHMENT ZONING OF NUCLEAR THERMAL ROCKETS By BENJAMIN W. AMIRI A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by Benjamin W. Amiri

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This document is dedicated to the explora tion of space for the betterment of all mankind.

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iv ACKNOWLEDGMENTS I would like to thank Dr. Samim Anghai e, Dr. Edward Dugan, and Dr. David Poston for serving on my supervisory committee. Thanks go as well to Richard Kapernick and Tom Marcille of Los Alamos National Laboratory, and Steve Simpson of Marshall Space Flight Center for generously sharing their time and expertise. Finally, thanks go to my family, without wh om I would certainly not be where I am today.

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v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES...........................................................................................................ix ABSTRACT....................................................................................................................... xi CHAPTER 1 INTRODUCTION........................................................................................................1 Benefit of NTR Systems...............................................................................................1 The Rover Program.......................................................................................................2 Objectives..................................................................................................................... 3 2 METHODOLOGY.......................................................................................................5 MCNPX........................................................................................................................5 TMSS........................................................................................................................... .7 3 NUCLEAR ROCKET DESIGN.................................................................................10 4 NTRGEN AND NTRFILTER....................................................................................16 NTRgen.......................................................................................................................16 Thermal Expansion..............................................................................................18 Input Files............................................................................................................19 Primary input file (xxx.inp)..........................................................................20 Other required input files.............................................................................25 Optional input files.......................................................................................27 NTRFilter....................................................................................................................28 5 RESULTS...................................................................................................................33 Unzoned Core Calculations........................................................................................33 Zoning Calculations....................................................................................................41 906 Fuel Hex Core...............................................................................................41 1194 Fuel Hex Core.............................................................................................44

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vi 1518 Fuel Hex Core.............................................................................................46 1410 Fuel Hex Core.............................................................................................48 1770 Fuel Hex Core.............................................................................................50 Final Designs..............................................................................................................52 6 CONCLUSION...........................................................................................................60 APPENDIX A NTRGEN PRIMARY INPUT FILE...........................................................................62 B NTRGEN CELLCARDS INPUT FILE......................................................................64 C NTRGEN MATCARDS INPUT FILE.......................................................................67 D NTRGEN TEMPERATURE INPUT FILE................................................................69 E NTRGEN ZONE INPUT FILE..................................................................................70 F MCNPX INPUT FILE................................................................................................92 LIST OF REFERENCES.................................................................................................207 BIOGRAPHICAL SKETCH...........................................................................................208

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vii LIST OF TABLES Table page 2-1. Polynomials generated by TMSS.................................................................................7 4-1. Valid cell identifiers in cellcards ...............................................................................26 4-2. A sample NTRfilter zone structure............................................................................31 4-3. A sample NTRfilter rezoning calculation..................................................................31 5-1. Dimensions of considered NTR cores........................................................................37 5-2. Criticality results for unzoned NTR cores..................................................................37 5-3. Criticality and runtime co mparison for unzoned NTR cores.....................................38 5-4. Hex peaking factors for unzoned NTR cores.............................................................38 5-5. Criticality results for 906 fuel hex core zoning iterations..........................................42 5-6. Enrichment zone description for 906 fuel hex core zoning iterations........................42 5-7. Hex peaking factor for 906 fuel hex core zoning iterations.......................................43 5-8. Computation time for 906 fuel hex core zoning iterations.........................................43 5-9. Criticality results for 1194 fuel hex core zoning iterations........................................45 5-10. Enrichment zone description for 1194 fuel hex core zoning iterations....................45 5-11. Hex peaking factor for 1194 fuel hex core zoning iterations...................................46 5-12. Computation time for 1194 fuel hex core zoning iterations.....................................46 5-13. Criticality results for 1518 fuel hex core zoning iterations......................................47 5-14. Enrichment zone description for 1518 fuel hex core zoning iterations....................47 5-15. Hex peaking factor for 1518 fuel hex core zoning iterations...................................48 5-16. Computation time for 1518 fuel hex core zoning iterations.....................................48

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viii 5-17. Criticality results for 1410 fuel hex core zoning iterations......................................49 5-18. Enrichment zone description for 1410 fuel hex core zoning iterations....................49 5-19. Hex peaking factor for 1410 fuel hex core zoning iterations...................................49 5-20. Computation time for 1410 fuel hex core zoning iterations.....................................49 5-21. Criticality results for 1770 fuel hex core zoning iterations......................................50 5-22. Enrichment zone description for 1770 fuel hex core zoning iterations....................51 5-23. Hex peaking factor for 1770 fuel hex core zoning iterations...................................51 5-24. Computation time for 1770 fuel hex core zoning iterations.....................................51 5-25. Dimensions and nuclear charact eristics of final NTR designs.................................54 5-26. Nuclear characteristic anal ysis of final NTR designs...............................................56

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ix LIST OF FIGURES Figure page 3-1. NTR flow paths..........................................................................................................10 3-2. Axial view of a sample NTR system..........................................................................12 3-3. Axial view of flow inlet a nd outlet manifolds for NTR system................................12 3-4. Axial view of NTR system exit chamber..................................................................13 3-5. Overall layout of NTR core........................................................................................13 3-6. NTR core periphery and control drum.......................................................................14 3-7. NTR fuel hex and tie tube...........................................................................................14 4-1. MCNPX models produced by NTRgen......................................................................17 4-2. Axial view of expanded core periphery.....................................................................19 4-3. Core periphery............................................................................................................ 25 4-4. Outline of the NTRgen iterative procedure...............................................................32 5-1. Comparison of initial MCNPX runs for 906 fuel hex case.......................................34 5-2. Comparison of initial MCNPX runs for 1194 fuel hex case.....................................35 5-3. Comparison of initial MCNPX runs for 1518 fuel hex case.....................................35 5-4. Comparison of initial MCNPX runs for 1410 fuel hex case.....................................36 5-5. Comparison of initial MCNPX runs for 1770 fuel hex case.....................................36 5-6. Relative fission rate in the unzoned 906 fuel hex core..............................................39 5-7. Relative fission rate in the unzoned 1194 fuel hex core............................................39 5-8. Relative fission rate in the unzoned 1518 fuel hex core............................................40 5-9. Relative fission rate in the unzoned 1410 fuel hex core............................................40

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x 5-10. Relative fission rate in the unzoned 1770 fuel hex core..........................................41 5-11. Relative fission rate in the 906 fu el hex core through zoning iterations.................43 5-12. Radial layout of zoned 906 fuel hex core................................................................44 5-13. Detailed view of enrichment zoning in 906 fuel hex core.......................................45 5-14. Relative fission rate in the 1194 fu el hex core through zoning iterations...............47 5-15. Relative fission rate in the 1518 fu el hex core through zoning iterations...............48 5-16. Relative fission rate in the 1410 fu el hex core through zoning iterations...............50 5-17. Relative fission rate in the 1770 fuel hex core through zoning iterations................52 5-18. Expanded partially homogenized k-eff for zoned NTR cores..................................53 5-19. Shutdown swing versus height -to-diameter ratio for NTR cores............................56 5-21. Fission rate distribution for final 1194 fuel hex NTR core design..........................58 5-22. Fission rate distribution for final 1518 fuel hex NTR core design..........................58 5-23. Fission rate distribution for final 1410 fuel hex NTR core design..........................59 5-24. Fission rate distribution for final 1770 fuel hex NTR core design..........................59

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xi Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ITERATIVE PROCEDURE FOR ENRICHMENT ZONING OF NUCLEAR THERMAL ROCKETS By Benjamin W. Amiri August 2006 Chair: Samim Anghaie Major Department: Nuclear and Radiological Engineering Nuclear thermal rockets were designed a nd tested during the Rover program, which lasted from 1955 to 1973. By using hydrogen as the propellant, these systems have the potential to reach a specific impulse more than twice that of conventional chemical rockets. This thesis describes the developmen t and implementation of NTRgen and NTRfilter, two programs which can be used in concert to design nuclear thermal rocket cores. NTRgen produces detailed MCNP X decks as well as MCNPX decks which include partial homogenization of some core components to accelerate the calculation. NTRgen accounts for axially varying thermal e xpansion of the core as well as providing a core mass estimate. NTRfilter reads fission ra te tallies which are written by NTRgen and run with MCNPX. Based on these tallies NTRfilter will produce an enrichment zone map to reduce the core radial peaking factor. This zone map can subsequently be read by

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xii NTRgen to produce MCNPX models of a zoned core. By iterating between NTRgen and NTRfilter one can arrive at a core design w ith a radial peaking factor less than 1.15. The final design chosen in this study c ontains 1194 fuel hexes arranged in a hexagonal lattice and has a reactor mass of 2855.2 kg. The hex peaking factor calculated for this core is 1.10737 using the partia lly homogenized expanded MCNPX model.

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1 CHAPTER 1 INTRODUCTION As the exploration of space progresses, more ambitious missions will be planned requiring systems that produce more power a nd can provide faster transit times than traditional chemical systems. Nuclear fission is a logical successor to these chemical systems, as fission is an established technol ogy for terrestrial power applications and has the potential to meet the more demanding system requirements. Nuclear fission power can be utilized in space to provide propul sion via nuclear electric propulsion (NEP) or nuclear thermal propulsion (NTP). An NEP system uses the heat from fission to produce electricity, which powers a propulsion drive (oft en an ion thruster). The focus of this study is NTP, which uses the heat from fission to heat a fluid which is then ejected from the core to provide thrust. An NTP system of this type is referred to as a nuclear thermal rocket (NTR). Benefit of NTR Systems The performance of a rocket can be e xpressed in terms of specific impulse ( Isp). The formula for specific impulse is given below: M T m F Isp In this equation, specific impulse, Isp, is equal to F the thrust (the force imparted upon the rocket by the exiting propellant) overm the propellant mass flow rate. Specific impulse is proportional to the square root of the exiting propellant temperature, T over the molecular weight of the propellant, M For a given propellant mass flow rate, a

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2 system with a higher Isp will get more thrust from the propellant than a system with a lower Isp. Similarly, for a given thrust level the higher Isp system will require less propellant mass to achieve the same thrust level as a lower Isp system. Chemical rocket systems combine hydrogen (H2) and oxygen (O2) to form H2O with a molecular weight of ~18 to be used as propellant. Nuclear thermal rockets use H2 which has been heated from fission as the propellant. Since H2 has a molecular weight of ~2 we would expect an NTR system operating with the same propellant exit temperature as a chemical system to have a specific impulse great er than the chemical system by about a factor of 3 ( 2 / 18). In practice, the exit propellant temperature is lower for NTR systems than for chemical systems, resulting in a specific impulse of solid -core rockets about twic e as large as that of chemical rockets (9600 m/s for NTR syst ems vs. 4400 m/s for chemical rockets) [1]. A higher specific impulse system for a ma nned mission (i.e., to Mars) implies that the craft will be able to travel faster, t hus reducing transit time and minimizing astronaut exposure to cosmic radiation. For an un manned mission, the higher specific impulse system will be able to devote more of its mass allotment to cargo and/or science equipment. The Rover Program Significant development and testing of NTR systems was done during the Rover program, which lasted from 1955 to 1973. Th e Rover program began as a research program to develop new means of deploying la rge-scale weapons. However, decreases in the weight of weapons systems as well as improvements in the capabilities of chemical rockets led to a shift in focu s of the Rover program from weapons deployment to space exploration. Nineteen major nuclear test s were performed in support of the Rover

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3 program. These tests began with the Kiwi series of reactors, whose purpose was to demonstrate the feasibility of NTR technology. After the successful Kiwi tests was the NRX series, followed by the Phoebus series. Later NTR tests included the XE, Peewee and finally Nuclear Furnace in 1972. Among the records set by these tests were the highest steady-state power leve l ever achieved in a reacto r (over 4,000 MW in the June 1968 Phoebus-2A test) as well as the highest operating temperature and average power density (2,550 K and 2,340 MW/m3 in the December 1968 Peewee test) [2]. The Rover program demonstrated the vi ability of NTR systems by designing, building, testing and operating these reactors. The integr ation of knowledge obtained during this program led to the small engine design. Unfortunate ly, though a technical success, changing national prio rities eventually led to cance llation of the Rover program before small engine could be built and test ed. The small engine design is the starting point for the NTR systems considered in this study, and will be discussed in Chapter 3. Objectives The objective of this task was to develop the process and tools with which one could arrive at a neutronically feasible NTR design. MCNPX was to be used as the primary neutronic analysis code. There are three standard modes by which reactivity can be affected throughout the life of a nuclear rocket: thermal expansion (increased dimensions and corresponding density reducti on), temperature-depe ndent cross-section effects (Doppler broadening), and core burnup. NTRgen accounts for thermal expansion explicitly, and the othe r effects are assumed to be no more than 2.5%. Thus, to ensure that the core can operate through its desi gned life the beginnin g-of-life thermally expanded k-eff should be above 1.025. As this approximation becomes more refined only incidental changes in the overall design process will be required. The beginning-of-

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4 life shutdown k-eff (i.e., all control drums turned in) should be below 0.985 to ensure pre-launch subcriticality. A summar y of objectives is given below: Create a program that can generate neut ronic (MCNPX) models of NTR cores. This program should do the following: th ermally expand the core, write tallies necessary to determine peaking factors, pa rtially homogenize the core to accelerate the calculation with a minimal loss in accuracy, provide a mass estimate of the reactor system. Calculate and implement an enrichment zoning scheme to reduce the hex peaking factor. Use these tools to arrive at a design with a radial peaking factor below 1.15, a beginning-of-life thermally expanded k-eff above 1.025 and beginning-of-life shutdown k-eff below 0.985.

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5 CHAPTER 2 METHODOLOGY Two codes which played a major rule in execution of this study were MCNPX and TMSS (Thermal-Mechanical SpreadSheet). MCNPX is used to analyze the neutronic characteristics of a system, while TMSS performs thermal analysis. MCNPX Neutronic analysis of the NTR cores was performed with MCNPX, a widely used Monte Carlo transport code developed a nd maintained at Los Alamos National Laboratory. The Monte Carlo method is a tec hnique which allows one to simulate any process for which one has probabilistic data. MCNPX allows one to simulate a detailed geometry and to essentially conduct a “numer ical experiment” by tracking the behavior of simulated particles through the system. Since the Monte Carlo method is by nature a stochastic process, statistical e rrors will inevitably exist [3]. The first step in the Monte Carlo method is to determine the probability density function (pdf), p(x) of the process being considered. The pdf has the characteristic that integrating over its entire range (in this case from xL to xU) yields 1. U Lx xdx x p 1 ) ( The cumulative distribution function (CDF), P(x) is then given by x d x p x Px xL ) ( ) ( One can then simulate this statistical pr ocess by setting the CDF equal to a random number between 0 and 1, and sampling.

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6 ) ( ; ) (1x P x x P In the case of a neutron traveling thr ough a medium, the pdf for the distance the neutron travels in the medium without collision is given as dx e dx x px tt ) ( This equation is indeed a valid pdf, as it satisfies the criteria of integrating to 1 over its range (in the case of a traveling particle its range is from 0 to ). We then obtain the CDF following the procedure given above. x x tx d e x Pt0) ( ; xte 1 By then solving for x the sampled flight distance, one can generate a series of random numbers, and statistically simulate th e free-flight neutron distance. t tx ) ln( ) 1 ln( MCNPX employs this technique not just fo r neutron flight, but for all statistical processes that make up a fission system. By tracking particle hi stories the overall neutronic behavior of the system, including multiplication factor, reaction rates and flux profiles, can be ascertained. Running more particle histor ies decreases th e statistical uncertainty of the calculation. The Monte Carlo method has the disadvantag e that it tends to be relatively time consuming compared to deterministic techni ques. However, one can simulate complex geometries readily and use continuous energy cr oss-sections. The cro ss-sections used in this study were generated from the Evaluate d Nuclear Data Files library ENDF/B-VI. The ENDF/B-VI files were processed using the NJOY Nuclear Data Processing System.

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7 TMSS TMSS is a thermal-mechanical analysis tool developed for nuclear thermal rockets by Richard Kapernick of Los Alamos Nationa l Laboratory. TMSS has the ability to generate polynomials for fuel he x pitch (the flat-to-flat dist ance of an individual hex) and coolant channel diameter as a function of the core height. The coolant channel diameter is set such that the pressure drop through the core does not exceed 2.6 MPa. Fuel hex pitch is set so that maximum fuel centerlin e temperature is 3050 K. Core exit coolant temperature is fixed at 2700 K. TMSS also calculates the necessary thermal power in the core, which for these designs is 1608.84 MW. It should be noted that these cores are designed to operate for 10 full-power hours. The polynomials are given in Table 2-1, where the polynomial fit for each dimension follows the formula 22 1 0 h A h A A d where d is the dimension of interest (fuel pitch or coolan t diameter, given in cm) and h is core height in cm. The polynomials are shown in Figure 2-1 and 2-2. Table 2-1. Polynomials generated by TMSS. Fuel hexes Fuel pitch A0 A1 A2 Coolant diameter A0 A1 A2 906 1194 1518 1410 1770 -1.1039e0 8.0749e-1 3.8015e-1 4.2688e-1 6.3551e-1 3.2853e-2 5.7636e-3 1.5681e-2 1.4214e-2 8.8134e-3 -8.5073e-5 4.2062e-5 2.7919e-5 2.3639e-5 1.1355e-4 1.9209e-1 1.6708e-1 1.5075e-1 1.5331e-1 1.3869e-1 4.5098e-4 5.1683e-4 5.2037e-4 5.7035e-4 5.9786e-4 -6.2840e-7 -9.9251e-7 -1.0894e-6 -1.3457e-6 -1.6937e-6 These dimensions are set by the limiting fuel hex, i.e., the fuel hex that produces the most power. Since the maximum power hex in effect drives the design, it is advantageous to have as uniform a power di stribution as possible, hence the importance of enrichment zoning.

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8 1.500 1.600 1.700 1.800 1.900 2.000 2.100 60.0080.00100.00120.00140.00160.00 Core height (cm)Fuel hex pitch (cm) 906 1194 1518 1410 1770Figure 2-1. Fuel hex pitch polynomial generated by TMSS. 0.1500 0.1600 0.1700 0.1800 0.1900 0.2000 0.2100 0.2200 0.2300 0.2400 0.2500 60.0080.00100.00120.00140.00160.00 Core height (cm)Coolant channel diameter (cm) 906 1194 1518 1410 1770Figure 2-2. Coolant diameter polynomial generated by TMSS.

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9 There are other means by which the effect of maximum power hexes can be offset, such as controlling the flow distribution through the core usin g variable size orifices, but this method tends to increase pressure drop. The TMSS polynomials serve to ensure that the final core design is not attractive simply from a neutronic sta ndpoint, but that the design is thermally feasible as well. While the TMSS polynomials were employed for this study, they are not necessary to the link between NTRgen and NTRfilter which will be described in Chapter 4.

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10 CHAPTER 3 NUCLEAR ROCKET DESIGN The NTR system examined in this study is similar to those developed during the Rover program. The small engine flow cycle, fuel form, and dimensions were used as a starting point in arriving at a new design. A simplified flow diagram is given in Figure 3-1 [4]. Figure 3-1. NTR flow paths. PUMP TURBINE TANK Flow manifolds Core Reflector Exit chamber Nozzle Flow paths: Tank feed Fuel Tie tube Nozzle/reflector

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11 Liquid hydrogen is pumped out of the propellan t tank (not shown to scale) at which point the flow is split between two paths. A portion of the hydrogen flows down through the center of the tie tubes and up through the out er portion of the tie tubes. This flow serves to cool the tie tubes, and the heated hydrogen then flows through a turbine which powers the pump. After exiting the turbine, the hydrogen flows through the fuel where it is heated before exiting through the nozzle as propellant. The hydrogen that does not enter the tie tubes is used to cool the no zzle. After cooling the nozzle, this hydrogen flows up through the reflector where it mixes with hydrogen exiting the turbine before entering the core through the fuel coolant manifold, then flowing through the core and exiting the nozzle as heated propellant. An axial view of the MCNPX model is given in Figure 3-2. Figure 3-3 shows the flow control manifolds while Figure 3-4 shows the core exit chamber. Reactivity is controlle d through the use of rotating dr ums in the radial reflector. These drums contain a beryllium oxide (B eO) neutron reflector and a boron carbide (B4C) neutron poison. By rotating the drums su ch that the poison is nearest to the core, reactivity can be decreased and the core shut down. The overall radial core layout is given in Figure 3-5, while a more detailed view of a control drum in the most reactive position (poison turned out) is given in Figure 3-6. The reactor core is made up of fuel he xes and tie tubes. These components are shown in Figures 3-6 and 3-7. The fuel form used in this study is a (U,Zr)-C graphite composite which was studied and tested during th e Rover program [5]. This fuel consists of 5.2% uranium (by weight), 56.0% zirconium, and 38.8% carbon.

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12 Figure 3-2. Axial view of a sample NTR system. Figure 3-3. Axial view of flow inle t and outlet manifolds for NTR system. Flow inlet and outlet manifolds Reactor core Exit chamber Closeup in Figure 3-3 Closeup in Figure 3-4 Fuel coolant inlet Tie tube coolant inlet (down pass) Tie tube coolant outlet (up pass) Expansion gap Tie tube Radial reflector Fuel hexes Drum poison Vessel coolant Outer vessel Shield Top interface plate Bottom interf. plate Support plate Control drum

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13 Figure 3-4. Axial view of NTR system exit chamber. Figure 3-5. Overall layout of NTR core. Each fuel hex contains 19 hydrogen coolan t channels. Each coolant channel is coated with a thin layer of zirconium car bide (ZrC) coating to prevent interaction between the hot flowing hydrogen and the fuel. The tie tube provide s structural support for the core. The tie tube stru ctural material is In conel-718. The tie tube also contains a zirconium hydride (ZrH) moderator to soften th e neutron spectrum. The tie tube insulator (low density zirconium carbide, ZrC) pr ovides thermal insula tion between the high temperature fuel and the tie tube moderator. The tie tube matrix is composed of ZrC at a density of 8.64 g/cc, whereas the low de nsity ZrC insulator is at 0.64 g/cc. Fuel coolant Tie tube coolant Exit chamber

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14 Figure 3-6. NTR core peri phery and control drum. Figure 3-7. NTR fuel hex and tie tube. Control drum Drum poison Radial reflector Vessel coolant Outer vessel Tie tube Fuel hex Reflector slat Tie tube coolant (down pass) Tie tube structure Tie tube moderator Tie tube coolant (up pass) Tie tube structure Tie tube insulation Tie tube matrix Fuel Fuel coolant Fuel coating

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15 The focus of this study is the use of NT Rgen and NTRfilter to flatten the power distribution in the core for the reasons describe d in Chapter 2. This issue arose during the Rover program and was addressed by varying the fuel loading through the core. During the Phoebus tests, four loading zones we re used initially bu t were found to be insufficient. A subsequent test containe d over twenty loading zones and achieved a significantly more uniform pow er distribution [6]. The goal of this study was to determine the effectiveness of using variab le fuel enrichment as a means of power shaping as opposed to va riable fuel loading.

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16 CHAPTER 4 NTRGEN AND NTRFILTER NTRgen and NTRfilter are codes which were developed to facilitate the generation of robust MCNPX NTR models and to quickly analyze prod uced data, respectively. NTRgen NTRgen is a Fortran 90 code used to ge nerate MCNPX models of nuclear thermal rockets within the preconceived design space de scribed in Chapter 3. NTRgen allows one to readily modify parameters such as core dimensions, materials, drum rotation angle, temperatures, etc. NTRgen also calculates the mass of the modeled system, including the fuel, tie tubes, radial reflector, pressure vessel, nozzle, flow manifolds, and internal shield. NTRgen produces several MCNPX decks for each scenario specified by the user. These decks include a fully discrete model, a partially discrete model, and a homogenized model. A comparison of how the fueled core is represented in each of the three models is given in Figure 4-1. As this figure shows, in the fully discrete model each individual coolant channel is explicitly modeled, as is each component of the tie tube. In the partially discrete model, the fuel hex is composed of a homogeneous mixture of fuel, coolant and coating. The tie tube is explicitly modele d in the example given in Figure 4-1B, but the user has the option of employing a homogenized model of the tie tube in the partially discrete model as well. The mass of each com ponent of the hex will be calculated, a new MCNPX material card will be written based on this calculation, and that homogenized material will be placed in th e hex. The partially discrete model has the

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17 advantage of using far fewer surfaces than th e fully discrete mode l, thus reducing the MCNPX computation time. Fi gure 4-1C shows the fully ho mogenized model, in which each ring of hexes is modeled as a homogenized cylinder. The center ring consists of one homogenized tie tube, the next ring consists of six homogenized fuel hexes, and so on. While this model uses the fewest surfaces of all models generated, it also employs more geometric assumptions than the other models The homogenized model is incapable of accounting for radial variations, limiting its usefulness in calculating peaking factors. Due to these limitations, the homogenized m odel was used sparingly in this study. Figure 4-1. MCNPX models produced by NTRgen. A) fully discrete. B) partially discrete. C) fully homogenized. A B C

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18 Thermal Expansion The user has the option of producing MC NPX decks that represent a thermally expanded NTR core. To activate this option, th e user must input the system temperatures in either the primary input file or in a separate temperature fi le, as will be discussed in the following sections. Since temperatures in a NTR can vary axially by over 2000 K NTRgen does not expand the core by a singl e average axial expansion, but allows the user to expand up to ten axial core regions independently. Th ermal expansion is dictated by the following equation, where hcold is an unexpanded core dimension such as radius or height, hhot is the expanded core dimension, is the temperature-dependent coefficient of thermal expansion (CTE), T is the temperature of the material, and T0 is room temperature (assumed to be 293 K). 0) ( 1 T T T h hcold hot Similarly, density is reduced by the following equation, where cold is an unexpanded material density and hot is the expanded material density. 3 0) ( 1 T T Tcold hot All fuel material in a given axial level is expanded uniformly based on the axial fuel temperature profile and fuel CTE (i.e., no radial expa nsion variation). Tie tube materials at each axial level are expanded usi ng an average tie tube temperature and the fuel CTE. An axial closeup of an expanded core periphery is given in Figure 4-2. In this figure, hydrogen is heated while flowing from core inlet (top) to exit (bottom). Since axial core temperature variation is modeled wh ereas radial reflector temperature is treated as uniform, the expansion gap decreases axially Reflector thermal expansion is assumed

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19 to be dictated by the radial reflector meat C TE at the radial reflector temperature given on the primary input file. Figure 4-2. Axial view of expanded core periphery. Input Files The primary input file for NTRgen must ha ve a “.inp” extension. For example, a case with the root name “test” would have a primary input file named “test.inp”. Two other required input files are named “cellcar ds” and “matcards”. In addition to the required input files, there are two optional input files: the te mperature file with a “.tmp” extension (in this case test.tmp), and the zone map with a “.zon” extension (giving test.zon). Core Control Drum Radial Reflector Expansion gap Axial expansion region

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20 Primary input file (xxx.inp) The primary input file must be ordered exact ly as described below. The input file line number is given, followed by the variable na me, the variable type (real, integer, or character), and a brief descripti on of the variable. The primary input file is the file with which the user has the most di rect interaction. A sample NTRgen primary input file is given in Appendix A. 1. difltt – a real variable, inner flow diam eter of the tie tubes, given in cm 2. titt – real, thickness of the inner tie tube structure, given in cm 3. tmott – real, thickness of the tie tube moderator, given in cm 4. tofltt – real, thickness of the outer tie tube flow, given in cm 5. tott – real, thickness of the outer tie tube structure, given in cm 6. tinstt – real, thickness of tie tube insulation, given in cm 7. nrfflw – an integer variable, number of coolan t channel rows in the fuel (1, 2, or 3). 1 = 1 coolant channel, 2 = 7 coolan t channels, 3 = 19 coolant channels. 8. dflfh – real, diameter of the fuel coolant channels, given in cm 9. tcotmin – real, thickness of the fuel coolan t channel coating at core inlet, given in cm 10. tcotmax – real, thickness of the fuel coolan t channel coating at co re outlet, given in cm. If tcotmax and tcotmin are the same the coating thickness will be uniform axially at beginning-of-life. The user ha s the option of increa sing coating thickness axially in which case the coating thickness wi ll be uniform in each axial region, but increase linearly throughout the core. 11. pflwsl – real, diameter of the slat hex c oolant channel, given in cm (if positive) OR fraction of the slat hex area used for c oolant, given in percent (if negative) 12. nttrmax,ncut OR tslhex – two integer vari ables, the number of rows of modules and the number of modules cut at the edge OR one real variable, the minimum thickness of slats at the edge given in cm (if negative). Number of modules cut at edge is shown in Figure 4-3. A module is defined as a tie tube surrounded by the appropriate number of hexes (this nu mber is set by nftrat, entry # 14). 13. pitch – real, the flat-to-flat distan ce of the fuel hexes, given in cm

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21 14. nftrat –integer, ratio of fuel hexes to tie tubes, (0, 2, 3, or 6). The “0” option indicates no tie tubes in the core. 15. blank line delimiter 16. dcore – real, diameter of the core (f uel, tie tubes, slats), given in cm 17. texgap – real, thickness of the expansion gap between the core and the reflector, given in cm. Note that if this dimens ion is insufficient to accommodate thermal expansion it will automatically be resized. 18. tbarl – real, thickness of the core barrel, given in cm 19. trr – real, thickness of the radi al reflector, given in cm 20. tvcgap – real, thickness of the coolant ga p between the radial reflector and the pressure vessel, given in cm 21. tves – real, thickness of the pr essure vessel, given in cm 22. zcore – real, core height, given in cm 23. nrr – integer, number of control drums 24. ddrum – real, diameter of the control drums, given in cm 25. tdrgap – real, thickness of the gap between the drum and the radial reflector, given in cm 26. tdrpoi – real, thickness of cont rol drum poison, given in cm 27. angdrp – real, angle transcended by the c ontrol drum poison, given in degrees 28. angrot – real, angle at which the drums ar e rotated, given in degrees, 0 being the most reactive (drums turned out), 180 be ing the least reactive (drums turned in) 29. blank line delimiter 30. naxcol – integer, number of axial coolant regions. Coolant density changes axially due to the large temperatur e and pressure gradients throughout the core. This variable indicates how many regions shoul d be used to represent that axial variation. This number also dictates how many axial regions will be used for axially varying thermal expansion. 31. tinlet – real, coolant temperature at core inlet, given in K 32. toutlet – real, coolant temperatur e at core outlet, given in K 33. pinlet – real, coolant pressure at core inlet, given in MPa

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22 34. pdrop – real, coolant pressure drop th rough the core, given in MPa. If no temperature input file is given then tinlet, toutlet, pinlet, and pdrop will be used to determine the axially varyi ng hydrogen coolant density using the ideal gas law. Temperature will be assumed to increase from tinlet to toutlet with a cosine distribution, while pressure is assumed to drop linearly from pinlet to (pinlet pdrop) linearly. 35. tintt – real, coolant temperature at tie tube inlet, given in K 36. toutt – real, coolant temperature at tie tube outlet, given in K 37. pintt – real, coolant pressure at tie tube inlet, given in MPa 38. pdroptt – real, coolant pressure drop through the tie tube, given in MPa 39. tempref – real, temperature of th e radial reflect or, given in K 40. zspgap – real, thickness of the gap between the top of the core and the support plate, given in cm 41. zsplat – real, thickness of th e support plate, given in cm 42. zttupm – real, thickness of the tie tu be up-flow manifold, given in cm 43. zbipl – real, thickness of the bottom interface plate, given in cm 44. zttdnm – real, thickness of the tie tu be down-flow manifold, given in cm 45. ztipl – real, thickness of the top interface plate, given in cm 46. zfcinm – real, thickness of the fuel coolant inlet manifold, given in cm 47. zshld – real, thickness of the internal shield, given in cm 48. dttipl – real, diameter of tie tube down-fl ow through interface plates, given in cm 49. tchnl – real, thickness of st ructure separating tie tube down-flow from tie tube up-flow in interface plates, given in cm 50. ttopl – real, thickness of tie tube up-flo w region through interface plates, given in cm 51. dfcpl – real, diameter of fuel coolant flow through interface plates, given in cm 52. ttupm, pttupm – two real variables, th e tie tube up-flow manifold coolant temperature given in K, a nd pressure given in MPa 53. ttdnm, pttdnm – two real variables, th e tie tube down-flow manifold coolant temperature given in K, a nd pressure given in MPa

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23 54. tfcinm, pfcinm – two real variables, the fuel coolant manifold inlet temperature given in K, and pressure given in MPa 55. zcham – real, length of the exit chamber, given in cm 56. tcham – real, thickness of the exit chamber, given in cm 57. ihom – integer (0, 1, or 2), if ihom=0 the core region (fuel hexes and tie tubes) will be modeled as one region and the radial reflector will be modeled using R-Z geometry in the homogenized case, if ihom=1 the core region will be homogenized by row and the radial reflector will be modeled using R-Z geometry in the homogenized case, if ihom=2 the the core region will be homogenized by row and the radial reflector will be discre tely modeled in the homogenized case. 58. ipar – integer (0 or 1), if ipar=0 the tie tube hex will be homogenized in the partially discrete case, if par=1 the tie tube will be discretely modeled in the partially discrete case. 59. ntal – integer, number of axial tally regions Only used in the cold, fully discrete model and should be equal to naxcol in most cases. 60. talline – character, type of tallies to be performed. “0” for none, “Peak” for peaking factor tallies based on fission rate 61. itmpex – integer, “0” for no thermal expansion, “1” for thermally expanded system 62. itmpxs – integer, “0” for no temperatur e-dependent cross-sections, “1” for temperature-dependent cross-sections 63. blank line delimiter 64. marr(0) – character, fuel material identifier. The following entries make up the material array, marr. This array is fille d with character identifiers corresponding to identifiers found for each MCNPX material in the matcards file, which will be discussed shortly. 65. marr(1) – character, fuel coating identifier 66. marr(2) – character, tie tube structure identifer 67. marr(3) – character, tie tube moderator identifier 68. marr(4) – character, tie t ube insulation identifier 69. marr(5) – character, tie tube matrix identifier 70. marr(6) – character, slat material identifier 71. marr(7) – character, core barrel identifier

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24 72. marr(8) – character, radial reflector identifier 73. marr(9) – character, drum poison identifier 74. marr(10) – character, pressure vessel identifier 75. marr(11) – character, coolant identifier 76. marr(13) – character, su pport plates identifier 77. marr(14) – character, shield material identifier 78. marr(15) – character, chamber identifier 79. blank line delimiter 80. nacc – integer, number of additional scenario s to be generated. This option allows one to produce multiple MCNPX decks re presenting various conditions with a single execution of NTRgen. If nacc=0 the i nput file stops at this line. If nacc>0, then the following nine variables must be supplied for each of the additional scenarios: 81. dcomm – character, a text de scription of the scenario be ing described. The first letter given will be the character identifie r for this scenario. For example, if dcomm is given as “b drums at 90 deg” and the input file is called test.inp the detailed MCNPX deck will be named testb 82. talline – same as talline described at line 60, but applied to the additional scenario 83. angrot – same as angrot described at line 28, but applied to th e additional scenario 84. itmpex – same as itmpex described at line 61, but applied to the additional scenario 85. itmpxs – same as itmpex described at line 62, but applied to the additional scenario 86. marr(17) – character, identifier for material to fill in-core coolant channels 87. marr(18) – character, identifier for material to fill vessel coolant channel 88. marr(19) – character, identifier for material to fill expansion gap and control drum gap 89. marr(20) – character, identifier fo r material surrounding the reactor

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25 Figure 4-3. Core periphery. A) 2 rows cut at edge. B) 3 rows cut at edge. Other required input files The other input files required fo r execution of NTRgen are the matcards and cellcards files. These input files rarely need to be altered when producing an NTR design. The cellcards file provides the basic framew ork of the MCNPX cell cards (an example cellcards file is given in Appendix B). Where a standard MCNPX cell card would have a material number and density, however, the cellcards file has an NTRgen cell identifier indicating what type of cell th e card represents. Table 4-1 gives a list of valid cell identifiers in cellcards as well as which element in the material array corresponds to that identifier. Note that not all cell types can be filled with a void, and that some of the material regions can be altered using the nacc option on the primary input file. The matcards file contains the material cards to be used in generating the MCNPX decks (an example matcards file is given in Appendix C). An NTRgen identifier must precede each material card. A sample NTRgen identifier is given below: c [Be/1.81] Be TD=1.85 / 98%=1.81 CTE[7.0,0.,0.,0.] A B

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26 Table 4-1. Valid cell identifiers in cellcards Identifier Material array Description Fuelmat Fuelcot Fuelout TTstrui TTstruo TTmod TTinsu TTmatrx Slatmat Barrel RRref RRpois Vessel Fuelflw Slatflw Coregap RRgap TTflowi TTflowo Vescool TTDn TTUp FCMan FCCham Plate Shield Extcore Corelat 0 0 1 1 2 2 3 4 5 6 7 8 9 10 11 or 17* 11 or 17* 19 19 11 or 17* 11 or 17* 12 or 18* 11 11 11 11 13 14 20 0 0 Fuel Coating between fuel and coolant Coating on outside of fuel hex Inner tie tube structure Outer tie tube structure Tie tube moderator Tie tube insulation Tie tube matrix Inner reflector slats Core barrel Radial reflector and control drum meat Control drum poison Outer pressure vessel Fuel coolant channels** Slat coolant channels** Gap between reflector slats and core barrel ** Gap between control drum and radial reflector ** Inner tie tube down-flow ** Outer tie tube up-flow ** Vessel coolant ** Tie tube down-flow coolant manifold Tie tube up-flow coolant manifold Fuel coolant manifold Fuel coolant exit chamber Interface plates Internal shield Exterior to core** Core lattice, calls a lattice filling subroutine Void *For the first case generated the first material array entry is used, for subsequent cases the second material array entry is used **Void may be placed in these cells The first character must be “c” followed by a space (thus the NTRgen identifier becomes a comment in the MCNPX deck). Th e character identifier and the density (in g/cc) are placed inside brackets, separated by “/”, in this case Be at 1.81 g/cc. The character identifier can be up to 7 characters long and co rresponds to the identifier filled in the material array of the primary input file as discussed in the pr evious section. If thermal expansion is to be performed using this material, the coefficients must be entered inside brackets preceded by the characters “CTE”. The four values in brackets, [ a,b,c,d ],

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27 where a b c and d are real values, give coefficient of thermal expansion, ,according to the following correlation, where T is temperature given in Kelvin: 6 3 210 ) ( ) ( d T c T b a T The CTE information is optional, and need only be provided for the fuel and reflector meat as these materials are assumed to dictate all thermal expansion. Note that the other characters in the identifier are comments which do not affect NTRgen. Optional input files The temperature file (xxx.tmp) gives an axial profile of the core temperature and fuel coolant density. A sample temperature file is given in Appendix D. Each line of the temperature file simply consists of a temp erature given in Kelvin and a fuel coolant density given in mg/cc. The core inlet is listed on the first line, and the number of entries must equal the number of axial coolant levels being considered (naxcol, line 30 of the primary input file). If no temperature file is provided, core temperature will be assumed to increase following a cosine distribution, where the core inlet temperature and outlet temperature given on the primary input file (tinlet and toutlet, lines 32 and 33 of the primary input file). In the absence of a temp erature file, fuel coolant density is estimated using the ideal gas law, where pressure drops linearly from inlet to outlet based on the given inlet pressure and core pressure dr op (pinlet and pdrop, lin es 34 and 35 of the primary input file). The other optional input file is the zone map (xxx.zon) which tells NTRgen what the enrichment of each fuel hex should be to reduce radial peaking. A zone map is produced by NTRfilter based on tallies writte n by NTRgen and executed by MCNPX. A sample zone map is given in Appendix E. Th e first entry in the z one map indicates how

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28 many zones are being described in the map (int eger variable named izlim, 10 for the case given in Appendix E). Following this entry ar e the enrichments to be implemented in the map. The number of enrichments listed should be equal to izlim, the first entry. NTRgen uses this initial data to create the appropria te MCNPX fuel material cards for the various enrichments. Following the initial data block in the zone file is the enrichment map. The enrichment map consists of the MCNPX hex indices for each fuel element, followed by the peaking factor and the enrichment calcula ted by NTRfilter to flatten the radial fission rate distribution and reduce radial peaking f actors (this calculation is discussed in the following section). When NTRgen is filling in the core lattice, it searches the zone file for the appropriate enrichment and applies th at enrichment to the corresponding hex. A sample zone file entry is given below: 15 -20 1.12 0.7093 In this entry, the MCNPX lattice indices are (15,-20), the peaking f actor in this hex is 1.12, and the hex should be filled with 70.93% enriched fuel. NTRgen processes the information in each of the input file s and produces MCNPX decks. A sample MCNPX deck which was generated by NTRgen is provided in Appendix F. NTRFilter The zone file is produced using NTRFilte r, a filter program which sorts through MCNPX tally data to produce an enrichment map that minimizes the radial peaking factor. NTRfilter analyzes an MCNPX mctal file, which contains a concise summary of tally data produced during the run. The mctal file also contains a comment line which is inserted by NTRgen to instruct NTRfilter as to how many fuel elements and how many axial levels are represented.

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29 A sample comment line is reproduced below: Limit: 23 Cold PD 10 This comment indicates the maximum index of any tallied element is 23, and that the case run was with a cold, partially discrete geometry using 10 axial levels. Since this comment is automatically inserted by NTRgen and read by NTRfilter, the user need not interact with the contents of the mctal file. NTRfilter will produce a hex peaking factor (HPFmax), defined as the maximum fission rate in any fuel hex divide d by the fission rate in an average fuel hex, as well as the indices of this maximum fission rate hex. NTRfilter will produce a hex minimum factor (HPFmin), defined as the minimum fission rate in any fuel hex divided by the fission rate in an averag e fuel hex, as well as the indices of this minimum fission rate hex. NTRfilter will also produce a to tal peaking factor (TPF), defined as the maximum fission rate in any fuel segment divided by the fission rate in an average fuel segment, as well as the indices of this maximum fission rate segment. If the mctal file being analyzed was produ ced using a zone map (generated from a previous run) this previous zone map s hould be renamed zones.old before executing NTRfilter if a new zone enrichment map is de sired. To rezone the core, NTRfilter first takes the tally value for each fuel segment and divides by the fuel enrichment in that segment (found in zones.old, if present) to ar rive at an approximation of what the fission rate distribution would look lik e if the core enrichment were uniform. This technique assumes that fission rate is directly proportional to fuel enrichment, and that the flux distribution is unperturbed by al tering fuel enrichment. While these assumptions are invalid when starting with either an unzoned or poorly zoned enrichment scheme, as the iterations progress these assumptions become valid and one can arrive at an optimum

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30 enrichment zoning. In this equation, UPFmin is the unzoned hex minimum factor and UPFmax is the unzoned hex peaking factor. These quantities are similar to HPFmax and HPFmin, with the difference being th at the effect of varying enrichment has been removed from UPFmax and UPFmin by dividing out fuel enrichment in each hex as described. NZ is the total number of zones desired, i is the individual zone number (between 1 and NZ ), and UPFbound(i) is the upper bound of zone i Thus, hexes with UPF between UPFbound(i-1) and UPFbound(i) would fall into zone i NZ i boundUPF UPF UPF i UPFmin max min) ( The representative unzoned p eaking factor of each zone, UPFmid(i) is given below. NZ i midUPF UPF UPF i UPF2 1 min max min) ( The appropriate enrichment for each zone is calculated using the following equation, where enrich(i) is the enrichment for each zone and enrmax is the maximum enrichment to be used. In this scheme, those zones w ith the highest unzoned peaking factor are assigned the lowest enrichment which is a ppropriate given the assumption that those regions with a higher fission rate should re quire less enrichment to achieve a uniform fission rate distribution. ) ( ) 1 ( ) (maxi UPF UPF enr i enrichmid mid An example zone structure is given in Table 4-2, where the unzoned hex peaking factor is 1.3660, the unzoned hex minimum factor is 0.5344, the maximum enrichment to be used is 93% and 3 zones are desired.

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31 Table 4-2. A sample NTRfilter zone structure. Zone Lower UPF bound Upper UPF bound Representative UPF Enrichment 1 2 3 0.7101 0.9637 1.3079 0.9637 1.3079 1.7751 0.8272 1.1227 1.5237 93.00% 68.52% 50.49% Table 4-3 goes through a sample calculati on using the zoning scheme from Table 4-2. New fission rate is calculated by multiplying the old fission rate by the ratio of the new enrichment to the old enrichment. Fo r example, region 5 gives 0.95*(68.52/56) = 1.1624. In this example the original enrich ment zoning is quite poor, considering that some drastic changes must be made (i.e., enrichment in region 2 goes from 93% to 50.49%, enrichment in region 6 goes from 80% to 50.49%). Changes such as these limit the validity of the stated assumptions, but as the iterations progress and new enrichment schemes are implemented the assumptions will become valid and one will approach the optimized enrichment map. Table 4-3. A sample NT Rfilter rezoning calculation. Region Fisson rate Peaking factor Enrich. Unzoned peaking factor Zone New enrich. New fission rate New peaking factor 1 2 3 4 5 6 1.1 2.3 1.4 0.8 0.95 1.9 0.7811 1.6331 0.9941 0.5680 0.6476 1.3491 93% 93% 56% 80% 56% 80% 0.8399 1.7561 1.7751 0.7101 1.2046 1.6864 1 3 3 1 2 3 93.00% 50.49% 50.49% 93.00% 68.52% 50.49% 1.1000 1.2486 1.2622 0.9300 1.1624 1.1991 0.9562 1.0854 1.0972 0.8084 1.0105 1.0423 Figure 4-4 gives a general description of the interaction between NTRgen, MCNPX and NTRfilter.

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32 Figure 4-4. Outline of the NTRgen iterative procedure. primary NTRgen input matcards cellcards MCNPX output file MCNPX mctal file zone file MCNPX decks NTRgen MCNPX NTRfilter use previous zone file (if present) use previous zone file (if present)

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33 CHAPTER 5 RESULTS By employing NTRgen and NTRfilter in concert, one can start with an unzoned core and systematically arrive at an enrich ment scheme which suits the reactor layout of interest. The five core la youts that were considered in this study come from the polynomials generated by TMSS which were pres ented at the end of Chapter 2. These initial runs are for unzoned cores w ith a uniform enrichment of 93%. Unzoned Core Calculations The partially homogenized (PH) cases genera lly ran in about 30% of the runtime of the fully discrete (FD) models (average of about 3.6 minutes for partially homogenized vs. 11.5 for the fully discrete). All computation times listed in this document are for a 2.4-GHz Optiron processor. Results from the initial runs are given in Figures 5-1 through 5-5. The numbers in parentheses in the figur e titles are the number of rows of modules and the number of rows cut at the edge give n in entry 12 of the primary input file, as described in the primary input file section of Chapter 4. A core with 8 total rows of hexes and 2 rows cut at the edge, for example, would result in 906 fuel hexes. A secondorder polynomial was fit to each of these curv es to determine which core dimensions will yield a beginning-of-life expanded k-eff of a bout 1.03. The target value of 1.03 was chosen because the subsequent rezoning will necessarily reduce the average enrichment of the core, as 93% is the maximum enrichment to be loaded in any hex. These initial runs were run to standard deviation of about 0.003, as they are only used to determine

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34 dimensions of the core with which to begi n zoning. No consideration was given to shutdown conditions at this point in the process. Once the dimensions for a core expected to yield a BOL expanded k-eff of about 1.03 were determined, that case was run to hi gher fidelity with fission rate tallies to determine the hex peaking factor in the core. The dimensions of these cases are given in Table 5-1, while the criticality results for these unzoned cores are given in Table 5-2. In Table 5-2, the standard deviat ion is reported in parentheses below the criticality result. Note that in all tables and figures “h ot” refers to the MCNPX run employing the thermally expanded geometry and does not ac count for temperature dependence in the cross sections. 906 Fuel Hexes (8,2) 0.80000 0.85000 0.90000 0.95000 1.00000 1.05000 1.10000 130.00135.00140.00145.00150.00155.00160.00165.00 Height (cm)k-eff BOL Cold PH BOL Hot PH Shutdown PH BOL Cold FD BOL Hot FD Shutdown FD Figure 5-1. Comparison of initial MCNPX runs for 906 fuel hex case.

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35 1194 Fuel Hexes (9,2) 0.85000 0.90000 0.95000 1.00000 1.05000 1.10000 1.15000 90.0095.00100.00105.00110.00115.00120.00 Height (cm)k-eff BOL Cold PH BOL Hot PH Shutdown PH BOL Cold FD BOL Hot FD Shutdown FD Figure 5-2. Comparison of initial MCNPX runs for 1194 fuel hex case. 1518 Fuel Hexes (10,2) 0.85000 0.90000 0.95000 1.00000 1.05000 1.10000 70.0075.0080.0085.0090.0095.00 Height (cm)k-eff BOL Cold PH BOL Hot PH Shutdown PH BOL Cold FD BOL Hot FD Shutdown FD Figure 5-3. Comparison of initial MCNPX runs for 1518 fuel hex case.

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36 1410 Fuel Hexes (10,3) 0.85000 0.90000 0.95000 1.00000 1.05000 1.10000 75.0080.0085.0090.0095.00100.00 Height (cm)k-eff BOL Cold PH BOL Hot PH Shutdown PH BOL Cold FD BOL Hot FD Shutdown FD Figure 5-4. Comparison of initial MCNPX runs for 1410 fuel hex case. 1770 Fuel Hexes (11,3) 0.85000 0.90000 0.95000 1.00000 1.05000 60.0062.0064.0066.0068.0070.0072.0074.0076.0078.0080.00 Height (cm)k-eff BOL Cold PH BOL Hot PH Shutdown PH BOL Cold FD BOL Hot FD Shutdown FD Figure 5-5. Comparison of initial MCNPX runs for 1770 fuel hex case.

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37 Table 5-1. Dimensions of considered NTR cores. Fuel hexes Total rows Rows cut Height (cm) Pitch (cm) Cool diam (cm) RR thick (cm) Outer diam. (cm) Fuel Vol. (cc) Mass (kg) 906 1194 1518 1410 1770 8 9 10 10 11 2 2 2 3 3 155.73 106.28 84.50 89.59 76.14 1.949 1.895 1.905 1.890 1.963 0.2471 0.2108 0.1869 0.1963 0.1744 8.00 8.00 8.00 8.00 8.00 71.00 79.00 89.00 86.00 99.00 326114 302210 327850 311900 379450 2729.0 2324.9 2361.3 2315.3 2640.5 Table 5-2. Criticality results for unzoned NTR cores. Fuel hexes BOL cold FD k-eff BOL cold PH k-eff BOL expnd FD k-eff BOL hot PH k-eff Shutdown FD k-eff Shutdown PH k-eff 906 1194 1518 1410 1770 1.04438 (0.00060) 1.05108 (0.00061) 1.04366 (0.00053) 1.05088 (0.00062) 1.04373 (0.00060) 1.04502 (0.00059) 1.05227 (0.00058) 1.04493 (0.00061) 1.05056 (0.00056) 1.04523 (0.00056) 1.03364 (0.00060) 1.03899 (0.00060) 1.02996 (0.00057) 1.03707 (0.00056) 1.02955 (0.00058) 1.03428 (0.00059) 1.03831 (0.00057) 1.03128 (0.00059) 1.03825 (0.00061) 1.03191 (0.00057) 0.93441 (0.00057) 0.97241 (0.00061) 0.98942 (0.00059) 0.98989 (0.00056) 1.00380 (0.00061) 0.93664 (0.00059) 0.97312 (0.00058) 0.99088 (0.00059) 0.99132 (0.00058) 1.00409 (0.00062) Table 5-3 gives a comparison of the critical ity results given in Table 5-2. For each condition, the difference between partially homogenized and fully discrete k-eff are given. Also provided in th is table are the fully discrete and partially homogenized runtimes for each case. For example, in the 906 fuel hex case the BOL cold fully discrete model took 1370 minutes whereas the BOL co ld partially homoge nized model took 596 minutes. The hex peaking factor for each one of these unzoned cores is given in Table 54 (the standard deviation of each peaking factor is reported in parentheses). Note that the shutdown criticality runs took dramatically less time because no peaking factor tallies were performed. Figures 5-6 through 510 are a comparison of the fission rate distribution in the each of the core layouts using cold and expanded geometry with both fully discrete and partially homogenized models. In addition to the average fission rate at each radial location are the maximum and mini mum fission rates (the dotted lines above

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38 and below each solid line). Note that the ma ximum relative fission rate in each one of the curves corresponds to the peaking factors f ound in Table 5-4. In many cases, the k-eff and hex peaking factor determined using the partially homogenized model is within the standard deviation of the fully discrete mode l. In some cases the difference is greater than the standard deviation, but this is to be expected due to the both the statistical nature of the simulation and the fact that some ge ometrical approximations have been made. Given the strong general agreement between fully discrete and partially homogenized models in both criticality and peaking fact or results (Tables 5-3 and 5-4) and the agreement in fission rate distri bution (Figures 5-6 through 5-10) it becomes clear that the advantage in runtime using th e partially homogenized models (a reduction of 50% or more in some tallied cases) outweighs any loss in accuracy. Table 5-3. Criticality and runtim e comparison for unzoned NTR cores. Fuel hexes BOL cold k-eff diff, PH FD BOL hot k-eff diff, PH FD Shutdown k-eff diff, PH FD BOL cold runtimes FD & PH (minutes) BOL hot runtimes FD & PH (minutes) Shutdown runtimes FD & PH (minutes) 906 1194 1518 1410 1770 0.00064 0.00119 0.00127 -0.00032 0.00150 0.00064 -0.00068 0.00132 0.00118 0.00236 0.00223 0.00071 0.00146 0.00143 0.00029 1370, 596 1754, 775 1966, 1009 1824, 978 1999, 1179 1358, 585 1526, 796 1932, 1000 1817, 873 2249, 1176 195, 49 182, 51 170, 53 173, 53 161, 52 Table 5-4. Hex peaking f actors for unzoned NTR cores. Fuel hexes BOL cold FD BOL cold PH BOL hot FD BOL hot PH 906 1194 1518 1410 1770 1.65400 (0.00613) 1.65540 (0.00704) 1.54465 (0.00763) 1.74392 (0.00782) 1.64281 (0.00896) 1.65628 (0.00615) 1.63262 (0.00686) 1.53860 (0.00765) 1.73470 (0.00781) 1.66858 (0.00880) 1.67678 (0.00608) 1.62037 (0.00691) 1.56310 (0.00765) 1.75460 (0.00789) 1.72717 (0.00904) 1.67140 (0.00612) 1.63005 (0.00688) 1.56745 (0.00768) 1.74926 (0.00803) 1.69125 (0.00869)

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39 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 05101520253035 Distance from center (cm)Relative fission rate Cold FD Hot FD Cold PH Hot PH Figure 5-6. Relative fission rate in the unzoned 906 fuel hex core. 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 0510152025303540 Distance from center (cm)Relative fission rate Cold FD Hot FD Cold PH Hot PH Figure 5-7. Relative fission rate in the unzoned 1194 fuel hex core.

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40 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 051015202530354045 Distance from center (cm)Relative fission rate Cold FD Hot FD Cold PH Hot PH Figure 5-8. Relative fission rate in the unzoned 1518 fuel hex core. 0.7 0.9 1.1 1.3 1.5 1.7 0510152025303540 Distance from center (cm)Relative fission rate Cold FD Hot FD Cold PH Hot PH Figure 5-9. Relative fission rate in the unzoned 1410 fuel hex core.

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41 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 05101520253035404550 Distance from center (cm)Relative fission rate Cold FD Hot FD Cold PH Hot PH Figure 5-10. Relative fission rate in the unzoned 1770 fuel hex core. Zoning Calculations Starting with the core layouts just desc ribed, three zoning iterations were performed on each core in an effort to reduce the hex peaking factor. Each zoning iteration consisted of running MCNPX to pr oduce fission rate tallie s, running NTRfilter on the tally data to produce an enrichment zoning map, running NTRgen using this zoning map to produce new MCNPX decks, then repeating the process. Ten enrichment zones were employed for each iteration. 906 Fuel Hex Core Criticality results for the 906 fuel hex core as a functi on of zoning iteration are given in Table 5-5. The trend is as one woul d expect – the largest drop in k-eff is from the unzoned core to the first zoning scheme. As the zoning iterations progress, the assumptions used by NTRfilter in calculating the zoning scheme become more valid

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42 (flux profile unchanged by rezoning, fissi on rate proportional to enrichment). A description of each zoning scheme is given in Table 5-6. This table summarizes the enrichment of each zone, and how many fuel he xes of each zone are present in the core. Table 5-7 contains the hex peaking factor at each iteration. Table 5-8 lists the computation times for the MCNPX runs. The ra dial fission rate distribution as a function of zoning iteration is given in Figure 5-11. These fission rate distributions were generated using the expanded, partially hom ogenized models. Note that the relative fission rate given in Figure 5-11 does not correspond to the hex peaking factor listed in Table 5-7. The key distinction is that the values found in Figure 5-11 are an average of the fission rates of all fuel hexes at a partic ular radius, whereas the hex peaking factor considers the maximum fission rate f ound in any individual fuel hex. Table 5-5. Criticality results for 906 fuel hex core zoning iterations. Iteration BOL cold FD k-eff BOL cold PH k-eff BOL hot FD k-eff BOL hot PH k-eff Average Enrichment (%) 0 (unzoned) 1 2 3 1.04438 (0.00060) 1.01539 (0.00055) 1.00797 (0.00056) 1.00741 (0.00056) 1.04502 (0.00059) 1.01688 (0.00059) 1.00995 (0.00060) 1.00885 (0.00056) 1.03364 (0.00060) 1.00552 (0.00056) 0.99728 (0.00059) 0.99657 (0.00058) 1.03428 (0.00059) 1.00504 (0.00055) 0.99776 (0.00058) 0.99698 (0.00053) 93.00 82.87 79.85 79.22 Table 5-6. Enrichment zone descripti on for 906 fuel hex core zoning iterations. Zone Iteration 1 Enrich (%) # Iteration 2 Enrich (%) # Iteration 3 Enrich (%) # 1 2 3 4 5 6 7 8 9 10 93.00 86.85 81.10 75.73 70.72 66.04 61.67 57.59 53.78 50.22 256 258 190 70 32 30 21 13 16 20 93.00 85.34 78.30 71.85 65.93 60.50 55.51 50.94 46.74 42.89 260 230 159 119 16 44 18 24 14 22 93.00 85.07 77.81 71.17 65.10 59.54 54.46 49.82 45.57 41.68 274 209 159 114 19 41 24 30 14 22

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43 Table 5-7. Hex peaking factor for 906 fuel hex core zoning iterations. Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH 0 1 2 3 1.65400 (0.00613) 1.16916 (0.00441) 1.08512 (0.00403) 1.07997 (0.00395) 1.65628 (0.00615) 1.18487 (0.00442) 1.09498 (0.00388) 1.08485 (0.00325) 1.67680 (0.00608) 1.18695 (0.00439) 1.08938 (0.00388) 1.07836 (0.00393) 1.67140 (0.00612) 1.16607 (0.00428) 1.09765 (0.00384) 1.08618 (0.00402) Table 5-8. Computation time for 9 06 fuel hex core zoning iterations. Iteration BOL cold FD (minutes) BOL cold PH (minutes) BOL hot FD (minutes) BOL hot PH (minutes) 0 1 2 3 1370 1356 1362 1391 596 591 616 621 1359 1435 1441 1399 585 645 638 620 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 05101520253035 Distance from center (cm)Relative fission rate Unzoned Zone 1 Zone 2 Zone 3 Figure 5-11. Relative fission rate in the 906 fuel hex core through zoning iterations. Tables 5-5 through 5-8 and Figure 5-11 indi cate that by the th ird zoning iteration the criticality results, zoning scheme, and fi ssion rate have appro ached the point that subsequent zoning iterati ons would not produce signifi cant enough perturbations to justify the additional computation time. A radi al view of the 906 fuel hex core with the

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44 third zoning iteration is given in Figure 5-12. Notice that th ere is some asymmetry due to statistical variations in the tallies. Figure 5-13 gives a more detailed view of the zone layout indicating how the enrichment zones (zones 1-10, given in Table 5-6) are distributed in the core. Figure 5-12. Radial layout of zoned 906 fuel hex core. 1194 Fuel Hex Core A similar process to that described above was followed for enrichment zoning of the 1194 fuel hex core. Table 5-9 contains the criticality results for each step, while Table 5-10 gives the enrichment zone descri ptions. Table 5-11 gives the hex peaking factors while Table 5-12 lists the computa tion times. The peaking factor was reduced from 1.63005 to 1.11039 using the expanded partially homogenized model.

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45 Figure 5-13. Detailed view of enri chment zoning in 906 fuel hex core. Table 5-9. Criticality results for 119 4 fuel hex core zoning iterations. Iteration BOL cold FD k-eff BOL cold PH k-eff BOL hot FD k-eff BOL hot PH k-eff Average Enrichment (%) 0 (unzoned) 1 2 3 1.05108 (0.00061) 1.01694 (0.00061) 1.00944 (0.00057) 1.00533 (0.00060) 1.05227 (0.00058) 1.01572 (0.00058) 1.00851 (0.00057) 1.00504 (0.00059) 1.03899 (0.00060) 1.00404 (0.00059) 0.99552 (0.00061) 0.99309 (0.00059) 1.03831 (0.00057) 1.00422 (0.00057) 0.99588 (0.00058) 0.99404 (0.00059) 93.00 81.22 78.25 77.24 The radial fission rate at each zoning iteration is given in Figure 5-14. The trend observed is similar to that found for the 906 fuel hex core. There is a dramatic improvement in the uniformity of fission rate from the unzoned core to the first zoning scheme. Subsequent iterations are less dram atic, with the third zoning iteration providing a nearly flat radial fission rate distribution. 4 3 2 1 4 6 5 9 8 7 10 3 2

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46 Table 5-10. Enrichment zone description for 1194 fuel hex core zoning iterations. Zone Iteration 1 Enrich (%) # Iteration 2 Enrich (%) # Iteration 3 Enrich (%) # 1 2 3 4 5 6 7 8 9 10 93.00 86.91 81.22 75.90 70.93 66.29 61.95 57.89 54.10 50.56 250 330 209 158 127 31 31 10 25 23 93.00 85.38 78.38 71.95 66.05 60.64 55.67 51.11 46.92 43.07 307 256 178 170 128 63 24 30 15 23 93.00 85.17 77.99 71.42 65.41 59.90 54.85 50.23 46.00 42.13 324 228 160 163 122 87 32 32 16 30 Table 5-11. Hex peaking factor for 1194 fuel hex core zoning iterations. Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH 0 1 2 3 1.65540 (0.00704) 1.17338 (0.00510) 1.10349 (0.00464) 1.10241 (0.00473) 1.63262 (0.00686) 1.18481 (0.00498) 1.10615 (0.00459) 1.09559 (0.00446) 1.62037 (0.00691) 1.17969 (0.00506) 1.10651 (0.00366) 1.09288 (0.00366) 1.63005 (0.00688) 1.17111 (0.00500) 1.11001 (0.00457) 1.11039 (0.00466) Table 5-12. Computation time for 1 194 fuel hex core zoning iterations. Iteration BOL cold FD (minutes) BOL cold PH (minutes) BOL hot FD (minutes) BOL hot PH (minutes) 0 1 2 3 1754 1667 1745 1723 775 810 822 826 1526 1689 1694 1657 796 805 811 825 1518 Fuel Hex Core Criticality data for the 1518 fuel hex core is given in Table 5-13. Tables 5-14 though 5-16 contain enrichment zone data, hex peaking factors, and computation times. Again, the zoning method performs well, re ducing the hex peaking factor from 1.56745 to 1.10907 in three iterations. Figure 5-15 show s radial fission rate for the 1518 fuel hex core.

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47 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 0510152025303540 Distance from center (cm)Relative fission rate Unzoned Zone 1 Zone 2 Zone 3 Figure 5-14. Relative fission rate in the 1194 fuel hex core through zoning iterations. Table 5-13. Criticality results for 151 8 fuel hex core zoning iterations. Iteration BOL cold FD k-eff BOL cold PH k-eff BOL hot FD k-eff BOL hot PH k-eff Average Enrichment (%) 0 (unzoned) 1 2 3 1.04366 (0.00053) 1.00151 (0.00061) 0.98969 (0.00054) 0.98442 (0.00058) 1.04493 (0.00061) 1.00096 (0.00057) 0.98857 (0.00060) 0.98533 (0.00057) 1.02996 (0.00057) 0.98712 (0.00058) 0.97463 (0.00057) 0.97255 (0.00059) 1.03128 (0.00059) 0.98857 (0.00058) 0.97627 (0.00056) 0.97302 (0.00056) 93.00 79.27 75.29 73.99 Table 5-14. Enrichment zone description for 1518 fuel hex core zoning iterations. Zone Iteration 1 Enrich (%) # Iteration 2 Enrich (%) # Iteration 3 Enrich (%) # 1 2 3 4 5 6 7 8 9 10 93.00 87.04 81.45 76.23 71.34 66.77 62.49 58.48 54.73 51.22 272 345 236 178 179 188 45 16 35 24 93.00 85.55 78.71 72.40 66.61 61.28 56.37 51.86 47.71 43.89 292 314 197 183 145 170 122 36 28 31 93.00 85.38 78.38 71.96 66.06 60.64 55.67 51.11 46.92 43.07 323 266 177 177 134 138 143 98 26 36

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48 Table 5-15. Hex peaking factor for 1518 fuel hex core zoning iterations. Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH 0 1 2 3 1.54465 (0.00763) 1.16592 (0.00419) 1.12827 (0.00418) 1.12862 (0.00424) 1.53860 (0.00765) 1.18619 (0.00448) 1.12928 (0.00415) 1.11567 (0.00408) 1.56310 (0.00765) 1.18589 (0.00591) 1.12504 (0.00540) 1.10932 (0.00541) 1.56745 (0.00768) 1.18210 (0.00585) 1.11116 (0.00417) 1.10907 (0.00523) Table 5-16. Computation time for 1 518 fuel hex core zoning iterations. Iteration BOL cold FD (minutes) BOL cold PH (minutes) BOL hot FD (minutes) BOL hot PH (minutes) 0 1 2 3 1966 2027 1932 1951 1009 1037 993 1004 1932 1963 2040 1889 1000 1034 1076 1093 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 051015202530354045 Distance from center (cm)Relative fission rate Unzoned Zone 1 Zone 2 Zone 3 Figure 5-15. Relative fission rate in the 1518 fuel hex core through zoning iterations. 1410 Fuel Hex Core Table 5-9 gives criticality results for th e 1410 fuel hex core, while Table 5-10 gives the enrichment zone descriptions. Table 511 contains the hex peak ing factors and Table 5-12 lists the computation times. Hex peaki ng factor in the 1410 core was reduced from

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49 1.74926 to 1.13030 in the expanded partially hom ogenized model after three iterations. The radial fission rate distribu tion is shown in Figure 5-16. Table 5-17. Criticality results for 141 0 fuel hex core zoning iterations. Iteration BOL cold FD k-eff BOL cold PH k-eff BOL hot FD k-eff BOL hot PH k-eff Average Enrichment (%) 0 (unzoned) 1 2 3 1.05088 (0.00062) 1.00459 (0.00060) 0.99449 (0.00058) 0.98851 (0.00059) 1.05056 (0.00056) 1.00634 (0.00060) 0.99550 (0.00059) 0.99012 (0.00059) 1.03707 (0.00056) 0.99299 (0.00058) 0.98248 (0.00059) 0.97675 (0.00056) 1.03825 (0.00061) 0.99332 (0.00056) 0.98323 (0.00060) 0.97918 (0.00055) 93.00 78.00 74.26 72.40 Table 5-18. Enrichment zone description for 1410 fuel hex core zoning iterations. Zone Iteration 1 Enrich (%) # Iteration 2 Enrich (%) # Iteration 3 Enrich (%) # 1 2 3 4 5 6 7 8 9 10 93.00 85.89 79.32 73.25 67.65 62.48 57.70 53.29 49.21 45.45 159 408 290 218 212 46 23 14 21 19 93.00 84.17 76.18 68.95 62.41 56.49 51.12 46.27 41.88 37.97 198 376 251 192 193 104 36 21 19 20 93.00 83.80 75.50 68.03 61.30 55.23 49.76 44.84 40.40 36.40 178 375 219 187 186 154 51 17 20 23 Table 5-19. Hex peaking factor for 1410 fuel hex core zoning iterations. Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH 0 1 2 3 1.74392 (0.00782) 1.19466 (0.00572) 1.12627 (0.00410) 1.10699 (0.00396) 1.73470 (0.00781) 1.17743 (0.00541) 1.14848 (0.00397) 1.10449 (0.00404) 1.75460 (0.00789) 1.20741 (0.00547) 1.14219 (0.00413) 1.13613 (0.00535) 1.74926 (0.00803) 1.19103 (0.00533) 1.11824 (0.00398) 1.13030 (0.00494) Table 5-20. Computation time for 1 410 fuel hex core zoning iterations. Iteration BOL cold FD (minutes) BOL cold PH (minutes) BOL hot FD (minutes) BOL hot PH (minutes) 0 1 2 3 1824 1939 2024 1885 978 1000 917 957 1817 1757 1773 1826 873 914 950 964

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50 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 0510152025303540 Distance from center (cm)Relative fission rate Unzoned Zone 1 Zone 2 Zone 3 Figure 5-16. Relative fission rate in the 1410 fuel hex core through zoning iterations. 1770 Fuel Hex Core Tables 5-21 though 5-24 contain enrichment zone data, hex peaking factors, and computation times for the 1770 fuel hex core. The decreased computation times listed for the third iteration in Table 5-24 arise fr om fewer particle histories being tracked (hence the larger standard devi ations for the third iteration in Tables 5-21 and 5-23). The relative fission rate distribution in th is core is presented in Figure 5-17. Table 5-21. Criticality results for 177 0 fuel hex core zoning iterations. Iteration BOL cold FD k-eff BOL cold PH k-eff BOL hot FD k-eff BOL hot PH k-eff Average Enrichment (%) 0 (unzoned) 1 2 3 1.04373 (0.00060) 0.98912 (0.00059) 0.97256 (0.00060) 0.96462 (0.00091) 1.04523 (0.00056) 0.98997 (0.00056) 0.97253 (0.00058) 0.96455 (0.00091) 1.02955 (0.00058) 0.97544 (0.00059) 0.95823 (0.00060) 0.95188 (0.00092) 1.03191 (0.00057) 0.97680 (0.00056) 0.95890 (0.00060) 0.95254 (0.00091) 93.00 75.79 70.31 67.95

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51 Table 5-22. Enrichment zone description for 1770 fuel hex core zoning iterations. Zone Iteration 1 Enrich (%) # Iteration 2 Enrich (%) # Iteration 3 Enrich (%) # 1 2 3 4 5 6 7 8 9 10 93.00 85.91 79.36 73.31 67.72 62.56 57.79 53.38 49.31 45.55 220 422 275 224 249 246 75 20 19 20 93.00 84.07 76.01 68.71 62.12 56.15 50.77 45.89 41.49 37.51 174 419 269 199 199 238 205 23 21 23 93.00 83.59 75.14 67.53 60.70 54.56 49.04 44.08 39.62 35.61 175 380 259 202 187 200 199 122 22 24 Table 5-23. Hex peaking factor for 1770 fuel hex core zoning iterations. Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH 0 1 2 3 1.64281 (0.00896) 1.20616 (0.00481) 1.14281 (0.00450) 1.15388 (0.00995) 1.66858 (0.00880) 1.19692 (0.00648) 1.15529 (0.00448) 1.12414 (0.00696) 1.72717 (0.00904) 1.18488 (0.00469) 1.14676 (0.00578) 1.15586 (0.00979) 1.69125 (0.00869) 1.19305 (0.00465) 1.13789 (0.00462) 1.15675 (0.00750) Table 5-24. Computation time for 1 770 fuel hex core zoning iterations. Iteration BOL cold FD (minutes) BOL cold PH (minutes) BOL hot FD (minutes) BOL hot PH (minutes) 0 1 2 3 1999 2187 2156 848 1179 1244 1240 489 2249 2155 2259 887 1176 1175 1222 489 Note that the final peaki ng factor (1.15675 in the expanded partially homogenized model) in this core is the hi ghest found out of all considered core layouts. One reason is that this core is larger (radially) than the ot hers. The effective radi us of the core is the radius of an equivalent circ le having the same area as all the tie tubes and fuel hexes combined. The effective radius of the 1770 fu el hex core is 93.67 cm, whereas the next largest core is the 1518 fuel he x core with an effective radi us of 84.18 cm. The larger radius implies that more fluctuations in th e radial neutron flux distribution may occur from iteration to iteration, thus taking more time for the assumptions made by NTRfilter during rezoning to become valid. The implicit assumption in this statement is that the

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52 neutron mean free path is the same for each of the cores. Each of the cores contains the same materials in roughly the same quantities, so one would expect the neutron spectrum (and therefore the mean free path) to be similar as well. 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 05101520253035404550 Distance from center (cm)Relative fission rate Unzoned Zone 1 Zone 2 Zone 3 Figure 5-17. Relative fission rate in the 1770 fuel hex core through zoning iterations. Final Designs The previous calculations resulted in th e production of an enrichment zoning map specific to each core layout. These zoning maps were then used to produce a neutronic core design that met both the TMSS criteria gi ven at the end of Chapter 2 (following the polynomials for coolant diameter and hex pitch) and the criticality conditions at the end of Chapter 1 (expanded BOL k-eff greater than 1.025, shutdown k-eff less than 0.985). Again, one could perform the iteration pr ocedure without the TMSS polynomials and arrive at a zoned core design. The TMSS anal ysis serves to ensure that temperature and pressure drop limits are consistent from desi gn to design, giving a more realistic picture

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53 of how the designs compare to one another. Similar curves to those presented in Figures 5-1 through 5-5 were generated for the zoned cores. The parameter of interest is expanded k-eff due to the critical ity criteria, and this value is given for each of the core layouts as a function of core heig ht in Figure 5-18. By interp olating from this figure, one can determine the appropriate core size fo r each layout and zoning scheme such that expanded k-eff is greater than 1.025. 0.88000 0.90000 0.92000 0.94000 0.96000 0.98000 1.00000 1.02000 1.04000 1.06000 1.08000 60.0080.00100.00120.00140.00160.00180.00 Core height (cm)Expanded PH k-eff 906 1194 1518 1410 1770 Figure 5-18. Expanded partially homoge nized k-eff for zoned NTR cores. Once the core size was determined, each de sign was run to higher fidelity using the zoning enrichment map to determine its nuclear characteristics. The results of these calculations are presented in Table 5-25.

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54 Table 5-25. Dimensions and nuclear characteristics of final NTR designs. Fuel hexes: 906 1194 1518 1410 1770 Hex pitch (cm) Cool channel diam (cm) Core height (cm) Effective diameter (cm) Height/diameter Fuel volume (cm3) Average enrichment (%) Burnup (%) Reactor mass (kg) BOL cold FD k-eff BOL hot FD k-eff Shutdown FD k-eff BOL cold PH k-eff BOL hot PH k-eff Shutdown PH k-eff BOL cold FD peaking factor BOL hot FD peaking factor BOL cold PH peaking factor BOL hot PH peaking factor BOL cold FD runtime (min) BOL hot FD runtime (min) Shutdown FD runtime (min) BOL cold PH runtime (min) BOL hot PH runtime (min) Shutdown PH runtime (min) 2.050 0.2526 178.48 69.99 2.55 423119 78.72 1.2 3440.5 1.03797 (0.00079) 1.02446 (0.00071) 0.93613 (0.00071) 1.03796 (0.00072) 1.02798 (0.00069) 0.93687 (0.00068) 1.08491 (0.00442) 1.08485 (0.00511) 1.08745 (0.00059) 1.08625 (0.00514) 853.90 846.00 128.20 389.84 391.78 34.27 2.022 0.2133 114.69 79.25 1.45 382350 77.07 1.4 2855.2 1.03585 (0.00074) 1.02366 (0.00070) 0.96309 (0.00074) 1.03736 (0.00071) 1.02479 (0.00076) 0.96763 (0.00069) 1.11252 (0.00484) 1.09713 (0.00480) 1.10721 (0.00494) 1.10737 (0.00465) 1077.27 1106.56 119.94 545.85 540.11 36.45 2.170 0.1911 97.29 95.89 1.01 510735 73.60 1.1 3451.8 1.03596 (0.00069) 1.02529 (0.00074) 0.98887 (0.00073) 1.03763 (0.00077) 1.02535 (0.00075) 0.98993 (0.00072) 1.14991 (0.00533) 1.15369 (0.00703) 1.12453 (0.00517) 1.14290 (0.00713) 1188.75 1389.18 107.38 732.39 741.03 36.83 2.090 0.1970 100.29 89.01 1.13 442718 71.55 1.3 3181.9 1.03549 (0.00072) 1.02531 (0.00069) 0.98260 (0.00074) 1.03708 (0.00068) 1.02473 (0.00072) 0.98460 (0.00072) 1.14045 (0.00502) 1.14311 (0.00654) 1.14159 (0.00516) 1.13744 (0.00634) 1112.25 1261.72 111.90 615.58 635.15 35.20 2.431 0.1796 92.87 116.00 0.80 748387 64.16 0.9% 4957.5 1.03509 (0.00072) 1.02386 (0.00069) 1.00536 (0.00072) 1.03609 (0.00070) 1.02596 (0.00072) 1.00616 (0.00070) 1.22706 (0.00838) 1.23446 (0.00812) 1.23029 (0.00795) 1.22166 (0.00080) 1432.43 1263.92 95.52 904.64 792.88 38.02 Based on the values presented in Table 525, three of the core layouts considered meet the shutdown criticality design criteria The 906, 1194, and 1410 fuel hex cores all have a k-eff of less and 0.985 in the shutdown state. These reactor s were designed using interpolation from the preliminary runs given in Figure 5-18, so all the reactors are at or

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55 near the expanded k-eff criteria of 1.025. All the core designs meet the hex peaking factor limit of 1.15 except for the 1770 fuel hex case which has a peaking factor of 1.22166 (in the expanded, partially homogenized case). As was discussed earlier, this larger core might benefit from another zoni ng iteration to reduce the hex peaking factor. However, considering that the shutdown k-eff is greater than 1, and that the mass of this design is already over 1000 kg heav ier than the next heaviest design, there is probably not much benefit to considering this design further. Table 5-26 compares some of the values presented in Table 5-25. The largest difference in k-eff between a fully discrete model and a partially homogenized model was 0.00454 in the shutdown case of the 1194 fuel he x core. The runtimes of the partially homogenized decks were between 45% and 64% that of the fully discrete models for cases with tallies, and between 26% and 40% that of the fully discrete models for cases with no tallies. Thermal expansion had a negative effect on reactivity in all the core designs considered. The extent of this negative effect ranged from 0.00998 to 0.01351. The 1770 fuel hex core had the smallest shutdow n swing of 0.01980. This small swing is largely due to the fact that this core has a he ight to diameter ratio (H/D) of 0.80, which is the smallest of all cores consid ered. In the taller designs (t hose with larger H/D) more poison can be placed near the core when the control drums are rotated in. The trend of larger H/D corresponding to larger s hutdown swing is shown in Figure 5-19.

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56 Table 5-26. Nuclear characteristi c analysis of final NTR designs. Fuel hexes: 906 1194 1518 1410 1770 BOL cold k-eff difference (PH minus FD) BOL hot k-eff difference (PH minus FD) Shutdown k-eff difference (PH minus FD) BOL cold time ratio (PH runtime over FD runtime) BOL hot time ratio (PH runtime over FD runtime) Shutdown time ratio (PH runtime over FD runtime) Expansion reactivity effect FD (hot minus cold k-eff) Expansion reactivity effect PH (hot minus cold k-eff) Shutdown k-eff swing FD (hot minus shutdown k-eff) Shutdown k-eff swing PH (hot minus shutdown k-eff) -0.00001 0.00352 0.00074 0.4565 0.4631 0.2673 -0.01351 -0.00998 0.08833 0.09111 0.00151 0.00113 0.00454 0.5067 0.4881 0.3039 -0.01219 -0.01257 0.06057 0.05716 0.00167 0.00006 0.00106 0.6161 0.5334 0.3430 -0.01067 -0.01228 0.03642 0.03542 0.00159 -0.00058 0.00200 0.5535 0.5034 0.3146 -0.01018 -0.01235 0.04271 0.04013 0.00100 0.00210 0.00080 0.6315 0.6273 0.3980 -0.01123 -0.01013 0.01850 0.01980 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 00.511.522.53 Height to diameter (H/D)Shutdown swing (hot minus shutdown k-eff) Fully discrete Partially homogenized Figure 5-19. Shutdown swing versus hei ght-to-diameter ratio for NTR cores.

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57 Figures 5-20 through 5-24 show the radial fission rate distribu tion in each of the final core design layouts at cold and expa nded geometries, using fully discrete and partially homogenized models. The initial fission rate in the unzoned core designs is also shown for comparison purposes. Note that th ese fission rates are plo tted as a function of number of hexes out from center as opposed to distance from center which was used in Figures 5-6 though 5-10. The hex pitch used in the initial core designs is different than that used for the final core designs, so plotting as a function of number of hexes facilitates an easier comparison of the fission rate distributions. 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 024681012141618 Number of hexes out from centerRelative fission rate Cold FD Final Hot FD Final Cold PH Final Hot PH Final Hot PH UnzonedFigure 5-20. Fission rate distribution fo r final 906 fuel hex NTR core design.

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58 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 05101520 Number of hexes out from centerRelative fission rate Cold FD Final Hot FD Final Cold PH Final Hot PH Final Hot PH Unzoned Figure 5-21. Fission rate distribution fo r final 1194 fuel hex NTR core design. 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 0510152025 Number of hexes out from centerRelative fission rate Cold FD Final Hot FD Final Cold PH Final Hot PH Final Hot PH Unzoned Figure 5-22. Fission rate distribution fo r final 1518 fuel hex NTR core design.

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59 0.7 0.9 1.1 1.3 1.5 1.7 05101520 Number of hexes out from centerRelative fission rate Cold FD Final Hot FD Final Cold PH Final Hot PH Final Hot PH Unzoned Figure 5-23. Fission rate distribution fo r final 1410 fuel hex NTR core design. 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 0510152025 Number of hexes out from centerRelative fission rate Cold FD Final Hot FD Final Cold PH Final Hot PH Final Hot PH Unzoned Figure 5-24. Fission rate distribution fo r final 1770 fuel hex NTR core design.

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60 CHAPTER 6 CONCLUSION The goal of this study was to develop a nd implement tools to aid the neutronic design of nuclear thermal rockets. Five nuclear rocket cores were systematically zoned in an effort to reduce the hex peaking factor. Reducing the hex peaking factor is important in NTR design because the maximum power hex must meet thermal criteria such as limits on peak fuel temperature and pressure drop. These criteria will demand smaller fuel hexes (to lower peak fuel temperature) and la rger coolant channels (to meet pressure drop requirements) both of which serve to decrease the amount of fuel, t hus requiring a larger (i.e. more massive) core to meet criticalit y conditions. Minimizing mass is a significant part of any space reactor design (and rockets ar e no exception), so there is a benefit to reducing the hex peaking factor. The partially homogenized MCNPX models proved to be a valuable tool in reducing computation time. In most cases the partially homogenized models ran in less than 60% the runtime of the fully discrete models. While there are some differences in both criticality in fission rate when employi ng the partially discrete model, NTRgen produces the fully discrete model as well, allowing the user to determine whether the potential loss in accuracy is worth the savings in runtime. Of the three core layouts considered in this study, three met the conditions for criticality and hex peaking f actor. The 906, 1194, and 1410 fuel hex cores can meet BOL hot k-eff of greater than 1. 025 and shutdown less than 0.985 with a hex peaking factor less than 1.15. Of the three successful de signs, the 1194 fuel hex core had the smallest

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61 mass at 2855 kg, making it the most attractive option. The 1518 and 1770 fuel hex cores did not have enough shutdown swing to satisfy the shutdown criteria, largely because of the smaller H/D ratio of these designs. There is ample possibility for future work building on this study. While NTRgen is a robust and capable tool, improvements such as modeling axial varia tion in the tie tube (similar to what is done with the fuel) could be made. NTRfilter currently treats each individual fuel hex, resulting in some asym metrical zoning schemes. NTRfilter could be altered to take advantage of core symmetry when calculating zoning schemes and peaking factors.

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62 APPENDIX A NTRGEN PRIMARY INPUT FILE 0.4192 $ Diameter of inner tie tube flow (cm) 0.0508 $ Thickness of inner tie tube (cm) 0.3238 $ Thickness of tie tube moderator (cm) 0.0940 $ Thickness of outer tie tube flow (cm) 0.0203 $ Thickness of outer tie tube (cm) 0.1080 $ Thickness of tie tube insulator (cm) 3 $ Row of flow channels in fuel hex, center-to-edge 0.2133 $ Diameter of flow channels (cm)negative is percent of fuel hex as flow (%) 0.010 $ Thickness of coating at inlet (cm) 0.010 $ Thickness of coating at outlet (cm) 5. $ Percent of hex as coolant hole in slat hex (%) 9,2 $ Min thickness of slat hexes at core perimeter (cm) 2.022 $ Hex pitch (cm) 6 $ Ratio of fuel hexes to tie tubes (0, 2, 3, or 6) 84.000 $ Core diameter (cm) 0.762 $ Expansion gap thickness (cm) 1.27 $ Barrel thickness (cm) 8.0 $ Radial reflector region thickness (cm) 0.318 $ Vessel coolant gap thickness (cm) 0.635 $ Vessel thickness (cm) 114.69 $ Core height (cm) 18 $ Number of control drums 7.0 $ Drum diameter (cm) 0.2 $ Drum gap (cm) 0.8 $ Drum poison thickness (cm) 90. $ Poison angle (degrees) 0. $ Drum rotation angle (deg rees 0 is most reactive, 180 is least reactive) 10 $ Number of axial coolant regions 287. $ Core inlet temperature (K) 2700.0 $ Core outlet temperature (K) 4.65 $ Core inlet pressure (MPa) 1.1 $ Core pressure drop (MPa) 20.3 $ Tie tube inlet temperature (K) 428.9 $ Tie tube outlet temperature (K) 5.722 $ Tie tube inlet pressure (MPa) 0.701 $ Tie tube pressure drop (MPa) 800. $ Reflector temperature 0.1 $ Gap between core and support plate (cm) 10.6 $ Support plate thickness (cm) 1.65 $ TT up-pass manifold thickness (cm) 1.0 $ Bottom interface plate thickness (cm) 1.65 $ TT down-pass manifold thickness (cm) 1.0 $ Top interface plate thickness (cm) 2.65 $ Fuel coolant manifold thickness (cm) 1.0 $ Shield thickness (cm)

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63 1.575 $ Diameter of inner tie tube flow in plates (cm) 0.025 $ Channel thickness (cm) 0.1375 $ Thickness of outer tie tube flow in plates (cm) 1.6 $ Diameter of fuel coolant channel in plates (cm) 500,6.89 $ TT up-pass manifold Temperature (K) and Pressure (MPa) 30,9.65 $ TT down-pass manifold Temperature (K) and Pressure (MPa) 300,5.03 $ Fuel coolant manifold Temperature (K) and Pressure (MPa) 25.4 $ Length of chamber (cm) 0.1 $ Thickness of chamber wall (cm) 2 $ ihomcards=0 for one core region, 1 for homogenization by row 1 $ 0 for homogenized TT in partially discrete, 1 for discrete TT in PD 10 $ Number of axial tally regions Peak $ Type of tallies to be performed (0 for none, Peak and/or Energy) 0 $ =0 for no thermal expansion, =1 for thermal expansion approximation 0 $ =0 for no temp-dependent XS in fuel, =1 for temp XS in fuel Comp180 $ Fuel matrix ZrC40 $ Fuel/Coolant channel coating Inc718 $ Tie tube structure ZrH $ Tie tube moderator ZrCLow $ Tie tube insulation ZrC40 $ Tie tube matrix Be $ Slat reflector material Be $ Core Barrel Be $ Radial reflector B4C $ Control drum poison Al $ Outer vessel Hyd $ Coolant Al $ Plates Al $ Shield Al $ Chamber Wall -----------Accident Cases 2 $ Number of accident cases to generate b Hot Peak $ Tallies desired (0 for none, Peak and/or Energy) 0. $ Drum rotation angle (degrees) 1 $ =0 for no thermal expansion, =1 for thermal expansion approximation 0 $ =0 for no temp-dependent XS in fuel, =1 for temp XS in fuel Hyd $ In-core flow fuel hexes and tie tubes Hyd $ Outer-core flow vessel coolant 0 $ Void gaps expansion gap and RR gap 0 $ External to core, surrounding material c Shutdown 0 $ Tallies desired (0 for none, Peak and/or Energy) 180. $ Drum rotation angle (degrees) 0 $ =0 for no thermal expansion, =1 for thermal expansion approximation 0 $ =0 for no temp-dependent XS in fuel, =1 for temp XS in fuel Hyd $ In-core flow fuel hexes and tie tubes Hyd $ Outer-core flow vessel coolant 0 $ Void gaps expansion gap and RR gap 0 $ External to core, surrounding material

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64 APPENDIX B NTRGEN CELLCARDS INPUT FILE NTRa2 small engine NTR c c Corfill 10 0 -10 -152 148 fill=1 imp:n=1 $ Core c 30 Coregap 10 -112 -152 148 imp:n=1 $ Expansion Gap c 104 Barrel 112 -114 -152 148 imp:n=1 $ Beryllium Barrel 105 RRref 114 -117 -152 148 106 Vescool 117 -118 -152 148 imp:n=1 $ Vessel Cool ant Gap 110 Vessel 118 -120 -152 148 imp:n=1 $ Aluminum vessel c c c Flood areas 186 Extcore -120 -890 146 imp:n=1 $ void below core 187 Extcore 10 -120 920 -928 imp:n=1 $ above core inner radial void 188 Extcore 120 -122 -154 146 imp:n=1 $ radial void 189 Extcore 29 -120 890 -900 imp:n=1 $ below core inner radial void 190 0 122:154:-146 imp:n=0 c c Hex and Pins (or empty hexes) for inner secti on 200 Corelat uses latfill subroutine to write core lattice c 220 Fuelmat (401 402 etc auto fill) u=1,4,7,10,... imp:n=1 $ Fuel 240 Fuelcot auto fill 260 Fuelflw (-401:-402:etc auto fill) u=1,4,7,10,... imp:n=1 $ Flow 280 Fuelout auto fill c 370 TTflowi -160 u=2 imp:n=1 $ TT flow 372 TTstrui 160 -162 u=2 imp:n=1 $ TT Inconel 374 TTmod 162 -164 u=2 imp:n=1 $ TT ZrH 376 TTflowo 164 -166 u=2 imp:n=1 $ TT flow 378 TTstruo 166 -168 u=2 imp:n=1 $ TT Inconel 380 TTinsu 168 -170 u=2 imp:n=1 $ TT insulation 382 TTmatrx 170 u=2 imp:n=1 $ TT matrix c 500 Slatflw -180 u=9 imp:n=1 $ Coolant hole in slats 502 Slatmat 180 u=9 imp: n=1 $ Be slats c c Control Drums Refdrum c c Plates, Hydrogen flow manifolds, chamber exit flow 600 0 920 -921 -10 fill=150 imp:n=1 $ Support plate gap 602 0 921 -922 -10 fill=151 imp:n=1 $ Support plate 604 0 922 -923 -10 fill=152 imp:n=1 $ TT Up pass Manifold 606 0 923 -924 -10 fill=153 imp:n=1 $ Bottom Interf plate

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65 608 0 924 -925 -10 fill=154 imp:n=1 $ TT Downpass Manifold 610 0 925 -926 -10 fill=155 imp:n=1 $ Top Interf plate 612 FCMan 926 -927 -10 imp:n=1 $ Fuel coolant manifold 614 Shield 927 -928 -10 imp:n=1 $ Shield 692 FCCham 890 -900 -108 imp:n=1 $ Coolant exiting core 694 Plate 890 -900 108 -29 imp:n=1 $ Chamber wall c 620 FCMan -600 u=61 imp:n=1 $ Fuel coolant in-flow 621 Plate 600 -601 u=61 imp:n=1 $ Fuel coolant channel 622 Extcore 601 u=61 imp:n=1 $ Gap b/n core & Sup Plate 623 TTDn -605 u=62 imp:n=1 $ TT Downflow 624 Plate 605 -606 u=62 imp:n=1 $ TT flow separation 625 TTUp 606 -607 u=62 imp:n=1 $ TT Upflow 626 Plate 607 -608 u=62 imp:n=1 $ TT Upflow channel 627 Extcore 608 u=62 imp:n=1 $ Gap b/n core & Sup Plate 628 Extcore -600 u=63 imp:n=1 $ Gap b/n core & Sup Plate 629 Extcore 600 u=63 imp:n=1 $ Gap b/n core & Sup Plate c 630 FCMan -600 u=64 imp:n=1 $ Fuel coolant in-flow 631 Plate 600 -601 u=64 imp:n=1 $ Fuel coolant channel 632 Plate 601 u=64 imp:n=1 $ Support Plate 633 TTDn -605 u=65 imp:n=1 $ TT Downflow 634 Plate 605 -606 u=65 imp:n=1 $ TT flow separation 635 TTUp 606 -607 u=65 imp:n=1 $ TT Upflow 636 Plate 607 u=65 imp:n=1 $ Support Plate 637 Plate -600 u=66 imp:n=1 $ Support Plate 638 Plate 600 u=66 imp:n=1 $ Support Plate c 640 FCMan -600 u=67 imp:n=1 $ Fuel coolant in-flow 641 Plate 600 -601 u=67 imp:n=1 $ Fuel coolant channel 642 TTUp 601 u=67 imp:n=1 $ TT Up-pass Manifold 643 TTDn -605 u=68 imp:n=1 $ TT Downflow 644 Plate 605 -606 u=68 imp:n=1 $ TT flow separation 645 TTUp 606 -607 u=68 imp:n=1 $ TT Upflow 646 TTUp 607 u=68 imp:n=1 $ TT Up-pass Manifold 647 TTUp -600 u=69 imp:n=1 $ TT Up-pass Manifold 648 TTUp 600 u=69 imp:n=1 $ TT Up-pass Manifold c 650 FCMan -600 u=70 imp:n=1 $ Fuel coolant in-flow 651 Plate 600 -601 u=70 imp:n=1 $ Fuel coolant channel 652 Plate 601 u=70 imp:n=1 $ Bottom Interface Plate 653 TTDn -605 u=71 imp:n=1 $ TT Downflow 654 Plate 605 -606 u=71 imp:n=1 $ TT flow separation 655 Plate 606 u=71 imp:n=1 $ Bottom Interface Plate 657 Plate -600 u=72 imp:n=1 $ Bottom Interface Plate 658 Plate 600 u=72 imp:n=1 $ Bottom Interface Plate c 660 FCMan -600 u=73 imp:n=1 $ Fuel coolant in-flow 661 Plate 600 -601 u=73 imp:n=1 $ Fuel coolant channel 662 TTDn 601 u=73 imp:n=1 $ TT Down-pass Manifold 663 TTDn -605 u=74 imp:n=1 $ TT Downflow 664 TTDn 605 u=74 imp:n=1 $ TT Down-pass Manifold 667 TTDn -600 u=75 imp:n=1 $ TT Down-pass Manifold 668 TTDn 600 u=75 imp:n=1 $ TT Down-pass Manifold c 670 FCMan -600 u=76 imp:n=1 $ Fuel coolant in-flow

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66 671 Plate 600 -601 u=76 imp:n=1 $ Fuel coolant channel 672 Plate 601 u=76 imp:n=1 $ Top Interface Plate 673 Plate -605 u=77 imp:n=1 $ Top Interface Plate 674 Plate 605 u=77 imp:n=1 $ Top Interface Plate 677 Plate -600 u=78 imp:n=1 $ Top Interface Plate 678 Plate 600 u=78 imp:n=1 $ Top Interface Plate c 680 0 -201 202 -203 204 -205 206 $ Support plate gap lat=2 u=150 imp:n=1 spgfill 682 0 -201 202 -203 204 -205 206 $ Support plate lat=2 u=151 imp:n=1 spfill 684 0 -201 202 -203 204 -205 206 $ TT UpPass Manifold lat=2 u=152 imp:n=1 ttufill 686 0 -201 202 -203 204 -205 206 $ Bottom Interf Plate lat=2 u=153 imp:n=1 bipfill 688 0 -201 202 -203 204 -205 206 $ TT DownPass Manifold lat=2 u=154 imp:n=1 ttdfill 690 0 -201 202 -203 204 -205 206 $ Top Interf Plate lat=2 u=155 imp:n=1 tipfill c end of cell cards

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67 APPENDIX C NTRGEN MATCARDS INPUT FILE c beginning of material cards c Material Card (number in parens is room temp density to be used) c [Comp180/3.49] CTE[6.6,0.,0.,0] m1 92234.30c -0.03692 92235.30c -4.836 92238.30c -0.327028 6000.30c -38.8 40090.30c -28.812 40091.30c -6.2832 40092.30c -9.604 40094.30c -9.7328 40096.30c -1.568 c [Comp399/3.61] CTE[6.6,0.,0.,0] m2 92234.30c -0.07881 92235.30c -10.545 92238.30c -0.69819 6000.30c -36.0 40090.30c -27.011 40091.30c -5.8905 40092.30c -9.004 40094.30c -9.1245 40096.30c -1.47 c [Comp598/3.64] CTE[6.6,0.,0.,0] m3 92234.30c -0.11644 92235.30c -15.58 92238.30c -1.03156 6000.30c -33.6 40090.30c -25.5192 40091.30c -5.5651 40092.30c -8.5064 40094.30c -8.6205 40096.30c -1.3889 c c [ZrC40/8.640] 40v/o ZrC in C m4 6000.30c -2.24605E-01 40090.30c -3.93173E-01 40091.30c -8.669607-02 40092.30c -1.33973E-01 40094.30c -1.38727E-01 40096.30c -2.28260E-02 c [Inc718/8.18] Inconel718(8.18) m5 5010.30c -1.04165E-05 5011.30c -4.96296E-05 6000.30c -7.99685E-04 13027.30c -5.00094E-03 15031.30c -1.50369E-04 16032.30c -1.49673E-04 22000.30c -8.99863E-03 24050.30c -7.93239E-03 24052.30c -1.59022E-01 24053.30c -1.83764E-02 24054.30c -4.65735E-03 25055.30c -3.50533E-03 26054.30c -9.57669E-03 26056.30c -1.54414E-01 26057.30c -3.60316E-03 26058.30c -4.92188E-04 27059.30c -9.99324E-03 28058.30c -3.52802E-01 28060.30c -1.40580E-01 28061.30c -6.21189E-03 28062.30c -2.01325E-02 28064.30c -5.29817E-03 29063.30c -2.05126E-03 29065.30c -9.45622E-04 41093.30c -5.12410E-02 42000.30c -3.05047E-02 14028.30c -3.21667E-03 14029.30c -1.69170E-04 14030.30c -1.15357E-04 c [Be/1.81] Be TD=1.85 / 98%=1.81 CTE[7.0,0.,0.,0.] m6 4009.30c -1.0 mt6 be.01t c c [ZrH/5.47] ZrH(5.47g/cc) SNAP-2 ratios ignoring Hf and Nb m7 1001.30c -2.16180E-02 40090.30c -4.96099E-01 40091.30c -1.09392E-01 40092.30c -1.69046E-01 40094.30c -1.75043E-01 40096.30c -2.88015E-02 mt7 h/zr.01t c [ZrCLow/0.640] ZrC Low density insulator m8 6000.30c -1.16347E-01 40090.30c -4.48066E-01 40091.30c -9.88003E-02 40092.30c -1.52678E-01 40094.30c -1.58095E-01 40096.30c -2.60129E-02 c [BorCop/8.8] Borated Copper(8.8) m9 5010.30c -1.18249E-02 5011.30c -6.84296E-04

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68 29063.30c -6.74727E-01 29065.30c -3.12764E-01 c [Al/2.7] Aluminum(2.7) m10 13027.30c -1.0 c [Hyd/0.000614] Hydrogen m11 1001.30c -1.0 c [B4C/2.2] Boron carbide 95% enr TD=2.3 g/cc m12 5010.30c -7.28046E-01 5011.30c -4.21312E-02 6000.30c -2.29823E-01 c m12 5010.30c .76 5011.30c .04 6000.30c .20 c [Water/1.0] H2O(1.0) m50 1001.30c -1.11915E-01 8016.30c -8.88085E-01 mt50 lwtr.01t c m50 1001.60c 2 8016.60c 1 c c [Wetsand/2.056] (64%quartz at 2.65 g/cc)) m51 1001.30c -1.61499E-02 8016.30c -5.83856E-01 14028.30c -3.67490E-01 14029.30c -1.93260E-02 14030.30c -1.31787E-02 mt51 lwtr.01t c end of mat cards c print -128 prdmp 110 110 1 1 mode n kcode 4000 1.0 10 410 ksrc 8 -8 0 -8 8 0 9 7 0 -9 -7 0 3 3 5 -3 -3 -5 2 4 -5 -2 -4 5 7 0 10 8 0 -10 -8 0 10 -7 0 -10 5 0 15 6 0 -15 -6 0 15 -5 0 -15 9 4 20 -4 -9 -20 6 -8 25 -6 8 25 c end of deck

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69 APPENDIX D NTRGEN TEMPERATURE INPUT FILE 642.1 4.964 1040.3 4.884 1459.8 3.850 1846.4 2.617 2207.7 1.773 2518.9 1.368 2721.7 1.141 2821.5 0.924 2838.2 0.731 2822.3 0.613

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70 APPENDIX E NTRGEN ZONE INPUT FILE 10 0.9300 0.8523 0.7811 0.7158 0.6560 0.6012 0.5510 0.5050 0.4628 0.4241 10 -23 2.35 0.4241 11 -23 2.36 0.4241 7 -22 2.04 0.5050 8 -22 1.94 0.5050 9 -22 1.83 0.5510 11 -22 1.95 0.5050 14 -22 2.33 0.4241 15 -22 2.45 0.4241 4 -21 2.03 0.5050 5 -21 1.85 0.5510 6 -21 1.64 0.6012 8 -21 1.47 0.6560 9 -21 1.49 0.6560 10 -21 1.51 0.6560 11 -21 1.62 0.6012 12 -21 1.74 0.5510 13 -21 1.79 0.5510 15 -21 1.95 0.5050 18 -21 2.29 0.4241 19 -21 2.36 0.4241 1 -20 2.12 0.4628 2 -20 1.83 0.5510 3 -20 1.64 0.6012 5 -20 1.36 0.7158 6 -20 1.29 0.7811 7 -20 1.24 0.7811 8 -20 1.25 0.7811 9 -20 1.30 0.7811 10 -20 1.30 0.7811 12 -20 1.40 0.7158 13 -20 1.41 0.7158 14 -20 1.46 0.6560 15 -20 1.61 0.6012 16 -20 1.70 0.6012 17 -20 1.75 0.5510 19 -20 2.00 0.5050

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71 -2 -19 2.44 0.4241 -1 -19 2.05 0.5050 0 -19 1.77 0.5510 2 -19 1.38 0.7158 3 -19 1.29 0.7811 4 -19 1.22 0.8523 5 -19 1.17 0.8523 6 -19 1.14 0.8523 7 -19 1.13 0.8523 9 -19 1.15 0.8523 10 -19 1.13 0.8523 11 -19 1.19 0.8523 12 -19 1.20 0.8523 13 -19 1.27 0.7811 14 -19 1.32 0.7811 16 -19 1.37 0.7158 17 -19 1.40 0.7158 18 -19 1.52 0.6560 19 -19 1.80 0.5510 20 -19 2.14 0.4628 -3 -18 2.35 0.4241 -1 -18 1.56 0.6560 0 -18 1.36 0.7158 1 -18 1.25 0.7811 2 -18 1.18 0.8523 3 -18 1.11 0.9300 4 -18 1.09 0.9300 6 -18 1.08 0.9300 7 -18 1.06 0.9300 8 -18 1.06 0.9300 9 -18 1.07 0.9300 10 -18 1.09 0.9300 11 -18 1.09 0.9300 13 -18 1.14 0.8523 14 -18 1.16 0.8523 15 -18 1.17 0.8523 16 -18 1.19 0.8523 17 -18 1.29 0.7811 18 -18 1.40 0.7158 20 -18 1.89 0.5510 -3 -17 1.78 0.5510 -2 -17 1.48 0.6560 -1 -17 1.29 0.7811 0 -17 1.17 0.8523 1 -17 1.10 0.9300 3 -17 1.06 0.9300 4 -17 1.05 0.9300 5 -17 1.05 0.9300 6 -17 1.06 0.9300 7 -17 1.06 0.9300 8 -17 1.04 0.9300 10 -17 1.07 0.9300 11 -17 1.07 0.9300 12 -17 1.06 0.9300 13 -17 1.10 0.9300 14 -17 1.12 0.8523

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72 15 -17 1.08 0.9300 17 -17 1.20 0.8523 18 -17 1.24 0.7811 19 -17 1.41 0.7158 20 -17 1.69 0.6012 21 -17 2.12 0.4628 -4 -16 1.75 0.5510 -3 -16 1.43 0.7158 -2 -16 1.24 0.7811 0 -16 1.10 0.9300 1 -16 1.06 0.9300 2 -16 1.06 0.9300 3 -16 1.03 0.9300 4 -16 1.06 0.9300 5 -16 1.04 0.9300 7 -16 1.06 0.9300 8 -16 1.05 0.9300 9 -16 1.08 0.9300 10 -16 1.06 0.9300 11 -16 1.07 0.9300 12 -16 1.07 0.9300 14 -16 1.09 0.9300 15 -16 1.09 0.9300 16 -16 1.09 0.9300 17 -16 1.13 0.8523 18 -16 1.20 0.8523 19 -16 1.31 0.7811 21 -16 1.93 0.5050 -7 -15 2.43 0.4241 -6 -15 1.99 0.5050 -5 -15 1.67 0.6012 -3 -15 1.20 0.8523 -2 -15 1.12 0.8523 -1 -15 1.07 0.9300 0 -15 1.04 0.9300 1 -15 1.07 0.9300 2 -15 1.07 0.9300 4 -15 1.06 0.9300 5 -15 1.07 0.9300 6 -15 1.07 0.9300 7 -15 1.09 0.9300 8 -15 1.07 0.9300 9 -15 1.09 0.9300 11 -15 1.07 0.9300 12 -15 1.04 0.9300 13 -15 1.05 0.9300 14 -15 1.06 0.9300 15 -15 1.04 0.9300 16 -15 1.06 0.9300 18 -15 1.16 0.8523 19 -15 1.26 0.7811 20 -15 1.45 0.7158 21 -15 1.71 0.6012 22 -15 2.10 0.4628 -8 -14 2.36 0.4241 -6 -14 1.50 0.6560

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73 -5 -14 1.33 0.7811 -4 -14 1.17 0.8523 -3 -14 1.10 0.9300 -2 -14 1.07 0.9300 -1 -14 1.05 0.9300 1 -14 1.06 0.9300 2 -14 1.09 0.9300 3 -14 1.09 0.9300 4 -14 1.11 0.9300 5 -14 1.13 0.8523 6 -14 1.10 0.9300 8 -14 1.14 0.8523 9 -14 1.11 0.9300 10 -14 1.11 0.9300 11 -14 1.08 0.9300 12 -14 1.08 0.9300 13 -14 1.09 0.9300 15 -14 1.05 0.9300 16 -14 1.03 0.9300 17 -14 1.06 0.9300 18 -14 1.11 0.9300 19 -14 1.21 0.8523 20 -14 1.34 0.7158 22 -14 1.97 0.5050 -8 -13 1.79 0.5510 -7 -13 1.43 0.7158 -6 -13 1.27 0.7811 -5 -13 1.20 0.8523 -4 -13 1.10 0.9300 -2 -13 1.07 0.9300 -1 -13 1.06 0.9300 0 -13 1.08 0.9300 1 -13 1.11 0.9300 2 -13 1.14 0.8523 3 -13 1.15 0.8523 5 -13 1.19 0.8523 6 -13 1.17 0.8523 7 -13 1.16 0.8523 8 -13 1.19 0.8523 9 -13 1.16 0.8523 10 -13 1.14 0.8523 12 -13 1.12 0.8523 13 -13 1.10 0.9300 14 -13 1.06 0.9300 15 -13 1.04 0.9300 16 -13 1.03 0.9300 17 -13 1.07 0.9300 19 -13 1.15 0.8523 20 -13 1.23 0.7811 21 -13 1.46 0.6560 22 -13 1.82 0.5510 23 -13 2.27 0.4241 -9 -12 1.78 0.5510 -8 -12 1.42 0.7158 -7 -12 1.21 0.8523 -5 -12 1.09 0.9300

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86 -21 9 1.72 0.6012 -19 9 1.15 0.8523 -18 9 1.05 0.9300 -17 9 1.04 0.9300 -16 9 1.06 0.9300 -15 9 1.08 0.9300 -14 9 1.14 0.8523 -12 9 1.23 0.7811 -11 9 1.26 0.7811 -10 9 1.33 0.7811 -9 9 1.36 0.7158 -8 9 1.37 0.7158 -7 9 1.42 0.7158 -5 9 1.40 0.7158 -4 9 1.44 0.7158 -3 9 1.40 0.7158 -2 9 1.39 0.7158 -1 9 1.35 0.7158 0 9 1.34 0.7158 2 9 1.28 0.7811 3 9 1.20 0.8523 4 9 1.18 0.8523 5 9 1.14 0.8523 6 9 1.08 0.9300 7 9 1.05 0.9300 9 9 1.06 0.9300 10 9 1.09 0.9300 11 9 1.20 0.8523 12 9 1.39 0.7158 13 9 1.78 0.5510 -21 10 1.64 0.6012 -20 10 1.30 0.7811 -19 10 1.12 0.8523 -18 10 1.06 0.9300 -17 10 1.05 0.9300 -15 10 1.08 0.9300 -14 10 1.14 0.8523 -13 10 1.17 0.8523 -12 10 1.23 0.7811 -11 10 1.25 0.7811 -10 10 1.30 0.7811 -8 10 1.34 0.7158 -7 10 1.36 0.7158 -6 10 1.36 0.7158 -5 10 1.37 0.7158 -4 10 1.35 0.7158 -3 10 1.34 0.7158 -1 10 1.32 0.7811 0 10 1.27 0.7811 1 10 1.23 0.7811 2 10 1.18 0.8523 3 10 1.15 0.8523 4 10 1.11 0.9300 6 10 1.08 0.9300 7 10 1.06 0.9300 8 10 1.08 0.9300

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87 9 10 1.15 0.8523 10 10 1.28 0.7811 11 10 1.45 0.7158 13 10 2.28 0.4241 -22 11 1.94 0.5050 -21 11 1.50 0.6560 -20 11 1.23 0.7811 -18 11 1.06 0.9300 -17 11 1.03 0.9300 -16 11 1.05 0.9300 -15 11 1.05 0.9300 -14 11 1.12 0.9300 -13 11 1.16 0.8523 -11 11 1.22 0.7811 -10 11 1.28 0.7811 -9 11 1.29 0.7811 -8 11 1.27 0.7811 -7 11 1.30 0.7811 -6 11 1.30 0.7811 -4 11 1.29 0.7811 -3 11 1.29 0.7811 -2 11 1.24 0.7811 -1 11 1.23 0.7811 0 11 1.18 0.8523 1 11 1.16 0.8523 3 11 1.10 0.9300 4 11 1.08 0.9300 5 11 1.06 0.9300 6 11 1.10 0.9300 7 11 1.10 0.9300 8 11 1.16 0.8523 10 11 1.59 0.6560 11 11 1.90 0.5050 12 11 2.30 0.4241 -23 12 2.36 0.4241 -21 12 1.43 0.7158 -20 12 1.25 0.7811 -19 12 1.12 0.9300 -18 12 1.08 0.9300 -17 12 1.04 0.9300 -16 12 1.03 0.9300 -14 12 1.08 0.9300 -13 12 1.13 0.8523 -12 12 1.16 0.8523 -11 12 1.20 0.8523 -10 12 1.23 0.7811 -9 12 1.21 0.8523 -7 12 1.23 0.7811 -6 12 1.27 0.7811 -5 12 1.24 0.7811 -4 12 1.23 0.7811 -3 12 1.21 0.8523 -2 12 1.17 0.8523 0 12 1.15 0.8523 1 12 1.11 0.9300 2 12 1.09 0.9300

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88 3 12 1.05 0.9300 4 12 1.05 0.9300 5 12 1.07 0.9300 7 12 1.21 0.8523 8 12 1.39 0.7158 9 12 1.71 0.6012 -23 13 2.29 0.4241 -22 13 1.79 0.5510 -21 13 1.44 0.7158 -20 13 1.23 0.7811 -19 13 1.15 0.8523 -17 13 1.05 0.9300 -16 13 1.05 0.9300 -15 13 1.07 0.9300 -14 13 1.09 0.9300 -13 13 1.13 0.8523 -12 13 1.13 0.8523 -10 13 1.16 0.8523 -9 13 1.17 0.8523 -8 13 1.20 0.8523 -7 13 1.21 0.8523 -6 13 1.19 0.8523 -5 13 1.20 0.8523 -3 13 1.13 0.8523 -2 13 1.13 0.8523 -1 13 1.10 0.9300 0 13 1.09 0.9300 1 13 1.07 0.9300 2 13 1.06 0.9300 4 13 1.08 0.9300 5 13 1.15 0.8523 6 13 1.27 0.7811 7 13 1.42 0.7158 8 13 1.75 0.5510 -22 14 1.93 0.5050 -20 14 1.32 0.7811 -19 14 1.21 0.8523 -18 14 1.11 0.9300 -17 14 1.08 0.9300 -16 14 1.07 0.9300 -15 14 1.07 0.9300 -13 14 1.08 0.9300 -12 14 1.11 0.9300 -11 14 1.11 0.9300 -10 14 1.12 0.9300 -9 14 1.12 0.9300 -8 14 1.16 0.8523 -6 14 1.14 0.8523 -5 14 1.12 0.8523 -4 14 1.14 0.8523 -3 14 1.11 0.9300 -2 14 1.09 0.9300 -1 14 1.05 0.9300 1 14 1.05 0.9300 2 14 1.05 0.9300 3 14 1.06 0.9300

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89 4 14 1.13 0.8523 5 14 1.30 0.7811 6 14 1.49 0.6560 8 14 2.33 0.4241 -22 15 2.09 0.4628 -21 15 1.67 0.6012 -20 15 1.41 0.7158 -19 15 1.22 0.8523 -18 15 1.15 0.8523 -16 15 1.06 0.9300 -15 15 1.06 0.9300 -14 15 1.07 0.9300 -13 15 1.06 0.9300 -12 15 1.05 0.9300 -11 15 1.07 0.9300 -9 15 1.11 0.9300 -8 15 1.12 0.8523 -7 15 1.08 0.9300 -6 15 1.10 0.9300 -5 15 1.09 0.9300 -4 15 1.06 0.9300 -2 15 1.04 0.9300 -1 15 1.08 0.9300 0 15 1.06 0.9300 1 15 1.04 0.9300 2 15 1.08 0.9300 3 15 1.14 0.8523 5 15 1.64 0.6012 6 15 1.95 0.5050 7 15 2.45 0.4241 -21 16 1.86 0.5510 -19 16 1.30 0.7811 -18 16 1.21 0.8523 -17 16 1.11 0.9300 -16 16 1.08 0.9300 -15 16 1.08 0.9300 -14 16 1.07 0.9300 -12 16 1.09 0.9300 -11 16 1.08 0.9300 -10 16 1.09 0.9300 -9 16 1.10 0.9300 -8 16 1.09 0.9300 -7 16 1.09 0.9300 -5 16 1.05 0.9300 -4 16 1.06 0.9300 -3 16 1.03 0.9300 -2 16 1.05 0.9300 -1 16 1.06 0.9300 0 16 1.06 0.9300 2 16 1.19 0.8523 3 16 1.39 0.7158 4 16 1.74 0.5510 -21 17 2.05 0.5050 -20 17 1.68 0.6012 -19 17 1.42 0.7158 -18 17 1.25 0.7811

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90 -17 17 1.19 0.8523 -15 17 1.11 0.9300 -14 17 1.10 0.9300 -13 17 1.09 0.9300 -12 17 1.10 0.9300 -11 17 1.09 0.9300 -10 17 1.10 0.9300 -8 17 1.07 0.9300 -7 17 1.07 0.9300 -6 17 1.05 0.9300 -5 17 1.07 0.9300 -4 17 1.07 0.9300 -3 17 1.06 0.9300 -1 17 1.08 0.9300 0 17 1.14 0.8523 1 17 1.27 0.7811 2 17 1.38 0.7158 3 17 1.76 0.5510 -20 18 1.92 0.5050 -18 18 1.37 0.7158 -17 18 1.29 0.7811 -16 18 1.22 0.8523 -15 18 1.16 0.8523 -14 18 1.15 0.8523 -13 18 1.15 0.8523 -11 18 1.12 0.9300 -10 18 1.12 0.8523 -9 18 1.07 0.9300 -8 18 1.06 0.9300 -7 18 1.07 0.9300 -6 18 1.08 0.9300 -4 18 1.09 0.9300 -3 18 1.14 0.8523 -2 18 1.17 0.8523 -1 18 1.21 0.8523 0 18 1.33 0.7158 1 18 1.50 0.6560 3 18 2.29 0.4241 -20 19 2.17 0.4628 -19 19 1.76 0.5510 -18 19 1.54 0.6560 -17 19 1.45 0.7158 -16 19 1.39 0.7158 -14 19 1.28 0.7811 -13 19 1.26 0.7811 -12 19 1.22 0.7811 -11 19 1.20 0.8523 -10 19 1.15 0.8523 -9 19 1.12 0.8523 -7 19 1.11 0.9300 -6 19 1.14 0.8523 -5 19 1.17 0.8523 -4 19 1.21 0.8523 -3 19 1.29 0.7811 -2 19 1.39 0.7158 0 19 1.75 0.5510

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91 1 19 2.03 0.5050 2 19 2.39 0.4241 -19 20 2.07 0.4628 -17 20 1.75 0.5510 -16 20 1.72 0.6012 -15 20 1.61 0.6012 -14 20 1.52 0.6560 -13 20 1.43 0.7158 -12 20 1.40 0.7158 -10 20 1.30 0.7811 -9 20 1.25 0.7811 -8 20 1.25 0.7811 -7 20 1.27 0.7811 -6 20 1.32 0.7811 -5 20 1.40 0.7158 -3 20 1.68 0.6012 -2 20 1.82 0.5510 -1 20 2.15 0.4628 -19 21 2.43 0.4241 -18 21 2.33 0.4241 -15 21 1.98 0.5050 -13 21 1.78 0.5510 -12 21 1.72 0.6012 -11 21 1.62 0.6012 -10 21 1.51 0.6560 -9 21 1.41 0.7158 -8 21 1.50 0.6560 -6 21 1.70 0.6012 -5 21 1.90 0.5050 -4 21 2.13 0.4628 -15 22 2.45 0.4241 -14 22 2.37 0.4241 -11 22 1.97 0.5050 -9 22 1.82 0.5510 -8 22 1.96 0.5050 -7 22 2.10 0.4628 -11 23 2.32 0.4241 -10 23 2.28 0.4241

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92 APPENDIX F MCNPX INPUT FILE NTR Model b Hot Detailed c c 10 0 -10 909 -910 fill=100 imp:n=1 $ Core 11 0 -11 908 -909 fill=101 imp:n=1 $ Core 12 0 -12 907 -908 fill=102 imp:n=1 $ Core 13 0 -13 906 -907 fill=103 imp:n=1 $ Core 14 0 -14 905 -906 fill=104 imp:n=1 $ Core 15 0 -15 904 -905 fill=105 imp:n=1 $ Core 16 0 -16 903 -904 fill=106 imp:n=1 $ Core 17 0 -17 902 -903 fill=107 imp:n=1 $ Core 18 0 -18 901 -902 fill=108 imp:n=1 $ Core 19 0 -19 900 -901 fill=109 imp:n=1 $ Core c 30 0 10 -112 909 -910 imp:n=1 $ Core expansion gap 31 0 11 -112 908 -909 imp:n=1 $ Core expansion gap 32 0 12 -112 907 -908 imp:n=1 $ Core expansion gap 33 0 13 -112 906 -907 imp:n=1 $ Core expansion gap 34 0 14 -112 905 -906 imp:n=1 $ Core expansion gap 35 0 15 -112 904 -905 imp:n=1 $ Core expansion gap 36 0 16 -112 903 -904 imp:n=1 $ Core expansion gap 37 0 17 -112 902 -903 imp:n=1 $ Core expansion gap 38 0 18 -112 901 -902 imp:n=1 $ Core expansion gap 39 0 19 -112 900 -901 imp:n=1 $ Core expansion gap c 104 6 -1.79086 112 -114 -152 148 imp:n=1 $ Beryllium Barrel 105 6 -1.790865 114 -117 -152 148 #801 #802 #803 #804 #805 #806 #807 #808 #809 #810 #811 #812 #813 #814 #815 #816 #817 #818 imp:n=1 $ Reflector 106 11 -0.00061 117 -118 -152 148 imp:n=1 $ Vessel Coolant Gap 110 10 -2.67146 118 -120 -152 148 imp:n=1 $ Aluminum vessel c c c Flood areas 180 0 112 -120 152 -910 imp:n=1 182 0 112 -120 -148 900 imp:n=1 184 0 -120 -154 928 imp:n=1 $ void above core 186 0 -120 -890 146 imp:n=1 $ void below core 187 0 10 -120 920 -928 imp:n=1 $ above core inner radial 188 0 120 -122 -154 146 imp:n=1 $ radial void 189 0 29 -120 890 -900 imp:n=1 $ below core inner radial 190 0 122:154:-146 imp:n=0 c c Hex and Pins (or empty hexes) for inner secti on 200 0 -201 202 -203 204 -205 206 $ Hex

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93 lat=2 u=100 imp:n=1 fill=-29:29 -29:29 0:0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 207 207 206 2 207 3 3 209 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 207 206 205 2 204 204 204 205 206 206 2 207 3 3 209 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 208 206 205 2 203 202 202 202 202 202 2 203 203 204 205 205 206 2 207 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 207 206 2 203 202 201 201 201 201 2 201 201 201 201 202 202 2 203 203 204 206 208 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 2 204 203 202 201 1 1 2 1 1 1 1 1 1 2 201 201 201 201 202 203 2 206 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 206 204 202 201 1 2 1 1 1 1 1 1 2 1 1 1 1 201 1 2 201 202 203 205 208 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 206 203 202 2 1 1 1 1 1 1 2

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94 1 1 1 1 1 1 2 1 1 1 201 201 202 2 207 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 207 205 2 201 201 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 2 201 202 203 205 208 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 2 204 202 201 1 1 1 2 1 1 1 1 201 1 2 201 1 1 1 1 1 2 1 1 1 1 201 203 2 207 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 206 203 202 201 1 2 1 1 1 1 201 201 2 201 201 201 201 201 201 2 201 1 1 1 1 1 2 201 202 204 206 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 206 203 201 2 1 1 1 1 201 201 2 201 201 202 201 202 202 2 201 201 201 201 1 1 2 1 1 1 201 202 203 2 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 207 205 2 201 1 1 1 1 1 2 201 201 202 202 202 202 2 202 202 202 202 202 201 2 201 1 1 1 1 1 2 202 203 207 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 2 204 202 201 1 1 1 2 201 201 201 202 202 202 2 203 203 203 203 203 203 2 202 202 201 201 1 1 2 1 1 201 202 205 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 206 204 202 201 1 2 1 1 201 201 201 202 2 202 203 203 203 203 203 2 203 203 203 202 202 201 2 201 1 1 1 1 201 2 206 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 207 204 202 2 1 1 1 1 201 201 2 202 202 203 203 203 203 2 204 204 204 204 203 203 2 202 202 201 201 1 1 2 201 201 203 206 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 208 2 202 201 1 1 1 1 2 201 202 202 203 203 203 2 204 204 204 204 204 204 2 204 203 202 202 202 201 2 1 1 1 1 202 203 2 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 205 202 201 1 1 2 1 201 201 202 202 203 2 204 204 204 204 205 205 2 205 204 204 204 203 203 2 202 201 201 1 1 1 2 202 204 207 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 206 203 201 2 1 1 1 201 201 202 2 203 203 204 204 204 204 2 205 205 205 205 204 204 2 203 203 202 202 201 201 2 1 1 201 203 205 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 208 2 202 1 1 1 1 201 2 202 202 203 203 204 204 2 205 205 205 205 205 205 2 204 204 204 203 203 202 2 201 1 1 1 1 201 2 205 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 205 202 201 1 1 2 1 201 202 202 203 203 2 204 204 205 205 205 205 2 205 205 205 204 204 203 2 203 202 201 201 1 1 2 1 201 203 205 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 206 203 201 2 1 1 1 201 201 202 2 203 204 204 204 205 205 2 206 206 205 205 205 205 2

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95 204 203 203 202 202 201 2 1 1 1 1 201 203 2 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 208 2 202 1 1 1 1 1 2 201 202 203 204 204 204 2 205 205 205 205 205 205 2 205 204 204 204 203 203 2 202 201 1 1 1 1 2 202 204 207 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 206 203 201 1 1 2 1 201 201 202 202 203 2 204 204 205 205 205 205 2 205 205 205 205 204 204 2 203 203 202 201 201 1 2 1 1 201 203 205 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 207 204 202 2 1 1 1 1 201 202 2 203 203 204 204 205 205 2 205 205 205 205 205 205 2 204 204 203 203 202 202 2 1 1 1 1 201 202 2 208 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 2 203 202 1 1 1 1 2 201 202 202 203 204 204 2 205 205 205 205 205 205 2 205 205 204 204 204 203 2 202 201 1 1 1 1 2 201 203 206 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 206 203 201 1 2 1 201 201 201 202 203 2 204 204 205 205 205 205 2 205 205 205 205 204 204 2 203 203 202 201 201 1 2 1 1 1 202 205 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 205 2 201 1 1 1 201 201 2 202 203 203 204 204 204 2 205 205 205 205 205 205 2 204 204 203 203 202 202 2 201 1 1 1 1 202 2 207 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 205 202 201 1 1 2 201 201 202 202 203 203 2 204 204 204 204 205 205 2 204 204 204 203 203 203 2 202 201 201 1 1 1 2 201 203 206 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 207 204 202 2 1 1 1 201 201 202 2 203 203 204 204 204 204 2 204 204 204 204 204 204 2 203 202 202 201 201 1 2 1 1 201 202 205 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 2 203 202 1 1 1 1 2 201 202 202 203 203 203 2 204 204 204 204 204 204 2 203 203 203 202 201 201 2 1 1 1 1 1 202 2 207 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 206 203 201 1 2 1 1 201 201 202 202 2 203 203 203 204 204 203 2 204 203 203 203 203 202 2 201 201 1 1 1 1 2 201 203 207 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 205 2 201 1 1 1 1 201 2 202 202 202 203 203 203 2 203 203 203 203 203 203 2 202 201 201 201 1 1 2 1 1 201 203 206 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 205 202 201 1 1 2 1 201 201 202 202 202 2 203 203 203 203 203 203 2 202 202 202 201 201 1 2 1 1 1 201 202 203 2 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 207 204 202 2 1 1 1 1 1 201 2 202 202 202 202 202 202 2 202 202 202 202 201 201 2 1 1 1 1 1 201 2 204 207 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 2 203 202 1 1 1 1 2 1 201 201 201 202 201 2 202 202 202 202 201 201 2 201 1 1 1 1 1 2

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96 201 203 205 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 206 203 202 201 2 1 1 1 1 201 201 2 201 201 201 201 201 201 2 201 201 1 1 1 1 2 1 201 202 203 206 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 207 2 202 201 1 1 1 1 2 1 1 1 1 1 201 2 201 201 201 1 1 1 2 1 1 1 201 202 204 2 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 208 205 203 201 201 2 1 1 1 1 1 1 2 1 201 1 1 1 1 2 1 1 1 1 1 201 2 205 207 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 206 2 202 201 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 2 201 203 206 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 207 205 203 202 201 2 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 201 202 203 206 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 207 2 203 202 201 201 201 201 2 1 201 1 1 1 1 2 1 201 201 201 203 204 2 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 208 206 204 203 203 2 202 202 202 201 201 201 2 1 201 201 201 202 203 2 206 207 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 208 2 206 205 205 204 203 203 2 202 202 202 202 202 203 2 205 206 208 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 209 3 3 207 2 206 205 205 204 203 204 2 205 207 208 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 209 3 3 207 2 206 207 208 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 209 209 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

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97 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 201 0 -221 222 -223 224 -225 226 $ Hex lat=2 u=101 imp:n=1 fill=-29:29 -29:29 0:0 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 217 217 216 5 217 6 6 219 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 217 216 215 5 214 214 214 215 216 216 5 217 6 6 219 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 218 216 215 5 213 212 212 212 212 212 5 213 213 214 215 215 216 5 217 6 6 6 6 6

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98 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 217 216 5 213 212 211 211 211 211 5 211 211 211 211 212 212 5 213 213 214 216 218 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 5 214 213 212 211 4 4 5 4 4 4 4 4 4 5 211 211 211 211 212 213 5 216 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 216 214 212 211 4 5 4 4 4 4 4 4 5 4 4 4 4 211 4 5 211 212 213 215 218 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 216 213 212 5 4 4 4 4 4 4 5 4 4 4 4 4 4 5 4 4 4 211 211 212 5 217 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 217 215 5 211 211 4 4 4 4 5 4 4 4 4 4 4 5 4 4 4 4 4 4 5 211 212 213 215 218 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 5 214 212 211 4 4 4 5 4 4 4 4 211 4 5 211 4 4 4 4 4 5 4 4 4 4 211 213 5 217 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 216 213 212 211 4 5 4 4 4 4 211 211 5 211 211 211 211 211 211 5 211 4 4 4 4 4 5 211 212 214 216 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 216 213 211 5 4 4 4 4 211 211 5 211 211 212 211 212 212 5 211 211 211 211 4 4 5 4 4 4 211 212 213 5 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 217 215 5 211 4 4 4 4 4 5 211 211 212 212 212 212 5 212 212 212 212 212 211 5 211 4 4 4 4 4 5 212 213 217 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 5 214 212 211 4 4 4 5 211 211 211 212 212 212 5 213 213 213 213 213 213 5 212 212 211 211 4 4 5 4 4 211 212 215 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 216 214 212 211 4 5 4 4 211 211 211 212 5 212 213 213 213 213 213 5 213 213 213 212 212 211 5 211 4 4 4 4 211 5 216 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 217 214 212 5 4 4 4 4 211 211 5 212 212 213 213 213 213 5 214 214 214 214 213 213 5 212 212 211 211 4 4 5 211 211 213 216 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 218 5 212 211 4 4 4 4 5 211 212 212 213 213 213 5 214 214 214 214 214 214 5 214 213 212 212 212 211 5 4 4 4 4 212 213 5 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 215 212 211 4 4 5 4 211 211 212 212 213 5 214 214 214 214 215 215 5 215 214 214 214 213 213 5 212 211 211 4 4 4 5 212 214 217 6 6 6

PAGE 111

99 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 216 213 211 5 4 4 4 211 211 212 5 213 213 214 214 214 214 5 215 215 215 215 214 214 5 213 213 212 212 211 211 5 4 4 211 213 215 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 218 5 212 4 4 4 4 211 5 212 212 213 213 214 214 5 215 215 215 215 215 215 5 214 214 214 213 213 212 5 211 4 4 4 4 211 5 215 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 215 212 211 4 4 5 4 211 212 212 213 213 5 214 214 215 215 215 215 5 215 215 215 214 214 213 5 213 212 211 211 4 4 5 4 211 213 215 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 216 213 211 5 4 4 4 211 211 212 5 213 214 214 214 215 215 5 216 216 215 215 215 215 5 214 213 213 212 212 211 5 4 4 4 4 211 213 5 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 218 5 212 4 4 4 4 4 5 211 212 213 214 214 214 5 215 215 215 215 215 215 5 215 214 214 214 213 213 5 212 211 4 4 4 4 5 212 214 217 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 216 213 211 4 4 5 4 211 211 212 212 213 5 214 214 215 215 215 215 5 215 215 215 215 214 214 5 213 213 212 211 211 4 5 4 4 211 213 215 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 217 214 212 5 4 4 4 4 211 212 5 213 213 214 214 215 215 5 215 215 215 215 215 215 5 214 214 213 213 212 212 5 4 4 4 4 211 212 5 218 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 5 213 212 4 4 4 4 5 211 212 212 213 214 214 5 215 215 215 215 215 215 5 215 215 214 214 214 213 5 212 211 4 4 4 4 5 211 213 216 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 216 213 211 4 5 4 211 211 211 212 213 5 214 214 215 215 215 215 5 215 215 215 215 214 214 5 213 213 212 211 211 4 5 4 4 4 212 215 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 215 5 211 4 4 4 211 211 5 212 213 213 214 214 214 5 215 215 215 215 215 215 5 214 214 213 213 212 212 5 211 4 4 4 4 212 5 217 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 215 212 211 4 4 5 211 211 212 212 213 213 5 214 214 214 214 215 215 5 214 214 214 213 213 213 5 212 211 211 4 4 4 5 211 213 216 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 217 214 212 5 4 4 4 211 211 212 5 213 213 214 214 214 214 5 214 214 214 214 214 214 5 213 212 212 211 211 4 5 4 4 211 212 215 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 5 213 212 4 4 4 4 5 211 212 212 213 213 213 5 214 214 214 214 214 214 5 213 213 213 212 211 211 5 4 4 4 4 4 212 5 217 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 216 213 211 4 5 4 4 211 211 212 212 5 213 213 213 214 214 213 5 214 213 213 213 213 212 5 211 211 4 4 4 4 5 211 213 217 6 6 6 6 6 6 6 6 6 6

PAGE 112

100 6 6 6 6 6 6 6 6 6 6 6 6 6 215 5 211 4 4 4 4 211 5 212 212 212 213 213 213 5 213 213 213 213 213 213 5 212 211 211 211 4 4 5 4 4 211 213 216 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 215 212 211 4 4 5 4 211 211 212 212 212 5 213 213 213 213 213 213 5 212 212 212 211 211 4 5 4 4 4 211 212 213 5 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 217 214 212 5 4 4 4 4 4 211 5 212 212 212 212 212 212 5 212 212 212 212 211 211 5 4 4 4 4 4 211 5 214 217 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 5 213 212 4 4 4 4 5 4 211 211 211 212 211 5 212 212 212 212 211 211 5 211 4 4 4 4 4 5 211 213 215 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 216 213 212 211 5 4 4 4 4 211 211 5 211 211 211 211 211 211 5 211 211 4 4 4 4 5 4 211 212 213 216 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 217 5 212 211 4 4 4 4 5 4 4 4 4 4 211 5 211 211 211 4 4 4 5 4 4 4 211 212 214 5 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 218 215 213 211 211 5 4 4 4 4 4 4 5 4 211 4 4 4 4 5 4 4 4 4 4 211 5 215 217 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 216 5 212 211 4 4 4 4 5 4 4 4 4 4 4 5 4 4 4 4 4 4 5 211 213 216 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 217 215 213 212 211 5 4 4 4 4 4 4 5 4 4 4 4 4 4 5 4 211 212 213 216 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 217 5 213 212 211 211 211 211 5 4 211 4 4 4 4 5 4 211 211 211 213 214 5 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 218 216 214 213 213 5 212 212 212 211 211 211 5 4 211 211 211 212 213 5 216 217 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 218 5 216 215 215 214 213 213 5 212 212 212 212 212 213 5 215 216 218 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 219 6 6 217 5 216 215 215 214 213 214 5 215 217 218 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 219 6 6 217 5 216 217 218 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

PAGE 113

101 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 219 219 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 202 0 -241 242 -243 244 -245 246 $ Hex lat=2 u=102 imp:n=1 fill=-29:29 -29:29 0:0 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

PAGE 114

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PAGE 116

104 9 9 9 9 9 9 9 9 9 225 222 221 7 7 8 221 221 222 222 223 223 8 224 224 224 224 225 225 8 224 224 224 223 223 223 8 222 221 221 7 7 7 8 221 223 226 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 227 224 222 8 7 7 7 221 221 222 8 223 223 224 224 224 224 8 224 224 224 224 224 224 8 223 222 222 221 221 7 8 7 7 221 222 225 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 229 8 223 222 7 7 7 7 8 221 222 222 223 223 223 8 224 224 224 224 224 224 8 223 223 223 222 221 221 8 7 7 7 7 7 222 8 227 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 229 226 223 221 7 8 7 7 221 221 222 222 8 223 223 223 224 224 223 8 224 223 223 223 223 222 8 221 221 7 7 7 7 8 221 223 227 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 225 8 221 7 7 7 7 221 8 222 222 222 223 223 223 8 223 223 223 223 223 223 8 222 221 221 221 7 7 8 7 7 221 223 226 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 225 222 221 7 7 8 7 221 221 222 222 222 8 223 223 223 223 223 223 8 222 222 222 221 221 7 8 7 7 7 221 222 223 8 229 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 227 224 222 8 7 7 7 7 7 221 8 222 222 222 222 222 222 8 222 222 222 222 221 221 8 7 7 7 7 7 221 8 224 227 229 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 229 8 223 222 7 7 7 7 8 7 221 221 221 222 221 8 222 222 222 222 221 221 8 221 7 7 7 7 7 8 221 223 225 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 229 226 223 222 221 8 7 7 7 7 221 221 8 221 221 221 221 221 221 8 221 221 7 7 7 7 8 7 221 222 223 226 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 227 8 222 221 7 7 7 7 8 7 7 7 7 7 221 8 221 221 221 7 7 7 8 7 7 7 221 222 224 8 229 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 228 225 223 221 221 8 7 7 7 7 7 7 8 7 221 7 7 7 7 8 7 7 7 7 7 221 8 225 227 229 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 226 8 222 221 7 7 7 7 8 7 7 7 7 7 7 8 7 7 7 7 7 7 8 221 223 226 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 227 225 223 222 221 8 7 7 7 7 7 7 8 7 7 7 7 7 7 8 7 221 222 223 226 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 227 8 223 222 221 221 221 221 8 7 221 7 7 7 7 8 7 221 221 221 223 224 8 229 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

PAGE 117

105 9 9 9 9 9 9 9 9 9 228 226 224 223 223 8 222 222 222 221 221 221 8 7 221 221 221 222 223 8 226 227 229 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 228 8 226 225 225 224 223 223 8 222 222 222 222 222 223 8 225 226 228 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 229 229 9 9 227 8 226 225 225 224 223 224 8 225 227 228 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 229 229 9 9 227 8 226 227 228 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 229 229 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 203 0 -261 262 -263 264 -265 266 $ Hex lat=2 u=103 imp:n=1 fill=-29:29 -29:29 0:0 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12

PAGE 118

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PAGE 119

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PAGE 121

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PAGE 122

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PAGE 123

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PAGE 133

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135 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 299 299 30 30 297 29 296 295 295 294 293 294 29 295 297 298 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 299 299 30 30 297 29 296 297 298 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 299 299 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 c 0220 1 -3.465987 ( 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039) ( -211 212 -213 214 -215 216) u= 1 imp:n=1 $ Fuel 1001 301 -3.465987 ( 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039) ( -211 212 -213 214 -215 216) u=201 imp:n=1 $ Fuel 1002 302 -3.465987 ( 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039) ( -211 212 -213 214 -215 216) u=202 imp:n=1 $ Fuel 1003 303 -3.465987 ( 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039) ( -211 212 -213 214 -215 216) u=203 imp:n=1 $ Fuel 1004 304 -3.465987 ( 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039) ( -211 212 -213 214 -215 216) u=204 imp:n=1 $ Fuel 1005 305 -3.465987 ( 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039) ( -211 212 -213 214 -215 216) u=205 imp:n=1 $ Fuel

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136 1006 306 -3.465987 ( 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039) ( -211 212 -213 214 -215 216) u=206 imp:n=1 $ Fuel 1007 307 -3.465987 ( 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039) ( -211 212 -213 214 -215 216) u=207 imp:n=1 $ Fuel 1008 308 -3.465987 ( 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039) ( -211 212 -213 214 -215 216) u=208 imp:n=1 $ Fuel 1009 309 -3.465987 ( 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039) ( -211 212 -213 214 -215 216) u=209 imp:n=1 $ Fuel 0221 1 -3.438866 ( 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079) ( -231 232 -233 234 -235 236) u= 4 imp:n=1 $ Fuel 1011 301 -3.438866 ( 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079) ( -231 232 -233 234 -235 236) u=211 imp:n=1 $ Fuel 1012 302 -3.438866 ( 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079) ( -231 232 -233 234 -235 236) u=212 imp:n=1 $ Fuel 1013 303 -3.438866 ( 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079) ( -231 232 -233 234 -235 236) u=213 imp:n=1 $ Fuel 1014 304 -3.438866 ( 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079) ( -231 232 -233 234 -235 236) u=214 imp:n=1 $ Fuel 1015 305 -3.438866 ( 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079) ( -231 232 -233 234 -235 236) u=215 imp:n=1 $ Fuel 1016 306 -3.438866 ( 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079) ( -231 232 -233 234 -235 236) u=216 imp:n=1 $ Fuel 1017 307 -3.438866 ( 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079) ( -231 232 -233 234 -235 236) u=217 imp:n=1 $ Fuel 1018 308 -3.438866 ( 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079) ( -231 232 -233 234 -235 236) u=218 imp:n=1 $ Fuel 1019 309 -3.438866 ( 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079) ( -231 232 -233 234 -235 236) u=219 imp:n=1 $ Fuel 0222 1 -3.410598 ( 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119) ( -251 252 -253 254 -255 256) u= 7 imp:n=1 $ Fuel 1021 301 -3.410598 ( 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119) ( -251 252 -253 254 -255 256) u=221 imp:n=1 $ Fuel 1022 302 -3.410598 ( 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119) ( -251 252 -253 254 -255 256) u=222 imp:n=1 $ Fuel 1023 303 -3.410598 ( 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119) ( -251 252 -253 254 -255 256) u=223 imp:n=1 $ Fuel 1024 304 -3.410598 ( 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119)

PAGE 149

137 ( -251 252 -253 254 -255 256) u=224 imp:n=1 $ Fuel 1025 305 -3.410598 ( 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119) ( -251 252 -253 254 -255 256) u=225 imp:n=1 $ Fuel 1026 306 -3.410598 ( 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119) ( -251 252 -253 254 -255 256) u=226 imp:n=1 $ Fuel 1027 307 -3.410598 ( 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119) ( -251 252 -253 254 -255 256) u=227 imp:n=1 $ Fuel 1028 308 -3.410598 ( 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119) ( -251 252 -253 254 -255 256) u=228 imp:n=1 $ Fuel 1029 309 -3.410598 ( 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119) ( -251 252 -253 254 -255 256) u=229 imp:n=1 $ Fuel 0223 1 -3.384820 ( 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159) ( -271 272 -273 274 -275 276) u= 10 imp:n=1 $ Fuel 1031 301 -3.384820 ( 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159) ( -271 272 -273 274 -275 276) u=231 imp:n=1 $ Fuel 1032 302 -3.384820 ( 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159) ( -271 272 -273 274 -275 276) u=232 imp:n=1 $ Fuel 1033 303 -3.384820 ( 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159) ( -271 272 -273 274 -275 276) u=233 imp:n=1 $ Fuel 1034 304 -3.384820 ( 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159) ( -271 272 -273 274 -275 276) u=234 imp:n=1 $ Fuel 1035 305 -3.384820 ( 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159) ( -271 272 -273 274 -275 276) u=235 imp:n=1 $ Fuel 1036 306 -3.384820 ( 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159) ( -271 272 -273 274 -275 276) u=236 imp:n=1 $ Fuel 1037 307 -3.384820 ( 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159) ( -271 272 -273 274 -275 276) u=237 imp:n=1 $ Fuel 1038 308 -3.384820 ( 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159) ( -271 272 -273 274 -275 276) u=238 imp:n=1 $ Fuel 1039 309 -3.384820 ( 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159) ( -271 272 -273 274 -275 276) u=239 imp:n=1 $ Fuel 0224 1 -3.360965 ( 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199) ( -291 292 -293 294 -295 296) u= 13 imp:n=1 $ Fuel 1041 301 -3.360965 ( 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199) ( -291 292 -293 294 -295 296) u=241 imp:n=1 $ Fuel 1042 302 -3.360965 ( 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199) ( -291 292 -293 294 -295 296) u=242 imp:n=1 $ Fuel 1043 303 -3.360965 ( 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190

PAGE 150

138 1191 1192 1193 1194 1195 1196 1197 1198 1199) ( -291 292 -293 294 -295 296) u=243 imp:n=1 $ Fuel 1044 304 -3.360965 ( 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199) ( -291 292 -293 294 -295 296) u=244 imp:n=1 $ Fuel 1045 305 -3.360965 ( 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199) ( -291 292 -293 294 -295 296) u=245 imp:n=1 $ Fuel 1046 306 -3.360965 ( 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199) ( -291 292 -293 294 -295 296) u=246 imp:n=1 $ Fuel 1047 307 -3.360965 ( 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199) ( -291 292 -293 294 -295 296) u=247 imp:n=1 $ Fuel 1048 308 -3.360965 ( 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199) ( -291 292 -293 294 -295 296) u=248 imp:n=1 $ Fuel 1049 309 -3.360965 ( 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199) ( -291 292 -293 294 -295 296) u=249 imp:n=1 $ Fuel 0225 1 -3.340596 ( 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239) ( -311 312 -313 314 -315 316) u= 16 imp:n=1 $ Fuel 1051 301 -3.340596 ( 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239) ( -311 312 -313 314 -315 316) u=251 imp:n=1 $ Fuel 1052 302 -3.340596 ( 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239) ( -311 312 -313 314 -315 316) u=252 imp:n=1 $ Fuel 1053 303 -3.340596 ( 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239) ( -311 312 -313 314 -315 316) u=253 imp:n=1 $ Fuel 1054 304 -3.340596 ( 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239) ( -311 312 -313 314 -315 316) u=254 imp:n=1 $ Fuel 1055 305 -3.340596 ( 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239) ( -311 312 -313 314 -315 316) u=255 imp:n=1 $ Fuel 1056 306 -3.340596 ( 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239) ( -311 312 -313 314 -315 316) u=256 imp:n=1 $ Fuel 1057 307 -3.340596 ( 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239) ( -311 312 -313 314 -315 316) u=257 imp:n=1 $ Fuel 1058 308 -3.340596 ( 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239) ( -311 312 -313 314 -315 316) u=258 imp:n=1 $ Fuel 1059 309 -3.340596 ( 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239) ( -311 312 -313 314 -315 316) u=259 imp:n=1 $ Fuel 0226 1 -3.327412 ( 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279) ( -331 332 -333 334 -335 336) u= 19 imp:n=1 $ Fuel 1061 301 -3.327412 ( 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279) ( -331 332 -333 334 -335 336) u=261 imp:n=1 $ Fuel

PAGE 151

139 1062 302 -3.327412 ( 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279) ( -331 332 -333 334 -335 336) u=262 imp:n=1 $ Fuel 1063 303 -3.327412 ( 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279) ( -331 332 -333 334 -335 336) u=263 imp:n=1 $ Fuel 1064 304 -3.327412 ( 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279) ( -331 332 -333 334 -335 336) u=264 imp:n=1 $ Fuel 1065 305 -3.327412 ( 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279) ( -331 332 -333 334 -335 336) u=265 imp:n=1 $ Fuel 1066 306 -3.327412 ( 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279) ( -331 332 -333 334 -335 336) u=266 imp:n=1 $ Fuel 1067 307 -3.327412 ( 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279) ( -331 332 -333 334 -335 336) u=267 imp:n=1 $ Fuel 1068 308 -3.327412 ( 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279) ( -331 332 -333 334 -335 336) u=268 imp:n=1 $ Fuel 1069 309 -3.327412 ( 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279) ( -331 332 -333 334 -335 336) u=269 imp:n=1 $ Fuel 0227 1 -3.320949 ( 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319) ( -351 352 -353 354 -355 356) u= 22 imp:n=1 $ Fuel 1071 301 -3.320949 ( 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319) ( -351 352 -353 354 -355 356) u=271 imp:n=1 $ Fuel 1072 302 -3.320949 ( 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319) ( -351 352 -353 354 -355 356) u=272 imp:n=1 $ Fuel 1073 303 -3.320949 ( 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319) ( -351 352 -353 354 -355 356) u=273 imp:n=1 $ Fuel 1074 304 -3.320949 ( 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319) ( -351 352 -353 354 -355 356) u=274 imp:n=1 $ Fuel 1075 305 -3.320949 ( 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319) ( -351 352 -353 354 -355 356) u=275 imp:n=1 $ Fuel 1076 306 -3.320949 ( 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319) ( -351 352 -353 354 -355 356) u=276 imp:n=1 $ Fuel 1077 307 -3.320949 ( 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319) ( -351 352 -353 354 -355 356) u=277 imp:n=1 $ Fuel 1078 308 -3.320949 ( 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319) ( -351 352 -353 354 -355 356) u=278 imp:n=1 $ Fuel 1079 309 -3.320949 ( 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319) ( -351 352 -353 354 -355 356) u=279 imp:n=1 $ Fuel 0228 1 -3.319869 ( 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359)

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140 ( -371 372 -373 374 -375 376) u= 25 imp:n=1 $ Fuel 1081 301 -3.319869 ( 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359) ( -371 372 -373 374 -375 376) u=281 imp:n=1 $ Fuel 1082 302 -3.319869 ( 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359) ( -371 372 -373 374 -375 376) u=282 imp:n=1 $ Fuel 1083 303 -3.319869 ( 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359) ( -371 372 -373 374 -375 376) u=283 imp:n=1 $ Fuel 1084 304 -3.319869 ( 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359) ( -371 372 -373 374 -375 376) u=284 imp:n=1 $ Fuel 1085 305 -3.319869 ( 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359) ( -371 372 -373 374 -375 376) u=285 imp:n=1 $ Fuel 1086 306 -3.319869 ( 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359) ( -371 372 -373 374 -375 376) u=286 imp:n=1 $ Fuel 1087 307 -3.319869 ( 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359) ( -371 372 -373 374 -375 376) u=287 imp:n=1 $ Fuel 1088 308 -3.319869 ( 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359) ( -371 372 -373 374 -375 376) u=288 imp:n=1 $ Fuel 1089 309 -3.319869 ( 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359) ( -371 372 -373 374 -375 376) u=289 imp:n=1 $ Fuel 0229 1 -3.320898 ( 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399) ( -391 392 -393 394 -395 396) u= 28 imp:n=1 $ Fuel 1091 301 -3.320898 ( 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399) ( -391 392 -393 394 -395 396) u=291 imp:n=1 $ Fuel 1092 302 -3.320898 ( 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399) ( -391 392 -393 394 -395 396) u=292 imp:n=1 $ Fuel 1093 303 -3.320898 ( 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399) ( -391 392 -393 394 -395 396) u=293 imp:n=1 $ Fuel 1094 304 -3.320898 ( 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399) ( -391 392 -393 394 -395 396) u=294 imp:n=1 $ Fuel 1095 305 -3.320898 ( 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399) ( -391 392 -393 394 -395 396) u=295 imp:n=1 $ Fuel 1096 306 -3.320898 ( 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399) ( -391 392 -393 394 -395 396) u=296 imp:n=1 $ Fuel 1097 307 -3.320898 ( 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399) ( -391 392 -393 394 -395 396) u=297 imp:n=1 $ Fuel 1098 308 -3.320898 ( 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399) ( -391 392 -393 394 -395 396) u=298 imp:n=1 $ Fuel 1099 309 -3.320898 ( 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390

PAGE 153

141 1391 1392 1393 1394 1395 1396 1397 1398 1399) ( -391 392 -393 394 -395 396) u=299 imp:n=1 $ Fuel 0240 4 -8.580552 (1001 -1021):(1002 -1022):(1003 -1023): (1004 -1024):(1005 -1025):(1006 -1026):(1007 -1027):(1008 -1028): (1009 -1029):(1010 -1030):(1011 -1031):(1012 -1032):(1013 -1033): (1014 -1034):(1015 -1035):(1016 -1036):(1017 -1037):(1018 -1038): (1019 -1039) u= 1 imp:n=1 $ Coating 1101 4 -8.580552 (1001 -1021):(1002 -1022):(1003 -1023): (1004 -1024):(1005 -1025):(1006 -1026):(1007 -1027):(1008 -1028): (1009 -1029):(1010 -1030):(1011 -1031):(1012 -1032):(1013 -1033): (1014 -1034):(1015 -1035):(1016 -1036):(1017 -1037):(1018 -1038): (1019 -1039) u=201 imp:n=1 $ Coating 1102 4 -8.580552 (1001 -1021):(1002 -1022):(1003 -1023): (1004 -1024):(1005 -1025):(1006 -1026):(1007 -1027):(1008 -1028): (1009 -1029):(1010 -1030):(1011 -1031):(1012 -1032):(1013 -1033): (1014 -1034):(1015 -1035):(1016 -1036):(1017 -1037):(1018 -1038): (1019 -1039) u=202 imp:n=1 $ Coating 1103 4 -8.580552 (1001 -1021):(1002 -1022):(1003 -1023): (1004 -1024):(1005 -1025):(1006 -1026):(1007 -1027):(1008 -1028): (1009 -1029):(1010 -1030):(1011 -1031):(1012 -1032):(1013 -1033): (1014 -1034):(1015 -1035):(1016 -1036):(1017 -1037):(1018 -1038): (1019 -1039) u=203 imp:n=1 $ Coating 1104 4 -8.580552 (1001 -1021):(1002 -1022):(1003 -1023): (1004 -1024):(1005 -1025):(1006 -1026):(1007 -1027):(1008 -1028): (1009 -1029):(1010 -1030):(1011 -1031):(1012 -1032):(1013 -1033): (1014 -1034):(1015 -1035):(1016 -1036):(1017 -1037):(1018 -1038): (1019 -1039) u=204 imp:n=1 $ Coating 1105 4 -8.580552 (1001 -1021):(1002 -1022):(1003 -1023): (1004 -1024):(1005 -1025):(1006 -1026):(1007 -1027):(1008 -1028): (1009 -1029):(1010 -1030):(1011 -1031):(1012 -1032):(1013 -1033): (1014 -1034):(1015 -1035):(1016 -1036):(1017 -1037):(1018 -1038): (1019 -1039) u=205 imp:n=1 $ Coating 1106 4 -8.580552 (1001 -1021):(1002 -1022):(1003 -1023): (1004 -1024):(1005 -1025):(1006 -1026):(1007 -1027):(1008 -1028): (1009 -1029):(1010 -1030):(1011 -1031):(1012 -1032):(1013 -1033): (1014 -1034):(1015 -1035):(1016 -1036):(1017 -1037):(1018 -1038): (1019 -1039) u=206 imp:n=1 $ Coating 1107 4 -8.580552 (1001 -1021):(1002 -1022):(1003 -1023): (1004 -1024):(1005 -1025):(1006 -1026):(1007 -1027):(1008 -1028): (1009 -1029):(1010 -1030):(1011 -1031):(1012 -1032):(1013 -1033): (1014 -1034):(1015 -1035):(1016 -1036):(1017 -1037):(1018 -1038): (1019 -1039) u=207 imp:n=1 $ Coating 1108 4 -8.580552 (1001 -1021):(1002 -1022):(1003 -1023): (1004 -1024):(1005 -1025):(1006 -1026):(1007 -1027):(1008 -1028): (1009 -1029):(1010 -1030):(1011 -1031):(1012 -1032):(1013 -1033): (1014 -1034):(1015 -1035):(1016 -1036):(1017 -1037):(1018 -1038): (1019 -1039) u=208 imp:n=1 $ Coating 1109 4 -8.580552 (1001 -1021):(1002 -1022):(1003 -1023): (1004 -1024):(1005 -1025):(1006 -1026):(1007 -1027):(1008 -1028): (1009 -1029):(1010 -1030):(1011 -1031):(1012 -1032):(1013 -1033): (1014 -1034):(1015 -1035):(1016 -1036):(1017 -1037):(1018 -1038): (1019 -1039) u=209 imp:n=1 $ Coating 0241 4 -8.513410 (1041 -1061):(1042 -1062):(1043 -1063): (1044 -1064):(1045 -1065):(1046 -1066):(1047 -1067):(1048 -1068): (1049 -1069):(1050 -1070):(1051 -1071):(1052 -1072):(1053 -1073): (1054 -1074):(1055 -1075):(1056 -1076):(1057 -1077):(1058 -1078):

PAGE 154

142 (1059 -1079) u= 4 imp:n=1 $ Coating 1111 4 -8.513410 (1041 -1061):(1042 -1062):(1043 -1063): (1044 -1064):(1045 -1065):(1046 -1066):(1047 -1067):(1048 -1068): (1049 -1069):(1050 -1070):(1051 -1071):(1052 -1072):(1053 -1073): (1054 -1074):(1055 -1075):(1056 -1076):(1057 -1077):(1058 -1078): (1059 -1079) u=211 imp:n=1 $ Coating 1112 4 -8.513410 (1041 -1061):(1042 -1062):(1043 -1063): (1044 -1064):(1045 -1065):(1046 -1066):(1047 -1067):(1048 -1068): (1049 -1069):(1050 -1070):(1051 -1071):(1052 -1072):(1053 -1073): (1054 -1074):(1055 -1075):(1056 -1076):(1057 -1077):(1058 -1078): (1059 -1079) u=212 imp:n=1 $ Coating 1113 4 -8.513410 (1041 -1061):(1042 -1062):(1043 -1063): (1044 -1064):(1045 -1065):(1046 -1066):(1047 -1067):(1048 -1068): (1049 -1069):(1050 -1070):(1051 -1071):(1052 -1072):(1053 -1073): (1054 -1074):(1055 -1075):(1056 -1076):(1057 -1077):(1058 -1078): (1059 -1079) u=213 imp:n=1 $ Coating 1114 4 -8.513410 (1041 -1061):(1042 -1062):(1043 -1063): (1044 -1064):(1045 -1065):(1046 -1066):(1047 -1067):(1048 -1068): (1049 -1069):(1050 -1070):(1051 -1071):(1052 -1072):(1053 -1073): (1054 -1074):(1055 -1075):(1056 -1076):(1057 -1077):(1058 -1078): (1059 -1079) u=214 imp:n=1 $ Coating 1115 4 -8.513410 (1041 -1061):(1042 -1062):(1043 -1063): (1044 -1064):(1045 -1065):(1046 -1066):(1047 -1067):(1048 -1068): (1049 -1069):(1050 -1070):(1051 -1071):(1052 -1072):(1053 -1073): (1054 -1074):(1055 -1075):(1056 -1076):(1057 -1077):(1058 -1078): (1059 -1079) u=215 imp:n=1 $ Coating 1116 4 -8.513410 (1041 -1061):(1042 -1062):(1043 -1063): (1044 -1064):(1045 -1065):(1046 -1066):(1047 -1067):(1048 -1068): (1049 -1069):(1050 -1070):(1051 -1071):(1052 -1072):(1053 -1073): (1054 -1074):(1055 -1075):(1056 -1076):(1057 -1077):(1058 -1078): (1059 -1079) u=216 imp:n=1 $ Coating 1117 4 -8.513410 (1041 -1061):(1042 -1062):(1043 -1063): (1044 -1064):(1045 -1065):(1046 -1066):(1047 -1067):(1048 -1068): (1049 -1069):(1050 -1070):(1051 -1071):(1052 -1072):(1053 -1073): (1054 -1074):(1055 -1075):(1056 -1076):(1057 -1077):(1058 -1078): (1059 -1079) u=217 imp:n=1 $ Coating 1118 4 -8.513410 (1041 -1061):(1042 -1062):(1043 -1063): (1044 -1064):(1045 -1065):(1046 -1066):(1047 -1067):(1048 -1068): (1049 -1069):(1050 -1070):(1051 -1071):(1052 -1072):(1053 -1073): (1054 -1074):(1055 -1075):(1056 -1076):(1057 -1077):(1058 -1078): (1059 -1079) u=218 imp:n=1 $ Coating 1119 4 -8.513410 (1041 -1061):(1042 -1062):(1043 -1063): (1044 -1064):(1045 -1065):(1046 -1066):(1047 -1067):(1048 -1068): (1049 -1069):(1050 -1070):(1051 -1071):(1052 -1072):(1053 -1073): (1054 -1074):(1055 -1075):(1056 -1076):(1057 -1077):(1058 -1078): (1059 -1079) u=219 imp:n=1 $ Coating 0242 4 -8.443428 (1081 -1101):(1082 -1102):(1083 -1103): (1084 -1104):(1085 -1105):(1086 -1106):(1087 -1107):(1088 -1108): (1089 -1109):(1090 -1110):(1091 -1111):(1092 -1112):(1093 -1113): (1094 -1114):(1095 -1115):(1096 -1116):(1097 -1117):(1098 -1118): (1099 -1119) u= 7 imp:n=1 $ Coating 1121 4 -8.443428 (1081 -1101):(1082 -1102):(1083 -1103): (1084 -1104):(1085 -1105):(1086 -1106):(1087 -1107):(1088 -1108): (1089 -1109):(1090 -1110):(1091 -1111):(1092 -1112):(1093 -1113): (1094 -1114):(1095 -1115):(1096 -1116):(1097 -1117):(1098 -1118): (1099 -1119) u=221 imp:n=1 $ Coating

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143 1122 4 -8.443428 (1081 -1101):(1082 -1102):(1083 -1103): (1084 -1104):(1085 -1105):(1086 -1106):(1087 -1107):(1088 -1108): (1089 -1109):(1090 -1110):(1091 -1111):(1092 -1112):(1093 -1113): (1094 -1114):(1095 -1115):(1096 -1116):(1097 -1117):(1098 -1118): (1099 -1119) u=222 imp:n=1 $ Coating 1123 4 -8.443428 (1081 -1101):(1082 -1102):(1083 -1103): (1084 -1104):(1085 -1105):(1086 -1106):(1087 -1107):(1088 -1108): (1089 -1109):(1090 -1110):(1091 -1111):(1092 -1112):(1093 -1113): (1094 -1114):(1095 -1115):(1096 -1116):(1097 -1117):(1098 -1118): (1099 -1119) u=223 imp:n=1 $ Coating 1124 4 -8.443428 (1081 -1101):(1082 -1102):(1083 -1103): (1084 -1104):(1085 -1105):(1086 -1106):(1087 -1107):(1088 -1108): (1089 -1109):(1090 -1110):(1091 -1111):(1092 -1112):(1093 -1113): (1094 -1114):(1095 -1115):(1096 -1116):(1097 -1117):(1098 -1118): (1099 -1119) u=224 imp:n=1 $ Coating 1125 4 -8.443428 (1081 -1101):(1082 -1102):(1083 -1103): (1084 -1104):(1085 -1105):(1086 -1106):(1087 -1107):(1088 -1108): (1089 -1109):(1090 -1110):(1091 -1111):(1092 -1112):(1093 -1113): (1094 -1114):(1095 -1115):(1096 -1116):(1097 -1117):(1098 -1118): (1099 -1119) u=225 imp:n=1 $ Coating 1126 4 -8.443428 (1081 -1101):(1082 -1102):(1083 -1103): (1084 -1104):(1085 -1105):(1086 -1106):(1087 -1107):(1088 -1108): (1089 -1109):(1090 -1110):(1091 -1111):(1092 -1112):(1093 -1113): (1094 -1114):(1095 -1115):(1096 -1116):(1097 -1117):(1098 -1118): (1099 -1119) u=226 imp:n=1 $ Coating 1127 4 -8.443428 (1081 -1101):(1082 -1102):(1083 -1103): (1084 -1104):(1085 -1105):(1086 -1106):(1087 -1107):(1088 -1108): (1089 -1109):(1090 -1110):(1091 -1111):(1092 -1112):(1093 -1113): (1094 -1114):(1095 -1115):(1096 -1116):(1097 -1117):(1098 -1118): (1099 -1119) u=227 imp:n=1 $ Coating 1128 4 -8.443428 (1081 -1101):(1082 -1102):(1083 -1103): (1084 -1104):(1085 -1105):(1086 -1106):(1087 -1107):(1088 -1108): (1089 -1109):(1090 -1110):(1091 -1111):(1092 -1112):(1093 -1113): (1094 -1114):(1095 -1115):(1096 -1116):(1097 -1117):(1098 -1118): (1099 -1119) u=228 imp:n=1 $ Coating 1129 4 -8.443428 (1081 -1101):(1082 -1102):(1083 -1103): (1084 -1104):(1085 -1105):(1086 -1106):(1087 -1107):(1088 -1108): (1089 -1109):(1090 -1110):(1091 -1111):(1092 -1112):(1093 -1113): (1094 -1114):(1095 -1115):(1096 -1116):(1097 -1117):(1098 -1118): (1099 -1119) u=229 imp:n=1 $ Coating 0243 4 -8.379613 (1121 -1141):(1122 -1142):(1123 -1143): (1124 -1144):(1125 -1145):(1126 -1146):(1127 -1147):(1128 -1148): (1129 -1149):(1130 -1150):(1131 -1151):(1132 -1152):(1133 -1153): (1134 -1154):(1135 -1155):(1136 -1156):(1137 -1157):(1138 -1158): (1139 -1159) u= 10 imp:n=1 $ Coating 1131 4 -8.379613 (1121 -1141):(1122 -1142):(1123 -1143): (1124 -1144):(1125 -1145):(1126 -1146):(1127 -1147):(1128 -1148): (1129 -1149):(1130 -1150):(1131 -1151):(1132 -1152):(1133 -1153): (1134 -1154):(1135 -1155):(1136 -1156):(1137 -1157):(1138 -1158): (1139 -1159) u=231 imp:n=1 $ Coating 1132 4 -8.379613 (1121 -1141):(1122 -1142):(1123 -1143): (1124 -1144):(1125 -1145):(1126 -1146):(1127 -1147):(1128 -1148): (1129 -1149):(1130 -1150):(1131 -1151):(1132 -1152):(1133 -1153): (1134 -1154):(1135 -1155):(1136 -1156):(1137 -1157):(1138 -1158): (1139 -1159) u=232 imp:n=1 $ Coating 1133 4 -8.379613 (1121 -1141):(1122 -1142):(1123 -1143):

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144 (1124 -1144):(1125 -1145):(1126 -1146):(1127 -1147):(1128 -1148): (1129 -1149):(1130 -1150):(1131 -1151):(1132 -1152):(1133 -1153): (1134 -1154):(1135 -1155):(1136 -1156):(1137 -1157):(1138 -1158): (1139 -1159) u=233 imp:n=1 $ Coating 1134 4 -8.379613 (1121 -1141):(1122 -1142):(1123 -1143): (1124 -1144):(1125 -1145):(1126 -1146):(1127 -1147):(1128 -1148): (1129 -1149):(1130 -1150):(1131 -1151):(1132 -1152):(1133 -1153): (1134 -1154):(1135 -1155):(1136 -1156):(1137 -1157):(1138 -1158): (1139 -1159) u=234 imp:n=1 $ Coating 1135 4 -8.379613 (1121 -1141):(1122 -1142):(1123 -1143): (1124 -1144):(1125 -1145):(1126 -1146):(1127 -1147):(1128 -1148): (1129 -1149):(1130 -1150):(1131 -1151):(1132 -1152):(1133 -1153): (1134 -1154):(1135 -1155):(1136 -1156):(1137 -1157):(1138 -1158): (1139 -1159) u=235 imp:n=1 $ Coating 1136 4 -8.379613 (1121 -1141):(1122 -1142):(1123 -1143): (1124 -1144):(1125 -1145):(1126 -1146):(1127 -1147):(1128 -1148): (1129 -1149):(1130 -1150):(1131 -1151):(1132 -1152):(1133 -1153): (1134 -1154):(1135 -1155):(1136 -1156):(1137 -1157):(1138 -1158): (1139 -1159) u=236 imp:n=1 $ Coating 1137 4 -8.379613 (1121 -1141):(1122 -1142):(1123 -1143): (1124 -1144):(1125 -1145):(1126 -1146):(1127 -1147):(1128 -1148): (1129 -1149):(1130 -1150):(1131 -1151):(1132 -1152):(1133 -1153): (1134 -1154):(1135 -1155):(1136 -1156):(1137 -1157):(1138 -1158): (1139 -1159) u=237 imp:n=1 $ Coating 1138 4 -8.379613 (1121 -1141):(1122 -1142):(1123 -1143): (1124 -1144):(1125 -1145):(1126 -1146):(1127 -1147):(1128 -1148): (1129 -1149):(1130 -1150):(1131 -1151):(1132 -1152):(1133 -1153): (1134 -1154):(1135 -1155):(1136 -1156):(1137 -1157):(1138 -1158): (1139 -1159) u=238 imp:n=1 $ Coating 1139 4 -8.379613 (1121 -1141):(1122 -1142):(1123 -1143): (1124 -1144):(1125 -1145):(1126 -1146):(1127 -1147):(1128 -1148): (1129 -1149):(1130 -1150):(1131 -1151):(1132 -1152):(1133 -1153): (1134 -1154):(1135 -1155):(1136 -1156):(1137 -1157):(1138 -1158): (1139 -1159) u=239 imp:n=1 $ Coating 0244 4 -8.320556 (1161 -1181):(1162 -1182):(1163 -1183): (1164 -1184):(1165 -1185):(1166 -1186):(1167 -1187):(1168 -1188): (1169 -1189):(1170 -1190):(1171 -1191):(1172 -1192):(1173 -1193): (1174 -1194):(1175 -1195):(1176 -1196):(1177 -1197):(1178 -1198): (1179 -1199) u= 13 imp:n=1 $ Coating 1141 4 -8.320556 (1161 -1181):(1162 -1182):(1163 -1183): (1164 -1184):(1165 -1185):(1166 -1186):(1167 -1187):(1168 -1188): (1169 -1189):(1170 -1190):(1171 -1191):(1172 -1192):(1173 -1193): (1174 -1194):(1175 -1195):(1176 -1196):(1177 -1197):(1178 -1198): (1179 -1199) u=241 imp:n=1 $ Coating 1142 4 -8.320556 (1161 -1181):(1162 -1182):(1163 -1183): (1164 -1184):(1165 -1185):(1166 -1186):(1167 -1187):(1168 -1188): (1169 -1189):(1170 -1190):(1171 -1191):(1172 -1192):(1173 -1193): (1174 -1194):(1175 -1195):(1176 -1196):(1177 -1197):(1178 -1198): (1179 -1199) u=242 imp:n=1 $ Coating 1143 4 -8.320556 (1161 -1181):(1162 -1182):(1163 -1183): (1164 -1184):(1165 -1185):(1166 -1186):(1167 -1187):(1168 -1188): (1169 -1189):(1170 -1190):(1171 -1191):(1172 -1192):(1173 -1193): (1174 -1194):(1175 -1195):(1176 -1196):(1177 -1197):(1178 -1198): (1179 -1199) u=243 imp:n=1 $ Coating 1144 4 -8.320556 (1161 -1181):(1162 -1182):(1163 -1183): (1164 -1184):(1165 -1185):(1166 -1186):(1167 -1187):(1168 -1188):

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145 (1169 -1189):(1170 -1190):(1171 -1191):(1172 -1192):(1173 -1193): (1174 -1194):(1175 -1195):(1176 -1196):(1177 -1197):(1178 -1198): (1179 -1199) u=244 imp:n=1 $ Coating 1145 4 -8.320556 (1161 -1181):(1162 -1182):(1163 -1183): (1164 -1184):(1165 -1185):(1166 -1186):(1167 -1187):(1168 -1188): (1169 -1189):(1170 -1190):(1171 -1191):(1172 -1192):(1173 -1193): (1174 -1194):(1175 -1195):(1176 -1196):(1177 -1197):(1178 -1198): (1179 -1199) u=245 imp:n=1 $ Coating 1146 4 -8.320556 (1161 -1181):(1162 -1182):(1163 -1183): (1164 -1184):(1165 -1185):(1166 -1186):(1167 -1187):(1168 -1188): (1169 -1189):(1170 -1190):(1171 -1191):(1172 -1192):(1173 -1193): (1174 -1194):(1175 -1195):(1176 -1196):(1177 -1197):(1178 -1198): (1179 -1199) u=246 imp:n=1 $ Coating 1147 4 -8.320556 (1161 -1181):(1162 -1182):(1163 -1183): (1164 -1184):(1165 -1185):(1166 -1186):(1167 -1187):(1168 -1188): (1169 -1189):(1170 -1190):(1171 -1191):(1172 -1192):(1173 -1193): (1174 -1194):(1175 -1195):(1176 -1196):(1177 -1197):(1178 -1198): (1179 -1199) u=247 imp:n=1 $ Coating 1148 4 -8.320556 (1161 -1181):(1162 -1182):(1163 -1183): (1164 -1184):(1165 -1185):(1166 -1186):(1167 -1187):(1168 -1188): (1169 -1189):(1170 -1190):(1171 -1191):(1172 -1192):(1173 -1193): (1174 -1194):(1175 -1195):(1176 -1196):(1177 -1197):(1178 -1198): (1179 -1199) u=248 imp:n=1 $ Coating 1149 4 -8.320556 (1161 -1181):(1162 -1182):(1163 -1183): (1164 -1184):(1165 -1185):(1166 -1186):(1167 -1187):(1168 -1188): (1169 -1189):(1170 -1190):(1171 -1191):(1172 -1192):(1173 -1193): (1174 -1194):(1175 -1195):(1176 -1196):(1177 -1197):(1178 -1198): (1179 -1199) u=249 imp:n=1 $ Coating 0245 4 -8.270130 (1201 -1221):(1202 -1222):(1203 -1223): (1204 -1224):(1205 -1225):(1206 -1226):(1207 -1227):(1208 -1228): (1209 -1229):(1210 -1230):(1211 -1231):(1212 -1232):(1213 -1233): (1214 -1234):(1215 -1235):(1216 -1236):(1217 -1237):(1218 -1238): (1219 -1239) u= 16 imp:n=1 $ Coating 1151 4 -8.270130 (1201 -1221):(1202 -1222):(1203 -1223): (1204 -1224):(1205 -1225):(1206 -1226):(1207 -1227):(1208 -1228): (1209 -1229):(1210 -1230):(1211 -1231):(1212 -1232):(1213 -1233): (1214 -1234):(1215 -1235):(1216 -1236):(1217 -1237):(1218 -1238): (1219 -1239) u=251 imp:n=1 $ Coating 1152 4 -8.270130 (1201 -1221):(1202 -1222):(1203 -1223): (1204 -1224):(1205 -1225):(1206 -1226):(1207 -1227):(1208 -1228): (1209 -1229):(1210 -1230):(1211 -1231):(1212 -1232):(1213 -1233): (1214 -1234):(1215 -1235):(1216 -1236):(1217 -1237):(1218 -1238): (1219 -1239) u=252 imp:n=1 $ Coating 1153 4 -8.270130 (1201 -1221):(1202 -1222):(1203 -1223): (1204 -1224):(1205 -1225):(1206 -1226):(1207 -1227):(1208 -1228): (1209 -1229):(1210 -1230):(1211 -1231):(1212 -1232):(1213 -1233): (1214 -1234):(1215 -1235):(1216 -1236):(1217 -1237):(1218 -1238): (1219 -1239) u=253 imp:n=1 $ Coating 1154 4 -8.270130 (1201 -1221):(1202 -1222):(1203 -1223): (1204 -1224):(1205 -1225):(1206 -1226):(1207 -1227):(1208 -1228): (1209 -1229):(1210 -1230):(1211 -1231):(1212 -1232):(1213 -1233): (1214 -1234):(1215 -1235):(1216 -1236):(1217 -1237):(1218 -1238): (1219 -1239) u=254 imp:n=1 $ Coating 1155 4 -8.270130 (1201 -1221):(1202 -1222):(1203 -1223): (1204 -1224):(1205 -1225):(1206 -1226):(1207 -1227):(1208 -1228): (1209 -1229):(1210 -1230):(1211 -1231):(1212 -1232):(1213 -1233):

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146 (1214 -1234):(1215 -1235):(1216 -1236):(1217 -1237):(1218 -1238): (1219 -1239) u=255 imp:n=1 $ Coating 1156 4 -8.270130 (1201 -1221):(1202 -1222):(1203 -1223): (1204 -1224):(1205 -1225):(1206 -1226):(1207 -1227):(1208 -1228): (1209 -1229):(1210 -1230):(1211 -1231):(1212 -1232):(1213 -1233): (1214 -1234):(1215 -1235):(1216 -1236):(1217 -1237):(1218 -1238): (1219 -1239) u=256 imp:n=1 $ Coating 1157 4 -8.270130 (1201 -1221):(1202 -1222):(1203 -1223): (1204 -1224):(1205 -1225):(1206 -1226):(1207 -1227):(1208 -1228): (1209 -1229):(1210 -1230):(1211 -1231):(1212 -1232):(1213 -1233): (1214 -1234):(1215 -1235):(1216 -1236):(1217 -1237):(1218 -1238): (1219 -1239) u=257 imp:n=1 $ Coating 1158 4 -8.270130 (1201 -1221):(1202 -1222):(1203 -1223): (1204 -1224):(1205 -1225):(1206 -1226):(1207 -1227):(1208 -1228): (1209 -1229):(1210 -1230):(1211 -1231):(1212 -1232):(1213 -1233): (1214 -1234):(1215 -1235):(1216 -1236):(1217 -1237):(1218 -1238): (1219 -1239) u=258 imp:n=1 $ Coating 1159 4 -8.270130 (1201 -1221):(1202 -1222):(1203 -1223): (1204 -1224):(1205 -1225):(1206 -1226):(1207 -1227):(1208 -1228): (1209 -1229):(1210 -1230):(1211 -1231):(1212 -1232):(1213 -1233): (1214 -1234):(1215 -1235):(1216 -1236):(1217 -1237):(1218 -1238): (1219 -1239) u=259 imp:n=1 $ Coating 0246 4 -8.237490 (1241 -1261):(1242 -1262):(1243 -1263): (1244 -1264):(1245 -1265):(1246 -1266):(1247 -1267):(1248 -1268): (1249 -1269):(1250 -1270):(1251 -1271):(1252 -1272):(1253 -1273): (1254 -1274):(1255 -1275):(1256 -1276):(1257 -1277):(1258 -1278): (1259 -1279) u= 19 imp:n=1 $ Coating 1161 4 -8.237490 (1241 -1261):(1242 -1262):(1243 -1263): (1244 -1264):(1245 -1265):(1246 -1266):(1247 -1267):(1248 -1268): (1249 -1269):(1250 -1270):(1251 -1271):(1252 -1272):(1253 -1273): (1254 -1274):(1255 -1275):(1256 -1276):(1257 -1277):(1258 -1278): (1259 -1279) u=261 imp:n=1 $ Coating 1162 4 -8.237490 (1241 -1261):(1242 -1262):(1243 -1263): (1244 -1264):(1245 -1265):(1246 -1266):(1247 -1267):(1248 -1268): (1249 -1269):(1250 -1270):(1251 -1271):(1252 -1272):(1253 -1273): (1254 -1274):(1255 -1275):(1256 -1276):(1257 -1277):(1258 -1278): (1259 -1279) u=262 imp:n=1 $ Coating 1163 4 -8.237490 (1241 -1261):(1242 -1262):(1243 -1263): (1244 -1264):(1245 -1265):(1246 -1266):(1247 -1267):(1248 -1268): (1249 -1269):(1250 -1270):(1251 -1271):(1252 -1272):(1253 -1273): (1254 -1274):(1255 -1275):(1256 -1276):(1257 -1277):(1258 -1278): (1259 -1279) u=263 imp:n=1 $ Coating 1164 4 -8.237490 (1241 -1261):(1242 -1262):(1243 -1263): (1244 -1264):(1245 -1265):(1246 -1266):(1247 -1267):(1248 -1268): (1249 -1269):(1250 -1270):(1251 -1271):(1252 -1272):(1253 -1273): (1254 -1274):(1255 -1275):(1256 -1276):(1257 -1277):(1258 -1278): (1259 -1279) u=264 imp:n=1 $ Coating 1165 4 -8.237490 (1241 -1261):(1242 -1262):(1243 -1263): (1244 -1264):(1245 -1265):(1246 -1266):(1247 -1267):(1248 -1268): (1249 -1269):(1250 -1270):(1251 -1271):(1252 -1272):(1253 -1273): (1254 -1274):(1255 -1275):(1256 -1276):(1257 -1277):(1258 -1278): (1259 -1279) u=265 imp:n=1 $ Coating 1166 4 -8.237490 (1241 -1261):(1242 -1262):(1243 -1263): (1244 -1264):(1245 -1265):(1246 -1266):(1247 -1267):(1248 -1268): (1249 -1269):(1250 -1270):(1251 -1271):(1252 -1272):(1253 -1273): (1254 -1274):(1255 -1275):(1256 -1276):(1257 -1277):(1258 -1278):

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147 (1259 -1279) u=266 imp:n=1 $ Coating 1167 4 -8.237490 (1241 -1261):(1242 -1262):(1243 -1263): (1244 -1264):(1245 -1265):(1246 -1266):(1247 -1267):(1248 -1268): (1249 -1269):(1250 -1270):(1251 -1271):(1252 -1272):(1253 -1273): (1254 -1274):(1255 -1275):(1256 -1276):(1257 -1277):(1258 -1278): (1259 -1279) u=267 imp:n=1 $ Coating 1168 4 -8.237490 (1241 -1261):(1242 -1262):(1243 -1263): (1244 -1264):(1245 -1265):(1246 -1266):(1247 -1267):(1248 -1268): (1249 -1269):(1250 -1270):(1251 -1271):(1252 -1272):(1253 -1273): (1254 -1274):(1255 -1275):(1256 -1276):(1257 -1277):(1258 -1278): (1259 -1279) u=268 imp:n=1 $ Coating 1169 4 -8.237490 (1241 -1261):(1242 -1262):(1243 -1263): (1244 -1264):(1245 -1265):(1246 -1266):(1247 -1267):(1248 -1268): (1249 -1269):(1250 -1270):(1251 -1271):(1252 -1272):(1253 -1273): (1254 -1274):(1255 -1275):(1256 -1276):(1257 -1277):(1258 -1278): (1259 -1279) u=269 imp:n=1 $ Coating 0247 4 -8.221490 (1281 -1301):(1282 -1302):(1283 -1303): (1284 -1304):(1285 -1305):(1286 -1306):(1287 -1307):(1288 -1308): (1289 -1309):(1290 -1310):(1291 -1311):(1292 -1312):(1293 -1313): (1294 -1314):(1295 -1315):(1296 -1316):(1297 -1317):(1298 -1318): (1299 -1319) u= 22 imp:n=1 $ Coating 1171 4 -8.221490 (1281 -1301):(1282 -1302):(1283 -1303): (1284 -1304):(1285 -1305):(1286 -1306):(1287 -1307):(1288 -1308): (1289 -1309):(1290 -1310):(1291 -1311):(1292 -1312):(1293 -1313): (1294 -1314):(1295 -1315):(1296 -1316):(1297 -1317):(1298 -1318): (1299 -1319) u=271 imp:n=1 $ Coating 1172 4 -8.221490 (1281 -1301):(1282 -1302):(1283 -1303): (1284 -1304):(1285 -1305):(1286 -1306):(1287 -1307):(1288 -1308): (1289 -1309):(1290 -1310):(1291 -1311):(1292 -1312):(1293 -1313): (1294 -1314):(1295 -1315):(1296 -1316):(1297 -1317):(1298 -1318): (1299 -1319) u=272 imp:n=1 $ Coating 1173 4 -8.221490 (1281 -1301):(1282 -1302):(1283 -1303): (1284 -1304):(1285 -1305):(1286 -1306):(1287 -1307):(1288 -1308): (1289 -1309):(1290 -1310):(1291 -1311):(1292 -1312):(1293 -1313): (1294 -1314):(1295 -1315):(1296 -1316):(1297 -1317):(1298 -1318): (1299 -1319) u=273 imp:n=1 $ Coating 1174 4 -8.221490 (1281 -1301):(1282 -1302):(1283 -1303): (1284 -1304):(1285 -1305):(1286 -1306):(1287 -1307):(1288 -1308): (1289 -1309):(1290 -1310):(1291 -1311):(1292 -1312):(1293 -1313): (1294 -1314):(1295 -1315):(1296 -1316):(1297 -1317):(1298 -1318): (1299 -1319) u=274 imp:n=1 $ Coating 1175 4 -8.221490 (1281 -1301):(1282 -1302):(1283 -1303): (1284 -1304):(1285 -1305):(1286 -1306):(1287 -1307):(1288 -1308): (1289 -1309):(1290 -1310):(1291 -1311):(1292 -1312):(1293 -1313): (1294 -1314):(1295 -1315):(1296 -1316):(1297 -1317):(1298 -1318): (1299 -1319) u=275 imp:n=1 $ Coating 1176 4 -8.221490 (1281 -1301):(1282 -1302):(1283 -1303): (1284 -1304):(1285 -1305):(1286 -1306):(1287 -1307):(1288 -1308): (1289 -1309):(1290 -1310):(1291 -1311):(1292 -1312):(1293 -1313): (1294 -1314):(1295 -1315):(1296 -1316):(1297 -1317):(1298 -1318): (1299 -1319) u=276 imp:n=1 $ Coating 1177 4 -8.221490 (1281 -1301):(1282 -1302):(1283 -1303): (1284 -1304):(1285 -1305):(1286 -1306):(1287 -1307):(1288 -1308): (1289 -1309):(1290 -1310):(1291 -1311):(1292 -1312):(1293 -1313): (1294 -1314):(1295 -1315):(1296 -1316):(1297 -1317):(1298 -1318): (1299 -1319) u=277 imp:n=1 $ Coating

PAGE 160

148 1178 4 -8.221490 (1281 -1301):(1282 -1302):(1283 -1303): (1284 -1304):(1285 -1305):(1286 -1306):(1287 -1307):(1288 -1308): (1289 -1309):(1290 -1310):(1291 -1311):(1292 -1312):(1293 -1313): (1294 -1314):(1295 -1315):(1296 -1316):(1297 -1317):(1298 -1318): (1299 -1319) u=278 imp:n=1 $ Coating 1179 4 -8.221490 (1281 -1301):(1282 -1302):(1283 -1303): (1284 -1304):(1285 -1305):(1286 -1306):(1287 -1307):(1288 -1308): (1289 -1309):(1290 -1310):(1291 -1311):(1292 -1312):(1293 -1313): (1294 -1314):(1295 -1315):(1296 -1316):(1297 -1317):(1298 -1318): (1299 -1319) u=279 imp:n=1 $ Coating 0248 4 -8.218816 (1321 -1341):(1322 -1342):(1323 -1343): (1324 -1344):(1325 -1345):(1326 -1346):(1327 -1347):(1328 -1348): (1329 -1349):(1330 -1350):(1331 -1351):(1332 -1352):(1333 -1353): (1334 -1354):(1335 -1355):(1336 -1356):(1337 -1357):(1338 -1358): (1339 -1359) u= 25 imp:n=1 $ Coating 1181 4 -8.218816 (1321 -1341):(1322 -1342):(1323 -1343): (1324 -1344):(1325 -1345):(1326 -1346):(1327 -1347):(1328 -1348): (1329 -1349):(1330 -1350):(1331 -1351):(1332 -1352):(1333 -1353): (1334 -1354):(1335 -1355):(1336 -1356):(1337 -1357):(1338 -1358): (1339 -1359) u=281 imp:n=1 $ Coating 1182 4 -8.218816 (1321 -1341):(1322 -1342):(1323 -1343): (1324 -1344):(1325 -1345):(1326 -1346):(1327 -1347):(1328 -1348): (1329 -1349):(1330 -1350):(1331 -1351):(1332 -1352):(1333 -1353): (1334 -1354):(1335 -1355):(1336 -1356):(1337 -1357):(1338 -1358): (1339 -1359) u=282 imp:n=1 $ Coating 1183 4 -8.218816 (1321 -1341):(1322 -1342):(1323 -1343): (1324 -1344):(1325 -1345):(1326 -1346):(1327 -1347):(1328 -1348): (1329 -1349):(1330 -1350):(1331 -1351):(1332 -1352):(1333 -1353): (1334 -1354):(1335 -1355):(1336 -1356):(1337 -1357):(1338 -1358): (1339 -1359) u=283 imp:n=1 $ Coating 1184 4 -8.218816 (1321 -1341):(1322 -1342):(1323 -1343): (1324 -1344):(1325 -1345):(1326 -1346):(1327 -1347):(1328 -1348): (1329 -1349):(1330 -1350):(1331 -1351):(1332 -1352):(1333 -1353): (1334 -1354):(1335 -1355):(1336 -1356):(1337 -1357):(1338 -1358): (1339 -1359) u=284 imp:n=1 $ Coating 1185 4 -8.218816 (1321 -1341):(1322 -1342):(1323 -1343): (1324 -1344):(1325 -1345):(1326 -1346):(1327 -1347):(1328 -1348): (1329 -1349):(1330 -1350):(1331 -1351):(1332 -1352):(1333 -1353): (1334 -1354):(1335 -1355):(1336 -1356):(1337 -1357):(1338 -1358): (1339 -1359) u=285 imp:n=1 $ Coating 1186 4 -8.218816 (1321 -1341):(1322 -1342):(1323 -1343): (1324 -1344):(1325 -1345):(1326 -1346):(1327 -1347):(1328 -1348): (1329 -1349):(1330 -1350):(1331 -1351):(1332 -1352):(1333 -1353): (1334 -1354):(1335 -1355):(1336 -1356):(1337 -1357):(1338 -1358): (1339 -1359) u=286 imp:n=1 $ Coating 1187 4 -8.218816 (1321 -1341):(1322 -1342):(1323 -1343): (1324 -1344):(1325 -1345):(1326 -1346):(1327 -1347):(1328 -1348): (1329 -1349):(1330 -1350):(1331 -1351):(1332 -1352):(1333 -1353): (1334 -1354):(1335 -1355):(1336 -1356):(1337 -1357):(1338 -1358): (1339 -1359) u=287 imp:n=1 $ Coating 1188 4 -8.218816 (1321 -1341):(1322 -1342):(1323 -1343): (1324 -1344):(1325 -1345):(1326 -1346):(1327 -1347):(1328 -1348): (1329 -1349):(1330 -1350):(1331 -1351):(1332 -1352):(1333 -1353): (1334 -1354):(1335 -1355):(1336 -1356):(1337 -1357):(1338 -1358): (1339 -1359) u=288 imp:n=1 $ Coating 1189 4 -8.218816 (1321 -1341):(1322 -1342):(1323 -1343):

PAGE 161

149 (1324 -1344):(1325 -1345):(1326 -1346):(1327 -1347):(1328 -1348): (1329 -1349):(1330 -1350):(1331 -1351):(1332 -1352):(1333 -1353): (1334 -1354):(1335 -1355):(1336 -1356):(1337 -1357):(1338 -1358): (1339 -1359) u=289 imp:n=1 $ Coating 0249 4 -8.221363 (1361 -1381):(1362 -1382):(1363 -1383): (1364 -1384):(1365 -1385):(1366 -1386):(1367 -1387):(1368 -1388): (1369 -1389):(1370 -1390):(1371 -1391):(1372 -1392):(1373 -1393): (1374 -1394):(1375 -1395):(1376 -1396):(1377 -1397):(1378 -1398): (1379 -1399) u= 28 imp:n=1 $ Coating 1191 4 -8.221363 (1361 -1381):(1362 -1382):(1363 -1383): (1364 -1384):(1365 -1385):(1366 -1386):(1367 -1387):(1368 -1388): (1369 -1389):(1370 -1390):(1371 -1391):(1372 -1392):(1373 -1393): (1374 -1394):(1375 -1395):(1376 -1396):(1377 -1397):(1378 -1398): (1379 -1399) u=291 imp:n=1 $ Coating 1192 4 -8.221363 (1361 -1381):(1362 -1382):(1363 -1383): (1364 -1384):(1365 -1385):(1366 -1386):(1367 -1387):(1368 -1388): (1369 -1389):(1370 -1390):(1371 -1391):(1372 -1392):(1373 -1393): (1374 -1394):(1375 -1395):(1376 -1396):(1377 -1397):(1378 -1398): (1379 -1399) u=292 imp:n=1 $ Coating 1193 4 -8.221363 (1361 -1381):(1362 -1382):(1363 -1383): (1364 -1384):(1365 -1385):(1366 -1386):(1367 -1387):(1368 -1388): (1369 -1389):(1370 -1390):(1371 -1391):(1372 -1392):(1373 -1393): (1374 -1394):(1375 -1395):(1376 -1396):(1377 -1397):(1378 -1398): (1379 -1399) u=293 imp:n=1 $ Coating 1194 4 -8.221363 (1361 -1381):(1362 -1382):(1363 -1383): (1364 -1384):(1365 -1385):(1366 -1386):(1367 -1387):(1368 -1388): (1369 -1389):(1370 -1390):(1371 -1391):(1372 -1392):(1373 -1393): (1374 -1394):(1375 -1395):(1376 -1396):(1377 -1397):(1378 -1398): (1379 -1399) u=294 imp:n=1 $ Coating 1195 4 -8.221363 (1361 -1381):(1362 -1382):(1363 -1383): (1364 -1384):(1365 -1385):(1366 -1386):(1367 -1387):(1368 -1388): (1369 -1389):(1370 -1390):(1371 -1391):(1372 -1392):(1373 -1393): (1374 -1394):(1375 -1395):(1376 -1396):(1377 -1397):(1378 -1398): (1379 -1399) u=295 imp:n=1 $ Coating 1196 4 -8.221363 (1361 -1381):(1362 -1382):(1363 -1383): (1364 -1384):(1365 -1385):(1366 -1386):(1367 -1387):(1368 -1388): (1369 -1389):(1370 -1390):(1371 -1391):(1372 -1392):(1373 -1393): (1374 -1394):(1375 -1395):(1376 -1396):(1377 -1397):(1378 -1398): (1379 -1399) u=296 imp:n=1 $ Coating 1197 4 -8.221363 (1361 -1381):(1362 -1382):(1363 -1383): (1364 -1384):(1365 -1385):(1366 -1386):(1367 -1387):(1368 -1388): (1369 -1389):(1370 -1390):(1371 -1391):(1372 -1392):(1373 -1393): (1374 -1394):(1375 -1395):(1376 -1396):(1377 -1397):(1378 -1398): (1379 -1399) u=297 imp:n=1 $ Coating 1198 4 -8.221363 (1361 -1381):(1362 -1382):(1363 -1383): (1364 -1384):(1365 -1385):(1366 -1386):(1367 -1387):(1368 -1388): (1369 -1389):(1370 -1390):(1371 -1391):(1372 -1392):(1373 -1393): (1374 -1394):(1375 -1395):(1376 -1396):(1377 -1397):(1378 -1398): (1379 -1399) u=298 imp:n=1 $ Coating 1199 4 -8.221363 (1361 -1381):(1362 -1382):(1363 -1383): (1364 -1384):(1365 -1385):(1366 -1386):(1367 -1387):(1368 -1388): (1369 -1389):(1370 -1390):(1371 -1391):(1372 -1392):(1373 -1393): (1374 -1394):(1375 -1395):(1376 -1396):(1377 -1397):(1378 -1398): (1379 -1399) u=299 imp:n=1 $ Coating 0260 11 -0.004964 (-1001:-1002:-1003:-1004:-1005:-1006:-1007:-1008:-1009: -1010:-1011:-1012:-1013:-1014:-1015:-1016:-1017:-1018:-1019)

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150 u= 1 imp:n=1 $ Flow 1201 11 -0.004964 (-1001:-1002:-1003:-1004:-1005:-1006:-1007:-1008:-1009: -1010:-1011:-1012:-1013:-1014:-1015:-1016:-1017:-1018:-1019) u=201 imp:n=1 $ Flow 1202 11 -0.004964 (-1001:-1002:-1003:-1004:-1005:-1006:-1007:-1008:-1009: -1010:-1011:-1012:-1013:-1014:-1015:-1016:-1017:-1018:-1019) u=202 imp:n=1 $ Flow 1203 11 -0.004964 (-1001:-1002:-1003:-1004:-1005:-1006:-1007:-1008:-1009: -1010:-1011:-1012:-1013:-1014:-1015:-1016:-1017:-1018:-1019) u=203 imp:n=1 $ Flow 1204 11 -0.004964 (-1001:-1002:-1003:-1004:-1005:-1006:-1007:-1008:-1009: -1010:-1011:-1012:-1013:-1014:-1015:-1016:-1017:-1018:-1019) u=204 imp:n=1 $ Flow 1205 11 -0.004964 (-1001:-1002:-1003:-1004:-1005:-1006:-1007:-1008:-1009: -1010:-1011:-1012:-1013:-1014:-1015:-1016:-1017:-1018:-1019) u=205 imp:n=1 $ Flow 1206 11 -0.004964 (-1001:-1002:-1003:-1004:-1005:-1006:-1007:-1008:-1009: -1010:-1011:-1012:-1013:-1014:-1015:-1016:-1017:-1018:-1019) u=206 imp:n=1 $ Flow 1207 11 -0.004964 (-1001:-1002:-1003:-1004:-1005:-1006:-1007:-1008:-1009: -1010:-1011:-1012:-1013:-1014:-1015:-1016:-1017:-1018:-1019) u=207 imp:n=1 $ Flow 1208 11 -0.004964 (-1001:-1002:-1003:-1004:-1005:-1006:-1007:-1008:-1009: -1010:-1011:-1012:-1013:-1014:-1015:-1016:-1017:-1018:-1019) u=208 imp:n=1 $ Flow 1209 11 -0.004964 (-1001:-1002:-1003:-1004:-1005:-1006:-1007:-1008:-1009: -1010:-1011:-1012:-1013:-1014:-1015:-1016:-1017:-1018:-1019) u=209 imp:n=1 $ Flow 0261 11 -0.004884 (-1041:-1042:-1043:-1044:-1045:-1046:-1047:-1048:-1049: -1050:-1051:-1052:-1053:-1054:-1055:-1056:-1057:-1058:-1059) u= 4 imp:n=1 $ Flow 1211 11 -0.004884 (-1041:-1042:-1043:-1044:-1045:-1046:-1047:-1048:-1049: -1050:-1051:-1052:-1053:-1054:-1055:-1056:-1057:-1058:-1059) u=211 imp:n=1 $ Flow 1212 11 -0.004884 (-1041:-1042:-1043:-1044:-1045:-1046:-1047:-1048:-1049: -1050:-1051:-1052:-1053:-1054:-1055:-1056:-1057:-1058:-1059) u=212 imp:n=1 $ Flow 1213 11 -0.004884 (-1041:-1042:-1043:-1044:-1045:-1046:-1047:-1048:-1049: -1050:-1051:-1052:-1053:-1054:-1055:-1056:-1057:-1058:-1059) u=213 imp:n=1 $ Flow 1214 11 -0.004884 (-1041:-1042:-1043:-1044:-1045:-1046:-1047:-1048:-1049: -1050:-1051:-1052:-1053:-1054:-1055:-1056:-1057:-1058:-1059) u=214 imp:n=1 $ Flow 1215 11 -0.004884 (-1041:-1042:-1043:-1044:-1045:-1046:-1047:-1048:-1049: -1050:-1051:-1052:-1053:-1054:-1055:-1056:-1057:-1058:-1059) u=215 imp:n=1 $ Flow 1216 11 -0.004884 (-1041:-1042:-1043:-1044:-1045:-1046:-1047:-1048:-1049: -1050:-1051:-1052:-1053:-1054:-1055:-1056:-1057:-1058:-1059) u=216 imp:n=1 $ Flow 1217 11 -0.004884 (-1041:-1042:-1043:-1044:-1045:-1046:-1047:-1048:-1049: -1050:-1051:-1052:-1053:-1054:-1055:-1056:-1057:-1058:-1059) u=217 imp:n=1 $ Flow 1218 11 -0.004884 (-1041:-1042:-1043:-1044:-1045:-1046:-1047:-1048:-1049: -1050:-1051:-1052:-1053:-1054:-1055:-1056:-1057:-1058:-1059) u=218 imp:n=1 $ Flow 1219 11 -0.004884 (-1041:-1042:-1043:-1044:-1045:-1046:-1047:-1048:-1049:

PAGE 163

151 -1050:-1051:-1052:-1053:-1054:-1055:-1056:-1057:-1058:-1059) u=219 imp:n=1 $ Flow 0262 11 -0.003850 (-1081:-1082:-1083:-1084:-1085:-1086:-1087:-1088:-1089: -1090:-1091:-1092:-1093:-1094:-1095:-1096:-1097:-1098:-1099) u= 7 imp:n=1 $ Flow 1221 11 -0.003850 (-1081:-1082:-1083:-1084:-1085:-1086:-1087:-1088:-1089: -1090:-1091:-1092:-1093:-1094:-1095:-1096:-1097:-1098:-1099) u=221 imp:n=1 $ Flow 1222 11 -0.003850 (-1081:-1082:-1083:-1084:-1085:-1086:-1087:-1088:-1089: -1090:-1091:-1092:-1093:-1094:-1095:-1096:-1097:-1098:-1099) u=222 imp:n=1 $ Flow 1223 11 -0.003850 (-1081:-1082:-1083:-1084:-1085:-1086:-1087:-1088:-1089: -1090:-1091:-1092:-1093:-1094:-1095:-1096:-1097:-1098:-1099) u=223 imp:n=1 $ Flow 1224 11 -0.003850 (-1081:-1082:-1083:-1084:-1085:-1086:-1087:-1088:-1089: -1090:-1091:-1092:-1093:-1094:-1095:-1096:-1097:-1098:-1099) u=224 imp:n=1 $ Flow 1225 11 -0.003850 (-1081:-1082:-1083:-1084:-1085:-1086:-1087:-1088:-1089: -1090:-1091:-1092:-1093:-1094:-1095:-1096:-1097:-1098:-1099) u=225 imp:n=1 $ Flow 1226 11 -0.003850 (-1081:-1082:-1083:-1084:-1085:-1086:-1087:-1088:-1089: -1090:-1091:-1092:-1093:-1094:-1095:-1096:-1097:-1098:-1099) u=226 imp:n=1 $ Flow 1227 11 -0.003850 (-1081:-1082:-1083:-1084:-1085:-1086:-1087:-1088:-1089: -1090:-1091:-1092:-1093:-1094:-1095:-1096:-1097:-1098:-1099) u=227 imp:n=1 $ Flow 1228 11 -0.003850 (-1081:-1082:-1083:-1084:-1085:-1086:-1087:-1088:-1089: -1090:-1091:-1092:-1093:-1094:-1095:-1096:-1097:-1098:-1099) u=228 imp:n=1 $ Flow 1229 11 -0.003850 (-1081:-1082:-1083:-1084:-1085:-1086:-1087:-1088:-1089: -1090:-1091:-1092:-1093:-1094:-1095:-1096:-1097:-1098:-1099) u=229 imp:n=1 $ Flow 0263 11 -0.002617 (-1121:-1122:-1123:-1124:-1125:-1126:-1127:-1128:-1129: -1130:-1131:-1132:-1133:-1134:-1135:-1136:-1137:-1138:-1139) u= 10 imp:n=1 $ Flow 1231 11 -0.002617 (-1121:-1122:-1123:-1124:-1125:-1126:-1127:-1128:-1129: -1130:-1131:-1132:-1133:-1134:-1135:-1136:-1137:-1138:-1139) u=231 imp:n=1 $ Flow 1232 11 -0.002617 (-1121:-1122:-1123:-1124:-1125:-1126:-1127:-1128:-1129: -1130:-1131:-1132:-1133:-1134:-1135:-1136:-1137:-1138:-1139) u=232 imp:n=1 $ Flow 1233 11 -0.002617 (-1121:-1122:-1123:-1124:-1125:-1126:-1127:-1128:-1129: -1130:-1131:-1132:-1133:-1134:-1135:-1136:-1137:-1138:-1139) u=233 imp:n=1 $ Flow 1234 11 -0.002617 (-1121:-1122:-1123:-1124:-1125:-1126:-1127:-1128:-1129: -1130:-1131:-1132:-1133:-1134:-1135:-1136:-1137:-1138:-1139) u=234 imp:n=1 $ Flow 1235 11 -0.002617 (-1121:-1122:-1123:-1124:-1125:-1126:-1127:-1128:-1129: -1130:-1131:-1132:-1133:-1134:-1135:-1136:-1137:-1138:-1139) u=235 imp:n=1 $ Flow 1236 11 -0.002617 (-1121:-1122:-1123:-1124:-1125:-1126:-1127:-1128:-1129: -1130:-1131:-1132:-1133:-1134:-1135:-1136:-1137:-1138:-1139) u=236 imp:n=1 $ Flow 1237 11 -0.002617 (-1121:-1122:-1123:-1124:-1125:-1126:-1127:-1128:-1129: -1130:-1131:-1132:-1133:-1134:-1135:-1136:-1137:-1138:-1139) u=237 imp:n=1 $ Flow

PAGE 164

152 1238 11 -0.002617 (-1121:-1122:-1123:-1124:-1125:-1126:-1127:-1128:-1129: -1130:-1131:-1132:-1133:-1134:-1135:-1136:-1137:-1138:-1139) u=238 imp:n=1 $ Flow 1239 11 -0.002617 (-1121:-1122:-1123:-1124:-1125:-1126:-1127:-1128:-1129: -1130:-1131:-1132:-1133:-1134:-1135:-1136:-1137:-1138:-1139) u=239 imp:n=1 $ Flow 0264 11 -0.001773 (-1161:-1162:-1163:-1164:-1165:-1166:-1167:-1168:-1169: -1170:-1171:-1172:-1173:-1174:-1175:-1176:-1177:-1178:-1179) u= 13 imp:n=1 $ Flow 1241 11 -0.001773 (-1161:-1162:-1163:-1164:-1165:-1166:-1167:-1168:-1169: -1170:-1171:-1172:-1173:-1174:-1175:-1176:-1177:-1178:-1179) u=241 imp:n=1 $ Flow 1242 11 -0.001773 (-1161:-1162:-1163:-1164:-1165:-1166:-1167:-1168:-1169: -1170:-1171:-1172:-1173:-1174:-1175:-1176:-1177:-1178:-1179) u=242 imp:n=1 $ Flow 1243 11 -0.001773 (-1161:-1162:-1163:-1164:-1165:-1166:-1167:-1168:-1169: -1170:-1171:-1172:-1173:-1174:-1175:-1176:-1177:-1178:-1179) u=243 imp:n=1 $ Flow 1244 11 -0.001773 (-1161:-1162:-1163:-1164:-1165:-1166:-1167:-1168:-1169: -1170:-1171:-1172:-1173:-1174:-1175:-1176:-1177:-1178:-1179) u=244 imp:n=1 $ Flow 1245 11 -0.001773 (-1161:-1162:-1163:-1164:-1165:-1166:-1167:-1168:-1169: -1170:-1171:-1172:-1173:-1174:-1175:-1176:-1177:-1178:-1179) u=245 imp:n=1 $ Flow 1246 11 -0.001773 (-1161:-1162:-1163:-1164:-1165:-1166:-1167:-1168:-1169: -1170:-1171:-1172:-1173:-1174:-1175:-1176:-1177:-1178:-1179) u=246 imp:n=1 $ Flow 1247 11 -0.001773 (-1161:-1162:-1163:-1164:-1165:-1166:-1167:-1168:-1169: -1170:-1171:-1172:-1173:-1174:-1175:-1176:-1177:-1178:-1179) u=247 imp:n=1 $ Flow 1248 11 -0.001773 (-1161:-1162:-1163:-1164:-1165:-1166:-1167:-1168:-1169: -1170:-1171:-1172:-1173:-1174:-1175:-1176:-1177:-1178:-1179) u=248 imp:n=1 $ Flow 1249 11 -0.001773 (-1161:-1162:-1163:-1164:-1165:-1166:-1167:-1168:-1169: -1170:-1171:-1172:-1173:-1174:-1175:-1176:-1177:-1178:-1179) u=249 imp:n=1 $ Flow 0265 11 -0.001368 (-1201:-1202:-1203:-1204:-1205:-1206:-1207:-1208:-1209: -1210:-1211:-1212:-1213:-1214:-1215:-1216:-1217:-1218:-1219) u= 16 imp:n=1 $ Flow 1251 11 -0.001368 (-1201:-1202:-1203:-1204:-1205:-1206:-1207:-1208:-1209: -1210:-1211:-1212:-1213:-1214:-1215:-1216:-1217:-1218:-1219) u=251 imp:n=1 $ Flow 1252 11 -0.001368 (-1201:-1202:-1203:-1204:-1205:-1206:-1207:-1208:-1209: -1210:-1211:-1212:-1213:-1214:-1215:-1216:-1217:-1218:-1219) u=252 imp:n=1 $ Flow 1253 11 -0.001368 (-1201:-1202:-1203:-1204:-1205:-1206:-1207:-1208:-1209: -1210:-1211:-1212:-1213:-1214:-1215:-1216:-1217:-1218:-1219) u=253 imp:n=1 $ Flow 1254 11 -0.001368 (-1201:-1202:-1203:-1204:-1205:-1206:-1207:-1208:-1209: -1210:-1211:-1212:-1213:-1214:-1215:-1216:-1217:-1218:-1219) u=254 imp:n=1 $ Flow 1255 11 -0.001368 (-1201:-1202:-1203:-1204:-1205:-1206:-1207:-1208:-1209: -1210:-1211:-1212:-1213:-1214:-1215:-1216:-1217:-1218:-1219) u=255 imp:n=1 $ Flow 1256 11 -0.001368 (-1201:-1202:-1203:-1204:-1205:-1206:-1207:-1208:-1209: -1210:-1211:-1212:-1213:-1214:-1215:-1216:-1217:-1218:-1219)

PAGE 165

153 u=256 imp:n=1 $ Flow 1257 11 -0.001368 (-1201:-1202:-1203:-1204:-1205:-1206:-1207:-1208:-1209: -1210:-1211:-1212:-1213:-1214:-1215:-1216:-1217:-1218:-1219) u=257 imp:n=1 $ Flow 1258 11 -0.001368 (-1201:-1202:-1203:-1204:-1205:-1206:-1207:-1208:-1209: -1210:-1211:-1212:-1213:-1214:-1215:-1216:-1217:-1218:-1219) u=258 imp:n=1 $ Flow 1259 11 -0.001368 (-1201:-1202:-1203:-1204:-1205:-1206:-1207:-1208:-1209: -1210:-1211:-1212:-1213:-1214:-1215:-1216:-1217:-1218:-1219) u=259 imp:n=1 $ Flow 0266 11 -0.001141 (-1241:-1242:-1243:-1244:-1245:-1246:-1247:-1248:-1249: -1250:-1251:-1252:-1253:-1254:-1255:-1256:-1257:-1258:-1259) u= 19 imp:n=1 $ Flow 1261 11 -0.001141 (-1241:-1242:-1243:-1244:-1245:-1246:-1247:-1248:-1249: -1250:-1251:-1252:-1253:-1254:-1255:-1256:-1257:-1258:-1259) u=261 imp:n=1 $ Flow 1262 11 -0.001141 (-1241:-1242:-1243:-1244:-1245:-1246:-1247:-1248:-1249: -1250:-1251:-1252:-1253:-1254:-1255:-1256:-1257:-1258:-1259) u=262 imp:n=1 $ Flow 1263 11 -0.001141 (-1241:-1242:-1243:-1244:-1245:-1246:-1247:-1248:-1249: -1250:-1251:-1252:-1253:-1254:-1255:-1256:-1257:-1258:-1259) u=263 imp:n=1 $ Flow 1264 11 -0.001141 (-1241:-1242:-1243:-1244:-1245:-1246:-1247:-1248:-1249: -1250:-1251:-1252:-1253:-1254:-1255:-1256:-1257:-1258:-1259) u=264 imp:n=1 $ Flow 1265 11 -0.001141 (-1241:-1242:-1243:-1244:-1245:-1246:-1247:-1248:-1249: -1250:-1251:-1252:-1253:-1254:-1255:-1256:-1257:-1258:-1259) u=265 imp:n=1 $ Flow 1266 11 -0.001141 (-1241:-1242:-1243:-1244:-1245:-1246:-1247:-1248:-1249: -1250:-1251:-1252:-1253:-1254:-1255:-1256:-1257:-1258:-1259) u=266 imp:n=1 $ Flow 1267 11 -0.001141 (-1241:-1242:-1243:-1244:-1245:-1246:-1247:-1248:-1249: -1250:-1251:-1252:-1253:-1254:-1255:-1256:-1257:-1258:-1259) u=267 imp:n=1 $ Flow 1268 11 -0.001141 (-1241:-1242:-1243:-1244:-1245:-1246:-1247:-1248:-1249: -1250:-1251:-1252:-1253:-1254:-1255:-1256:-1257:-1258:-1259) u=268 imp:n=1 $ Flow 1269 11 -0.001141 (-1241:-1242:-1243:-1244:-1245:-1246:-1247:-1248:-1249: -1250:-1251:-1252:-1253:-1254:-1255:-1256:-1257:-1258:-1259) u=269 imp:n=1 $ Flow 0267 11 -0.000924 (-1281:-1282:-1283:-1284:-1285:-1286:-1287:-1288:-1289: -1290:-1291:-1292:-1293:-1294:-1295:-1296:-1297:-1298:-1299) u= 22 imp:n=1 $ Flow 1271 11 -0.000924 (-1281:-1282:-1283:-1284:-1285:-1286:-1287:-1288:-1289: -1290:-1291:-1292:-1293:-1294:-1295:-1296:-1297:-1298:-1299) u=271 imp:n=1 $ Flow 1272 11 -0.000924 (-1281:-1282:-1283:-1284:-1285:-1286:-1287:-1288:-1289: -1290:-1291:-1292:-1293:-1294:-1295:-1296:-1297:-1298:-1299) u=272 imp:n=1 $ Flow 1273 11 -0.000924 (-1281:-1282:-1283:-1284:-1285:-1286:-1287:-1288:-1289: -1290:-1291:-1292:-1293:-1294:-1295:-1296:-1297:-1298:-1299) u=273 imp:n=1 $ Flow 1274 11 -0.000924 (-1281:-1282:-1283:-1284:-1285:-1286:-1287:-1288:-1289: -1290:-1291:-1292:-1293:-1294:-1295:-1296:-1297:-1298:-1299) u=274 imp:n=1 $ Flow 1275 11 -0.000924 (-1281:-1282:-1283:-1284:-1285:-1286:-1287:-1288:-1289:

PAGE 166

154 -1290:-1291:-1292:-1293:-1294:-1295:-1296:-1297:-1298:-1299) u=275 imp:n=1 $ Flow 1276 11 -0.000924 (-1281:-1282:-1283:-1284:-1285:-1286:-1287:-1288:-1289: -1290:-1291:-1292:-1293:-1294:-1295:-1296:-1297:-1298:-1299) u=276 imp:n=1 $ Flow 1277 11 -0.000924 (-1281:-1282:-1283:-1284:-1285:-1286:-1287:-1288:-1289: -1290:-1291:-1292:-1293:-1294:-1295:-1296:-1297:-1298:-1299) u=277 imp:n=1 $ Flow 1278 11 -0.000924 (-1281:-1282:-1283:-1284:-1285:-1286:-1287:-1288:-1289: -1290:-1291:-1292:-1293:-1294:-1295:-1296:-1297:-1298:-1299) u=278 imp:n=1 $ Flow 1279 11 -0.000924 (-1281:-1282:-1283:-1284:-1285:-1286:-1287:-1288:-1289: -1290:-1291:-1292:-1293:-1294:-1295:-1296:-1297:-1298:-1299) u=279 imp:n=1 $ Flow 0268 11 -0.000731 (-1321:-1322:-1323:-1324:-1325:-1326:-1327:-1328:-1329: -1330:-1331:-1332:-1333:-1334:-1335:-1336:-1337:-1338:-1339) u= 25 imp:n=1 $ Flow 1281 11 -0.000731 (-1321:-1322:-1323:-1324:-1325:-1326:-1327:-1328:-1329: -1330:-1331:-1332:-1333:-1334:-1335:-1336:-1337:-1338:-1339) u=281 imp:n=1 $ Flow 1282 11 -0.000731 (-1321:-1322:-1323:-1324:-1325:-1326:-1327:-1328:-1329: -1330:-1331:-1332:-1333:-1334:-1335:-1336:-1337:-1338:-1339) u=282 imp:n=1 $ Flow 1283 11 -0.000731 (-1321:-1322:-1323:-1324:-1325:-1326:-1327:-1328:-1329: -1330:-1331:-1332:-1333:-1334:-1335:-1336:-1337:-1338:-1339) u=283 imp:n=1 $ Flow 1284 11 -0.000731 (-1321:-1322:-1323:-1324:-1325:-1326:-1327:-1328:-1329: -1330:-1331:-1332:-1333:-1334:-1335:-1336:-1337:-1338:-1339) u=284 imp:n=1 $ Flow 1285 11 -0.000731 (-1321:-1322:-1323:-1324:-1325:-1326:-1327:-1328:-1329: -1330:-1331:-1332:-1333:-1334:-1335:-1336:-1337:-1338:-1339) u=285 imp:n=1 $ Flow 1286 11 -0.000731 (-1321:-1322:-1323:-1324:-1325:-1326:-1327:-1328:-1329: -1330:-1331:-1332:-1333:-1334:-1335:-1336:-1337:-1338:-1339) u=286 imp:n=1 $ Flow 1287 11 -0.000731 (-1321:-1322:-1323:-1324:-1325:-1326:-1327:-1328:-1329: -1330:-1331:-1332:-1333:-1334:-1335:-1336:-1337:-1338:-1339) u=287 imp:n=1 $ Flow 1288 11 -0.000731 (-1321:-1322:-1323:-1324:-1325:-1326:-1327:-1328:-1329: -1330:-1331:-1332:-1333:-1334:-1335:-1336:-1337:-1338:-1339) u=288 imp:n=1 $ Flow 1289 11 -0.000731 (-1321:-1322:-1323:-1324:-1325:-1326:-1327:-1328:-1329: -1330:-1331:-1332:-1333:-1334:-1335:-1336:-1337:-1338:-1339) u=289 imp:n=1 $ Flow 0269 11 -0.000613 (-1361:-1362:-1363:-1364:-1365:-1366:-1367:-1368:-1369: -1370:-1371:-1372:-1373:-1374:-1375:-1376:-1377:-1378:-1379) u= 28 imp:n=1 $ Flow 1291 11 -0.000613 (-1361:-1362:-1363:-1364:-1365:-1366:-1367:-1368:-1369: -1370:-1371:-1372:-1373:-1374:-1375:-1376:-1377:-1378:-1379) u=291 imp:n=1 $ Flow 1292 11 -0.000613 (-1361:-1362:-1363:-1364:-1365:-1366:-1367:-1368:-1369: -1370:-1371:-1372:-1373:-1374:-1375:-1376:-1377:-1378:-1379) u=292 imp:n=1 $ Flow 1293 11 -0.000613 (-1361:-1362:-1363:-1364:-1365:-1366:-1367:-1368:-1369: -1370:-1371:-1372:-1373:-1374:-1375:-1376:-1377:-1378:-1379) u=293 imp:n=1 $ Flow

PAGE 167

155 1294 11 -0.000613 (-1361:-1362:-1363:-1364:-1365:-1366:-1367:-1368:-1369: -1370:-1371:-1372:-1373:-1374:-1375:-1376:-1377:-1378:-1379) u=294 imp:n=1 $ Flow 1295 11 -0.000613 (-1361:-1362:-1363:-1364:-1365:-1366:-1367:-1368:-1369: -1370:-1371:-1372:-1373:-1374:-1375:-1376:-1377:-1378:-1379) u=295 imp:n=1 $ Flow 1296 11 -0.000613 (-1361:-1362:-1363:-1364:-1365:-1366:-1367:-1368:-1369: -1370:-1371:-1372:-1373:-1374:-1375:-1376:-1377:-1378:-1379) u=296 imp:n=1 $ Flow 1297 11 -0.000613 (-1361:-1362:-1363:-1364:-1365:-1366:-1367:-1368:-1369: -1370:-1371:-1372:-1373:-1374:-1375:-1376:-1377:-1378:-1379) u=297 imp:n=1 $ Flow 1298 11 -0.000613 (-1361:-1362:-1363:-1364:-1365:-1366:-1367:-1368:-1369: -1370:-1371:-1372:-1373:-1374:-1375:-1376:-1377:-1378:-1379) u=298 imp:n=1 $ Flow 1299 11 -0.000613 (-1361:-1362:-1363:-1364:-1365:-1366:-1367:-1368:-1369: -1370:-1371:-1372:-1373:-1374:-1375:-1376:-1377:-1378:-1379) u=299 imp:n=1 $ Flow 0280 4 -8.580552 ( 211: -212: 213: -214: 215: -216) u= 1 imp:n=1 $ Outer fuel Coating 1301 4 -8.580552 ( 211: -212: 213: -214: 215: -216) u=201 imp:n=1 $ Outer fuel Coating 1302 4 -8.580552 ( 211: -212: 213: -214: 215: -216) u=202 imp:n=1 $ Outer fuel Coating 1303 4 -8.580552 ( 211: -212: 213: -214: 215: -216) u=203 imp:n=1 $ Outer fuel Coating 1304 4 -8.580552 ( 211: -212: 213: -214: 215: -216) u=204 imp:n=1 $ Outer fuel Coating 1305 4 -8.580552 ( 211: -212: 213: -214: 215: -216) u=205 imp:n=1 $ Outer fuel Coating 1306 4 -8.580552 ( 211: -212: 213: -214: 215: -216) u=206 imp:n=1 $ Outer fuel Coating 1307 4 -8.580552 ( 211: -212: 213: -214: 215: -216) u=207 imp:n=1 $ Outer fuel Coating 1308 4 -8.580552 ( 211: -212: 213: -214: 215: -216) u=208 imp:n=1 $ Outer fuel Coating 1309 4 -8.580552 ( 211: -212: 213: -214: 215: -216) u=209 imp:n=1 $ Outer fuel Coating 0281 4 -8.513410 ( 231: -232: 233: -234: 235: -236) u= 4 imp:n=1 $ Outer fuel Coating 1311 4 -8.513410 ( 231: -232: 233: -234: 235: -236) u=211 imp:n=1 $ Outer fuel Coating 1312 4 -8.513410 ( 231: -232: 233: -234: 235: -236) u=212 imp:n=1 $ Outer fuel Coating 1313 4 -8.513410 ( 231: -232: 233: -234: 235: -236) u=213 imp:n=1 $ Outer fuel Coating 1314 4 -8.513410 ( 231: -232: 233: -234: 235: -236) u=214 imp:n=1 $ Outer fuel Coating 1315 4 -8.513410 ( 231: -232: 233: -234: 235: -236) u=215 imp:n=1 $ Outer fuel Coating 1316 4 -8.513410 ( 231: -232: 233: -234: 235: -236) u=216 imp:n=1 $ Outer fuel Coating 1317 4 -8.513410 ( 231: -232: 233: -234: 235: -236) u=217 imp:n=1 $ Outer fuel Coating 1318 4 -8.513410 ( 231: -232: 233: -234: 235: -236) u=218 imp:n=1 $ Outer fuel Coating 1319 4 -8.513410 ( 231: -232: 233: -234: 235: -236) u=219 imp:n=1 $ Outer fuel Coating 0282 4 -8.443428 ( 251: -252: 253: -254: 255: -256) u= 7 imp:n=1 $ Outer fuel Coating 1321 4 -8.443428 ( 251: -252: 253: -254: 255: -256) u=221 imp:n=1 $ Outer fuel Coating 1322 4 -8.443428 ( 251: -252: 253: -254: 255: -256) u=222 imp:n=1 $ Outer fuel Coating 1323 4 -8.443428 ( 251: -252: 253: -254: 255: -256) u=223 imp:n=1 $ Outer fuel Coating 1324 4 -8.443428 ( 251: -252: 253: -254: 255: -256) u=224 imp:n=1 $ Outer fuel Coating 1325 4 -8.443428 ( 251: -252: 253: -254: 255: -256) u=225 imp:n=1 $ Outer fuel Coating 1326 4 -8.443428 ( 251: -252: 253: -254: 255: -256) u=226 imp:n=1 $ Outer fuel Coating 1327 4 -8.443428 ( 251: -252: 253: -254: 255: -256) u=227 imp:n=1 $ Outer fuel Coating 1328 4 -8.443428 ( 251: -252: 253: -254: 255: -256) u=228 imp:n=1 $ Outer fuel Coating 1329 4 -8.443428 ( 251: -252: 253: -254: 255: -256) u=229 imp:n=1 $ Outer fuel Coating 0283 4 -8.379613 ( 271: -272: 273: -274: 275: -276) u= 10 imp:n=1 $ Outer fuel Coating 1331 4 -8.379613 ( 271: -272: 273: -274: 275: -276) u=231 imp:n=1 $ Outer fuel Coating 1332 4 -8.379613 ( 271: -272: 273: -274: 275: -276) u=232 imp:n=1 $ Outer fuel Coating 1333 4 -8.379613 ( 271: -272: 273: -274: 275: -276) u=233 imp:n=1 $ Outer fuel Coating 1334 4 -8.379613 ( 271: -272: 273: -274: 275: -276) u=234 imp:n=1 $ Outer fuel Coating 1335 4 -8.379613 ( 271: -272: 273: -274: 275: -276) u=235 imp:n=1 $ Outer fuel Coating 1336 4 -8.379613 ( 271: -272: 273: -274: 275: -276) u=236 imp:n=1 $ Outer fuel Coating 1337 4 -8.379613 ( 271: -272: 273: -274: 275: -276) u=237 imp:n=1 $ Outer fuel Coating

PAGE 168

156 1338 4 -8.379613 ( 271: -272: 273: -274: 275: -276) u=238 imp:n=1 $ Outer fuel Coating 1339 4 -8.379613 ( 271: -272: 273: -274: 275: -276) u=239 imp:n=1 $ Outer fuel Coating 0284 4 -8.320556 ( 291: -292: 293: -294: 295: -296) u= 13 imp:n=1 $ Outer fuel Coating 1341 4 -8.320556 ( 291: -292: 293: -294: 295: -296) u=241 imp:n=1 $ Outer fuel Coating 1342 4 -8.320556 ( 291: -292: 293: -294: 295: -296) u=242 imp:n=1 $ Outer fuel Coating 1343 4 -8.320556 ( 291: -292: 293: -294: 295: -296) u=243 imp:n=1 $ Outer fuel Coating 1344 4 -8.320556 ( 291: -292: 293: -294: 295: -296) u=244 imp:n=1 $ Outer fuel Coating 1345 4 -8.320556 ( 291: -292: 293: -294: 295: -296) u=245 imp:n=1 $ Outer fuel Coating 1346 4 -8.320556 ( 291: -292: 293: -294: 295: -296) u=246 imp:n=1 $ Outer fuel Coating 1347 4 -8.320556 ( 291: -292: 293: -294: 295: -296) u=247 imp:n=1 $ Outer fuel Coating 1348 4 -8.320556 ( 291: -292: 293: -294: 295: -296) u=248 imp:n=1 $ Outer fuel Coating 1349 4 -8.320556 ( 291: -292: 293: -294: 295: -296) u=249 imp:n=1 $ Outer fuel Coating 0285 4 -8.270130 ( 311: -312: 313: -314: 315: -316) u= 16 imp:n=1 $ Outer fuel Coating 1351 4 -8.270130 ( 311: -312: 313: -314: 315: -316) u=251 imp:n=1 $ Outer fuel Coating 1352 4 -8.270130 ( 311: -312: 313: -314: 315: -316) u=252 imp:n=1 $ Outer fuel Coating 1353 4 -8.270130 ( 311: -312: 313: -314: 315: -316) u=253 imp:n=1 $ Outer fuel Coating 1354 4 -8.270130 ( 311: -312: 313: -314: 315: -316) u=254 imp:n=1 $ Outer fuel Coating 1355 4 -8.270130 ( 311: -312: 313: -314: 315: -316) u=255 imp:n=1 $ Outer fuel Coating 1356 4 -8.270130 ( 311: -312: 313: -314: 315: -316) u=256 imp:n=1 $ Outer fuel Coating 1357 4 -8.270130 ( 311: -312: 313: -314: 315: -316) u=257 imp:n=1 $ Outer fuel Coating 1358 4 -8.270130 ( 311: -312: 313: -314: 315: -316) u=258 imp:n=1 $ Outer fuel Coating 1359 4 -8.270130 ( 311: -312: 313: -314: 315: -316) u=259 imp:n=1 $ Outer fuel Coating 0286 4 -8.237490 ( 331: -332: 333: -334: 335: -336) u= 19 imp:n=1 $ Outer fuel Coating 1361 4 -8.237490 ( 331: -332: 333: -334: 335: -336) u=261 imp:n=1 $ Outer fuel Coating 1362 4 -8.237490 ( 331: -332: 333: -334: 335: -336) u=262 imp:n=1 $ Outer fuel Coating 1363 4 -8.237490 ( 331: -332: 333: -334: 335: -336) u=263 imp:n=1 $ Outer fuel Coating 1364 4 -8.237490 ( 331: -332: 333: -334: 335: -336) u=264 imp:n=1 $ Outer fuel Coating 1365 4 -8.237490 ( 331: -332: 333: -334: 335: -336) u=265 imp:n=1 $ Outer fuel Coating 1366 4 -8.237490 ( 331: -332: 333: -334: 335: -336) u=266 imp:n=1 $ Outer fuel Coating 1367 4 -8.237490 ( 331: -332: 333: -334: 335: -336) u=267 imp:n=1 $ Outer fuel Coating 1368 4 -8.237490 ( 331: -332: 333: -334: 335: -336) u=268 imp:n=1 $ Outer fuel Coating 1369 4 -8.237490 ( 331: -332: 333: -334: 335: -336) u=269 imp:n=1 $ Outer fuel Coating 0287 4 -8.221490 ( 351: -352: 353: -354: 355: -356) u= 22 imp:n=1 $ Outer fuel Coating 1371 4 -8.221490 ( 351: -352: 353: -354: 355: -356) u=271 imp:n=1 $ Outer fuel Coating 1372 4 -8.221490 ( 351: -352: 353: -354: 355: -356) u=272 imp:n=1 $ Outer fuel Coating 1373 4 -8.221490 ( 351: -352: 353: -354: 355: -356) u=273 imp:n=1 $ Outer fuel Coating 1374 4 -8.221490 ( 351: -352: 353: -354: 355: -356) u=274 imp:n=1 $ Outer fuel Coating 1375 4 -8.221490 ( 351: -352: 353: -354: 355: -356) u=275 imp:n=1 $ Outer fuel Coating 1376 4 -8.221490 ( 351: -352: 353: -354: 355: -356) u=276 imp:n=1 $ Outer fuel Coating 1377 4 -8.221490 ( 351: -352: 353: -354: 355: -356) u=277 imp:n=1 $ Outer fuel Coating 1378 4 -8.221490 ( 351: -352: 353: -354: 355: -356) u=278 imp:n=1 $ Outer fuel Coating 1379 4 -8.221490 ( 351: -352: 353: -354: 355: -356) u=279 imp:n=1 $ Outer fuel Coating 0288 4 -8.218816 ( 371: -372: 373: -374: 375: -376) u= 25 imp:n=1 $ Outer fuel Coating 1381 4 -8.218816 ( 371: -372: 373: -374: 375: -376) u=281 imp:n=1 $ Outer fuel Coating 1382 4 -8.218816 ( 371: -372: 373: -374: 375: -376) u=282 imp:n=1 $ Outer fuel Coating 1383 4 -8.218816 ( 371: -372: 373: -374: 375: -376) u=283 imp:n=1 $ Outer fuel Coating 1384 4 -8.218816 ( 371: -372: 373: -374: 375: -376) u=284 imp:n=1 $ Outer fuel Coating 1385 4 -8.218816 ( 371: -372: 373: -374: 375: -376) u=285 imp:n=1 $ Outer fuel Coating 1386 4 -8.218816 ( 371: -372: 373: -374: 375: -376) u=286 imp:n=1 $ Outer fuel Coating 1387 4 -8.218816 ( 371: -372: 373: -374: 375: -376) u=287 imp:n=1 $ Outer fuel Coating 1388 4 -8.218816 ( 371: -372: 373: -374: 375: -376) u=288 imp:n=1 $ Outer fuel Coating 1389 4 -8.218816 ( 371: -372: 373: -374: 375: -376) u=289 imp:n=1 $ Outer fuel Coating 0289 4 -8.221363 ( 391: -392: 393: -394: 395: -396) u= 28 imp:n=1 $ Outer fuel Coating 1391 4 -8.221363 ( 391: -392: 393: -394: 395: -396) u=291 imp:n=1 $ Outer fuel Coating 1392 4 -8.221363 ( 391: -392: 393: -394: 395: -396) u=292 imp:n=1 $ Outer fuel Coating 1393 4 -8.221363 ( 391: -392: 393: -394: 395: -396) u=293 imp:n=1 $ Outer fuel Coating

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157 1394 4 -8.221363 ( 391: -392: 393: -394: 395: -396) u=294 imp:n=1 $ Outer fuel Coating 1395 4 -8.221363 ( 391: -392: 393: -394: 395: -396) u=295 imp:n=1 $ Outer fuel Coating 1396 4 -8.221363 ( 391: -392: 393: -394: 395: -396) u=296 imp:n=1 $ Outer fuel Coating 1397 4 -8.221363 ( 391: -392: 393: -394: 395: -396) u=297 imp:n=1 $ Outer fuel Coating 1398 4 -8.221363 ( 391: -392: 393: -394: 395: -396) u=298 imp:n=1 $ Outer fuel Coating 1399 4 -8.221363 ( 391: -392: 393: -394: 395: -396) u=299 imp:n=1 $ Outer fuel Coating c 300 11 -0.049224 -1800 u= 2 imp:n=1 $ TT flow, ax reg 1 301 11 -0.031497 -1810 u= 5 imp:n=1 $ TT flow, ax reg 2 302 11 -0.023106 -1820 u= 8 imp:n=1 $ TT flow, ax reg 3 303 11 -0.018214 -1830 u=11 imp:n=1 $ TT flow, ax reg 4 304 11 -0.015010 -1840 u=14 imp:n=1 $ TT flow, ax reg 5 305 11 -0.012748 -1850 u=17 imp:n=1 $ TT flow, ax reg 6 306 11 -0.011067 -1860 u=20 imp:n=1 $ TT flow, ax reg 7 307 11 -0.009768 -1870 u=23 imp:n=1 $ TT flow, ax reg 8 308 11 -0.008734 -1880 u=26 imp:n=1 $ TT flow, ax reg 9 309 11 -0.007891 -1890 u=29 imp:n=1 $ TT flow, ax reg 10 320 5 -8.168571 1800 -1801 u= 2 imp:n=1 $ TT Structure ax reg 1 321 5 -8.147208 1810 -1811 u= 5 imp:n=1 $ TT Structure ax reg 2 322 5 -8.124823 1820 -1821 u= 8 imp:n=1 $ TT Structure ax reg 3 323 5 -8.104301 1830 -1831 u=11 imp:n=1 $ TT Structure ax reg 4 324 5 -8.085217 1840 -1841 u=14 imp:n=1 $ TT Structure ax reg 5 325 5 -8.068851 1850 -1851 u=17 imp:n=1 $ TT Structure ax reg 6 326 5 -8.058222 1860 -1861 u=20 imp:n=1 $ TT Structure ax reg 7 327 5 -8.053002 1870 -1871 u=23 imp:n=1 $ TT Structure ax reg 8 328 5 -8.052129 1880 -1881 u=26 imp:n=1 $ TT Structure ax reg 9 329 5 -8.052960 1890 -1891 u=29 imp:n=1 $ TT Structure ax reg 10 340 7 -5.462357 1801 -1802 u= 2 imp:n=1 $ TT Moderator ax reg 1 341 7 -5.448071 1811 -1812 u= 5 imp:n=1 $ TT Moderator ax reg 2 342 7 -5.433102 1821 -1822 u= 8 imp:n=1 $ TT Moderator ax reg 3 343 7 -5.419380 1831 -1832 u=11 imp:n=1 $ TT Moderator ax reg 4 344 7 -5.406619 1841 -1842 u=14 imp:n=1 $ TT Moderator ax reg 5 345 7 -5.395674 1851 -1852 u=17 imp:n=1 $ TT Moderator ax reg 6 346 7 -5.388566 1861 -1862 u=20 imp:n=1 $ TT Moderator ax reg 7 347 7 -5.385076 1871 -1872 u=23 imp:n=1 $ TT Moderator ax reg 8 348 7 -5.384491 1881 -1882 u=26 imp:n=1 $ TT Moderator ax reg 9 349 7 -5.385047 1891 -1892 u=29 imp:n=1 $ TT Moderator ax reg 10 360 11 -0.002938 1802 -1803 u= 2 imp:n=1 $ TT Outer flow ax reg 1 361 11 -0.003159 1812 -1813 u= 5 imp:n=1 $ TT Outer flow ax reg 2 362 11 -0.003413 1822 -1823 u= 8 imp:n=1 $ TT Outer flow ax reg 3 363 11 -0.003709 1832 -1833 u=11 imp:n=1 $ TT Outer flow ax reg 4 364 11 -0.004057 1842 -1843 u=14 imp:n=1 $ TT Outer flow ax reg 5 365 11 -0.004474 1852 -1853 u=17 imp:n=1 $ TT Outer flow ax reg 6 366 11 -0.004980 1862 -1863 u=20 imp:n=1 $ TT Outer flow ax reg 7 367 11 -0.005609 1872 -1873 u=23 imp:n=1 $ TT Outer flow ax reg 8 368 11 -0.006412 1882 -1883 u=26 imp:n=1 $ TT Outer flow ax reg 9 369 11 -0.007472 1892 -1893 u=29 imp:n=1 $ TT Outer flow ax reg 10 380 5 -8.168571 1803 -1804 u= 2 imp:n=1 $ TT Structure ax reg 1 381 5 -8.147208 1813 -1814 u= 5 imp:n=1 $ TT Structure ax reg 2 382 5 -8.124823 1823 -1824 u= 8 imp:n=1 $ TT Structure ax reg 3 383 5 -8.104301 1833 -1834 u=11 imp:n=1 $ TT Structure ax reg 4 384 5 -8.085217 1843 -1844 u=14 imp:n=1 $ TT Structure ax reg 5 385 5 -8.068851 1853 -1854 u=17 imp:n=1 $ TT Structure ax reg 6 386 5 -8.058222 1863 -1864 u=20 imp:n=1 $ TT Structure ax reg 7 387 5 -8.053002 1873 -1874 u=23 imp:n=1 $ TT Structure ax reg 8 388 5 -8.052129 1883 -1884 u=26 imp:n=1 $ TT Structure ax reg 9

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158 389 5 -8.052960 1893 -1894 u=29 imp:n=1 $ TT Structure ax reg 10 400 8 -0.639106 1804 -1805 u= 2 imp:n=1 $ TT Insulator ax reg 1 401 8 -0.637434 1814 -1815 u= 5 imp:n=1 $ TT Insulator ax reg 2 402 8 -0.635683 1824 -1825 u= 8 imp:n=1 $ TT Insulator ax reg 3 403 8 -0.634077 1834 -1835 u=11 imp:n=1 $ TT Insulator ax reg 4 404 8 -0.632584 1844 -1845 u=14 imp:n=1 $ TT Insulator ax reg 5 405 8 -0.631304 1854 -1855 u=17 imp:n=1 $ TT Insulator ax reg 6 406 8 -0.630472 1864 -1865 u=20 imp:n=1 $ TT Insulator ax reg 7 407 8 -0.630064 1874 -1875 u=23 imp:n=1 $ TT Insulator ax reg 8 408 8 -0.629995 1884 -1885 u=26 imp:n=1 $ TT Insulator ax reg 9 409 8 -0.630060 1894 -1895 u=29 imp:n=1 $ TT Insulator ax reg 10 420 4 -8.516732 1805 u= 2 imp:n=1 $ TT Matrix ax reg 1 421 4 -8.391044 1815 u= 5 imp:n=1 $ TT Matrix ax reg 2 422 4 -8.261736 1825 u= 8 imp:n=1 $ TT Matrix ax reg 3 423 4 -8.145304 1835 u=11 imp:n=1 $ TT Matrix ax reg 4 424 4 -8.038791 1845 u=14 imp:n=1 $ TT Matrix ax reg 5 425 4 -7.948775 1855 u=17 imp:n=1 $ TT Matrix ax reg 6 426 4 -7.890957 1865 u=20 imp:n=1 $ TT Matrix ax reg 7 427 4 -7.862745 1875 u=23 imp:n=1 $ TT Matrix ax reg 8 428 4 -7.858038 1885 u=26 imp:n=1 $ TT Matrix ax reg 9 429 4 -7.862519 1895 u=29 imp:n=1 $ TT Matrix ax reg 10 c 500 11 -0.001409 -180 u= 3 imp:n=1 $ Coolant hole in slats 1 501 11 -0.001409 -181 u= 6 imp:n=1 $ Coolant hole in slats 2 502 11 -0.001409 -182 u= 9 imp:n=1 $ Coolant hole in slats 3 503 11 -0.001409 -183 u=12 imp:n=1 $ Coolant hole in slats 4 504 11 -0.001409 -184 u=15 imp:n=1 $ Coolant hole in slats 5 505 11 -0.001409 -185 u=18 imp:n=1 $ Coolant hole in slats 6 506 11 -0.001409 -186 u=21 imp:n=1 $ Coolant hole in slats 7 507 11 -0.001409 -187 u=24 imp:n=1 $ Coolant hole in slats 8 508 11 -0.001409 -188 u=27 imp:n=1 $ Coolant hole in slats 9 509 11 -0.001409 -189 u=30 imp:n=1 $ Coolant hole in slats10 520 6 -1.797546 180 u= 3 imp:n=1 $ Reflector slats 1 521 6 -1.783480 181 u= 6 imp:n=1 $ Reflector slats 2 522 6 -1.768820 182 u= 9 imp:n=1 $ Reflector slats 3 523 6 -1.755451 183 u=12 imp:n=1 $ Reflector slats 4 524 6 -1.743079 184 u=15 imp:n=1 $ Reflector slats 5 525 6 -1.732516 185 u=18 imp:n=1 $ Reflector slats 6 526 6 -1.725678 186 u=21 imp:n=1 $ Reflector slats 7 527 6 -1.722326 187 u=24 imp:n=1 $ Reflector slats 8 528 6 -1.721766 188 u=27 imp:n=1 $ Reflector slats 9 529 6 -1.722299 189 u=30 imp:n=1 $ Reflector slats 10 c c Control Drums 801 0 -800 -152 148 fill=80 imp:n=1 $ Ctr Dm 1 Rot: 0.00 802 like 801 but *trcl=(0 0 0 20. 70. 90 110. 20. 90) 803 like 801 but *trcl=(0 0 0 40. 50. 90 130. 40. 90) 804 like 801 but *trcl=(0 0 0 60. 30. 90 150. 60. 90) 805 like 801 but *trcl=(0 0 0 80. 10. 90 170. 80. 90) 806 like 801 but *trcl=(0 0 0 100. 10. 90 170. 100. 90) 807 like 801 but *trcl=(0 0 0 120. 30. 90 150. 120. 90) 808 like 801 but *trcl=(0 0 0 140. 50. 90 130. 140. 90) 809 like 801 but *trcl=(0 0 0 160. 70. 90 110. 160. 90) 810 like 801 but *trcl=(0 0 0 180. 90. 90 90. 180. 90) 811 like 801 but *trcl=(0 0 0 160. 110. 90 70. 160. 90) 812 like 801 but *trcl=(0 0 0 140. 130. 90 50. 140. 90)

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159 813 like 801 but *trcl=(0 0 0 120. 150. 90 30. 120. 90) 814 like 801 but *trcl=(0 0 0 100. 170. 90 10. 100. 90) 815 like 801 but *trcl=(0 0 0 80. 170. 90 10. 80. 90) 816 like 801 but *trcl=(0 0 0 60. 150. 90 30. 60. 90) 817 like 801 but *trcl=(0 0 0 40. 130. 90 50. 40. 90) 818 like 801 but *trcl=(0 0 0 20. 110. 90 70. 20. 90) 830 12 -2.17674 -802 804 812 814 u=80 imp:n=1 $ Drum poison 832 6 -1.79086 -802 #830 u=80 imp:n=1 $ Drum reflector 834 0 802 u=80 imp:n=1 $ Drum gap c c Plates, Hydrogen flow manifolds, chamber exit flow 600 0 920 -921 -10 fill=150 imp:n=1 $ Support plate gap 602 0 921 -922 -10 fill=151 imp:n=1 $ Support plate 604 0 922 -923 -10 fill=152 imp:n=1 $ TT Up pass Manifold 606 0 923 -924 -10 fill=153 imp:n=1 $ Bottom Interf plate 608 0 924 -925 -10 fill=154 imp:n=1 $ TT Downpass Manifold 610 0 925 -926 -10 fill=155 imp:n=1 $ Top Interf plate 612 11 -0.00406 926 -927 -10 imp:n=1 $ Fuel coolant manifold 614 10 -2.68142 927 -928 -10 imp:n=1 $ Shield 692 11 -0.00061 890 -900 -108 imp:n=1 $ Coolant exiting core 694 10 -2.68142 890 -900 108 -29 imp:n=1 $ Chamber wall c 620 11 -0.00406 -600 u=61 imp:n=1 $ Fuel coolant in-flow 621 10 -2.68142 600 -601 u=61 imp:n=1 $ Fuel coolant channel 622 0 601 u=61 imp:n=1 $ Gap b/n core & Sup Plat 623 11 -0.07799 -605 u=62 imp:n=1 $ TT Downflow 624 10 -2.68142 605 -606 u=62 imp:n=1 $ TT flow separation 625 11 -0.00334 606 -607 u=62 imp:n=1 $ TT Upflow 626 10 -2.68142 607 -608 u=62 imp:n=1 $ TT Upflow channel 627 0 608 u=62 imp:n=1 $ Gap b/n core & Sup Plat 628 0 -600 u=63 imp:n=1 $ Gap b/n core & Sup Plat 629 0 600 u=63 imp:n=1 $ Gap b/n core & Sup Plat c 630 11 -0.00406 -600 u=64 imp:n=1 $ Fuel coolant in-flow 631 10 -2.68142 600 -601 u=64 imp:n=1 $ Fuel coolant channel 632 10 -2.68142 601 u=64 imp:n=1 $ Support Plate 633 11 -0.07799 -605 u=65 imp:n=1 $ TT Downflow 634 10 -2.68142 605 -606 u=65 imp:n=1 $ TT flow separation 635 11 -0.00334 606 -607 u=65 imp:n=1 $ TT Upflow 636 10 -2.68142 607 u=65 imp:n=1 $ Support Plate 637 10 -2.68142 -600 u=66 imp:n=1 $ Support Plate 638 10 -2.68142 600 u=66 imp:n=1 $ Support Plate c 640 11 -0.00406 -600 u=67 imp:n=1 $ Fuel coolant in-flow 641 10 -2.68142 600 -601 u=67 imp:n=1 $ Fuel coolant channel 642 11 -0.00334 601 u=67 imp:n=1 $ TT Up-pass Manifold 643 11 -0.07799 -605 u=68 imp:n=1 $ TT Downflow 644 10 -2.68142 605 -606 u=68 imp:n=1 $ TT flow separation 645 11 -0.00334 606 -607 u=68 imp:n=1 $ TT Upflow 646 11 -0.00334 607 u=68 imp:n=1 $ TT Up-pass Manifold 647 11 -0.00334 -600 u=69 imp:n=1 $ TT Up-pass Manifold 648 11 -0.00334 600 u=69 imp:n=1 $ TT Up-pass Manifold c 650 11 -0.00406 -600 u=70 imp:n=1 $ Fuel coolant in-flow 651 10 -2.68142 600 -601 u=70 imp:n=1 $ Fuel coolant channel 652 10 -2.68142 601 u=70 imp:n=1 $ Bottom Interface Plate

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160 653 11 -0.07799 -605 u=71 imp:n=1 $ TT Downflow 654 10 -2.68142 605 -606 u=71 imp:n=1 $ TT flow separation 655 10 -2.68142 606 u=71 imp:n=1 $ Bottom Interface Plate 657 10 -2.68142 -600 u=72 imp:n=1 $ Bottom Interface Plate 658 10 -2.68142 600 u=72 imp:n=1 $ Bottom Interface Plate c 660 11 -0.00406 -600 u=73 imp:n=1 $ Fuel coolant in-flow 661 10 -2.68142 600 -601 u=73 imp:n=1 $ Fuel coolant channel 662 11 -0.07799 601 u=73 imp:n=1 $ TT Down-pass Manifold 663 11 -0.07799 -605 u=74 imp:n=1 $ TT Downflow 664 11 -0.07799 605 u=74 imp:n=1 $ TT Down-pass Manifold 667 11 -0.07799 -600 u=75 imp:n=1 $ TT Down-pass Manifold 668 11 -0.07799 600 u=75 imp:n=1 $ TT Down-pass Manifold c 670 11 -0.00406 -600 u=76 imp:n=1 $ Fuel coolant in-flow 671 10 -2.68142 600 -601 u=76 imp:n=1 $ Fuel coolant channel 672 10 -2.68142 601 u=76 imp:n=1 $ Top Interface Plate 673 10 -2.68142 -605 u=77 imp:n=1 $ Top Interface Plate 674 10 -2.68142 605 u=77 imp:n=1 $ Top Interface Plate 677 10 -2.68142 -600 u=78 imp:n=1 $ Top Interface Plate 678 10 -2.68142 600 u=78 imp:n=1 $ Top Interface Plate c 680 0 -201 202 -203 204 -205 206 $ Support plate gap lat=2 u=150 imp:n=1 fill=-29:29 -29:29 0:0 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 61 61 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 61 61 61 62 61 63 63 61 61 63 63 63 63 63 63 63 63 63

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183 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 78 78 78 78 78 78 78 78 78 78

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184 78 78 78 78 78 78 78 78 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78

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185 78 78 78 78 78 78 78 78 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 77 76 76 76 76 76 76 77 76 76 76 76 76 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 78 78 76 77 76 76 76 76 76 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 78 78 76 77 76 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 76 76 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78

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186 c end of cell cards c Surface Cards 105 cz 1.1970 $ Part hom hex rad 108 cz 42.5995 $ Chamber inner wall 110 cz 42.0000 $ Core block 112 cz 42.9138 $ Expansion gap 114 cz 44.1883 $ Barrel 117 cz 52.2167 $ Reflector 118 cz 52.5358 $ Vessel Coolant gap 120 cz 53.1730 $ Vessel 122 cz 103.1730 $ Flood void c 146 pz -107.5485 $ Flood 148 pz -57.5485 $ Bottom 152 pz 57.5485 $ Top 154 pz 107.5485 $ Flood c 10 cz 42.0968 $ Expanded core blockax reg 1 11 cz 42.2071 $ Expanded core blockax reg 2 12 cz 42.3234 $ Expanded core blockax reg 3 13 cz 42.4306 $ Expanded core blockax reg 4 14 cz 42.5308 $ Expanded core blockax reg 5 15 cz 42.6170 $ Expanded core blockax reg 6 16 cz 42.6732 $ Expanded core blockax reg 7 17 cz 42.7009 $ Expanded core blockax reg 8 18 cz 42.7055 $ Expanded core blockax reg 9 19 cz 42.7011 $ Expanded core blockax reg 10 29 cz 42.7011 $ Expanded core blockax reg 10 c Element hex axial region 1 201 px 1.01333 202 px -1.01333 203 p .57735 1 0 1.17009 204 p .57735 1 0 -1.17009 205 p -.57735 1 0 1.17009 206 p -.57735 1 0 -1.17009 c Coating axial region 1 211 px 1.00331 212 px -1.00331 213 p .57735 1 0 1.15852 214 p .57735 1 0 -1.15852 215 p -.57735 1 0 1.15852 216 p -.57735 1 0 -1.15852 c c Element hex axial region 2 221 px 1.01599 222 px -1.01599 223 p .57735 1 0 1.17316 224 p .57735 1 0 -1.17316 225 p -.57735 1 0 1.17316 226 p -.57735 1 0 -1.17316 c Coating axial region 2 231 px 1.00594 232 px -1.00594 233 p .57735 1 0 1.16156 234 p .57735 1 0 -1.16156

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187 235 p -.57735 1 0 1.16156 236 p -.57735 1 0 -1.16156 c c Element hex axial region 3 241 px 1.01879 242 px -1.01879 243 p .57735 1 0 1.17639 244 p .57735 1 0 -1.17639 245 p -.57735 1 0 1.17639 246 p -.57735 1 0 -1.17639 c Coating axial region 3 251 px 1.00871 252 px -1.00871 253 p .57735 1 0 1.16476 254 p .57735 1 0 -1.16476 255 p -.57735 1 0 1.16476 256 p -.57735 1 0 -1.16476 c c Element hex axial region 4 261 px 1.02137 262 px -1.02137 263 p .57735 1 0 1.17937 264 p .57735 1 0 -1.17937 265 p -.57735 1 0 1.17937 266 p -.57735 1 0 -1.17937 c Coating axial region 4 271 px 1.01126 272 px -1.01126 273 p .57735 1 0 1.16771 274 p .57735 1 0 -1.16771 275 p -.57735 1 0 1.16771 276 p -.57735 1 0 -1.16771 c c Element hex axial region 5 281 px 1.02378 282 px -1.02378 283 p .57735 1 0 1.18215 284 p .57735 1 0 -1.18215 285 p -.57735 1 0 1.18215 286 p -.57735 1 0 -1.18215 c Coating axial region 5 291 px 1.01365 292 px -1.01365 293 p .57735 1 0 1.17046 294 p .57735 1 0 -1.17046 295 p -.57735 1 0 1.17046 296 p -.57735 1 0 -1.17046 c c Element hex axial region 6 301 px 1.02585 302 px -1.02585 303 p .57735 1 0 1.18455 304 p .57735 1 0 -1.18455 305 p -.57735 1 0 1.18455 306 p -.57735 1 0 -1.18455 c Coating axial region 6

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188 311 px 1.01571 312 px -1.01571 313 p .57735 1 0 1.17284 314 p .57735 1 0 -1.17284 315 p -.57735 1 0 1.17284 316 p -.57735 1 0 -1.17284 c c Element hex axial region 7 321 px 1.02721 322 px -1.02721 323 p .57735 1 0 1.18611 324 p .57735 1 0 -1.18611 325 p -.57735 1 0 1.18611 326 p -.57735 1 0 -1.18611 c Coating axial region 7 331 px 1.01705 332 px -1.01705 333 p .57735 1 0 1.17438 334 p .57735 1 0 -1.17438 335 p -.57735 1 0 1.17438 336 p -.57735 1 0 -1.17438 c c Element hex axial region 8 341 px 1.02787 342 px -1.02787 343 p .57735 1 0 1.18688 344 p .57735 1 0 -1.18688 345 p -.57735 1 0 1.18688 346 p -.57735 1 0 -1.18688 c Coating axial region 8 351 px 1.01770 352 px -1.01770 353 p .57735 1 0 1.17514 354 p .57735 1 0 -1.17514 355 p -.57735 1 0 1.17514 356 p -.57735 1 0 -1.17514 c c Element hex axial region 9 361 px 1.02798 362 px -1.02798 363 p .57735 1 0 1.18701 364 p .57735 1 0 -1.18701 365 p -.57735 1 0 1.18701 366 p -.57735 1 0 -1.18701 c Coating axial region 9 371 px 1.01782 372 px -1.01782 373 p .57735 1 0 1.17527 374 p .57735 1 0 -1.17527 375 p -.57735 1 0 1.17527 376 p -.57735 1 0 -1.17527 c c Element hex axial region 10 381 px 1.02788 382 px -1.02788 383 p .57735 1 0 1.18689

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189 384 p .57735 1 0 -1.18689 385 p -.57735 1 0 1.18689 386 p -.57735 1 0 -1.18689 c Coating axial region 10 391 px 1.01771 392 px -1.01771 393 p .57735 1 0 1.17515 394 p .57735 1 0 -1.17515 395 p -.57735 1 0 1.17515 396 p -.57735 1 0 -1.17515 c c 600 cz 0.8018 $ Fuel coolant 601 cz 0.8269 $ Fuel coolant channel 605 cz 0.7893 $ TT Down flow 606 cz 0.8144 $ TT flow separation 607 cz 0.9522 $ TT Up flow 608 cz 0.9772 $ TT Up flow channel c 890 pz -83.6028 $ Chamber 900 pz -57.7788 $ Axial Coolant Regions 901 pz -46.2834 $ Axial Coolant Regions 902 pz -34.7578 $ Axial Coolant Regions 903 pz -23.2005 $ Axial Coolant Regions 904 pz -11.6139 $ Axial Coolant Regions 905 pz 0.0000 $ Axial Coolant Regions 906 pz 11.6375 $ Axial Coolant Regions 907 pz 23.2903 $ Axial Coolant Regions 908 pz 34.9507 $ Axial Coolant Regions 909 pz 46.6124 $ Axial Coolant Regions 910 pz 58.2728 $ Axial Coolant Regions 920 pz 58.2728 $ Axial Coolant Regions 921 pz 58.27294 $ Bottom Support Plate 922 pz 68.8974 $ Top Support Plate 923 pz 70.5512 $ TT Up-pass Manifold 924 pz 71.5535 $ Bottom Interface Plate 925 pz 73.2073 $ TT Down-pass Manifold 926 pz 74.2096 $ Top Interface Plate 927 pz 76.8657 $ Fuel Coolant Manifold 928 pz 77.8680 $ Shield c c Fuel flow channels 1001 c/z 0.000 0.000 0.097 $ Axial segment 1 1002 c/z 0.000 0.405 0.097 1003 c/z 0.000 -0.405 0.097 1004 c/z 0.351 0.203 0.097 1005 c/z 0.351 -0.203 0.097 1006 c/z -0.351 0.203 0.097 1007 c/z -0.351 -0.203 0.097 1008 c/z 0.000 0.811 0.097 1009 c/z 0.000 -0.811 0.097 1010 c/z 0.702 0.405 0.097 1011 c/z 0.702 -0.405 0.097 1012 c/z -0.702 0.405 0.097 1013 c/z -0.702 -0.405 0.097 1014 c/z 0.702 0.000 0.097

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190 1015 c/z -0.702 0.000 0.097 1016 c/z 0.351 0.608 0.097 1017 c/z 0.351 -0.608 0.097 1018 c/z -0.351 0.608 0.097 1019 c/z -0.351 -0.608 0.097 1021 c/z 0.000 0.000 0.107 $ Coating for ax 1 1022 c/z 0.000 0.405 0.107 1023 c/z 0.000 -0.405 0.107 1024 c/z 0.351 0.203 0.107 1025 c/z 0.351 -0.203 0.107 1026 c/z -0.351 0.203 0.107 1027 c/z -0.351 -0.203 0.107 1028 c/z 0.000 0.811 0.107 1029 c/z 0.000 -0.811 0.107 1030 c/z 0.702 0.405 0.107 1031 c/z 0.702 -0.405 0.107 1032 c/z -0.702 0.405 0.107 1033 c/z -0.702 -0.405 0.107 1034 c/z 0.702 0.000 0.107 1035 c/z -0.702 0.000 0.107 1036 c/z 0.351 0.608 0.107 1037 c/z 0.351 -0.608 0.107 1038 c/z -0.351 0.608 0.107 1039 c/z -0.351 -0.608 0.107 1041 c/z 0.000 0.000 0.097 $ Axial segment 2 1042 c/z 0.000 0.406 0.097 1043 c/z 0.000 -0.406 0.097 1044 c/z 0.352 0.203 0.097 1045 c/z 0.352 -0.203 0.097 1046 c/z -0.352 0.203 0.097 1047 c/z -0.352 -0.203 0.097 1048 c/z 0.000 0.813 0.097 1049 c/z 0.000 -0.813 0.097 1050 c/z 0.704 0.406 0.097 1051 c/z 0.704 -0.406 0.097 1052 c/z -0.704 0.406 0.097 1053 c/z -0.704 -0.406 0.097 1054 c/z 0.704 0.000 0.097 1055 c/z -0.704 0.000 0.097 1056 c/z 0.352 0.610 0.097 1057 c/z 0.352 -0.610 0.097 1058 c/z -0.352 0.610 0.097 1059 c/z -0.352 -0.610 0.097 1061 c/z 0.000 0.000 0.107 $ Coating for ax 2 1062 c/z 0.000 0.406 0.107 1063 c/z 0.000 -0.406 0.107 1064 c/z 0.352 0.203 0.107 1065 c/z 0.352 -0.203 0.107 1066 c/z -0.352 0.203 0.107 1067 c/z -0.352 -0.203 0.107 1068 c/z 0.000 0.813 0.107 1069 c/z 0.000 -0.813 0.107 1070 c/z 0.704 0.406 0.107 1071 c/z 0.704 -0.406 0.107 1072 c/z -0.704 0.406 0.107 1073 c/z -0.704 -0.406 0.107

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191 1074 c/z 0.704 0.000 0.107 1075 c/z -0.704 0.000 0.107 1076 c/z 0.352 0.610 0.107 1077 c/z 0.352 -0.610 0.107 1078 c/z -0.352 0.610 0.107 1079 c/z -0.352 -0.610 0.107 1081 c/z 0.000 0.000 0.097 $ Axial segment 3 1082 c/z 0.000 0.408 0.097 1083 c/z 0.000 -0.408 0.097 1084 c/z 0.353 0.204 0.097 1085 c/z 0.353 -0.204 0.097 1086 c/z -0.353 0.204 0.097 1087 c/z -0.353 -0.204 0.097 1088 c/z 0.000 0.815 0.097 1089 c/z 0.000 -0.815 0.097 1090 c/z 0.706 0.408 0.097 1091 c/z 0.706 -0.408 0.097 1092 c/z -0.706 0.408 0.097 1093 c/z -0.706 -0.408 0.097 1094 c/z 0.706 0.000 0.097 1095 c/z -0.706 0.000 0.097 1096 c/z 0.353 0.611 0.097 1097 c/z 0.353 -0.611 0.097 1098 c/z -0.353 0.611 0.097 1099 c/z -0.353 -0.611 0.097 1101 c/z 0.000 0.000 0.107 $ Coating for ax 3 1102 c/z 0.000 0.408 0.107 1103 c/z 0.000 -0.408 0.107 1104 c/z 0.353 0.204 0.107 1105 c/z 0.353 -0.204 0.107 1106 c/z -0.353 0.204 0.107 1107 c/z -0.353 -0.204 0.107 1108 c/z 0.000 0.815 0.107 1109 c/z 0.000 -0.815 0.107 1110 c/z 0.706 0.408 0.107 1111 c/z 0.706 -0.408 0.107 1112 c/z -0.706 0.408 0.107 1113 c/z -0.706 -0.408 0.107 1114 c/z 0.706 0.000 0.107 1115 c/z -0.706 0.000 0.107 1116 c/z 0.353 0.611 0.107 1117 c/z 0.353 -0.611 0.107 1118 c/z -0.353 0.611 0.107 1119 c/z -0.353 -0.611 0.107 1121 c/z 0.000 0.000 0.098 $ Axial segment 4 1122 c/z 0.000 0.409 0.098 1123 c/z 0.000 -0.409 0.098 1124 c/z 0.354 0.204 0.098 1125 c/z 0.354 -0.204 0.098 1126 c/z -0.354 0.204 0.098 1127 c/z -0.354 -0.204 0.098 1128 c/z 0.000 0.817 0.098 1129 c/z 0.000 -0.817 0.098 1130 c/z 0.708 0.409 0.098 1131 c/z 0.708 -0.409 0.098 1132 c/z -0.708 0.409 0.098

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192 1133 c/z -0.708 -0.409 0.098 1134 c/z 0.708 0.000 0.098 1135 c/z -0.708 0.000 0.098 1136 c/z 0.354 0.613 0.098 1137 c/z 0.354 -0.613 0.098 1138 c/z -0.354 0.613 0.098 1139 c/z -0.354 -0.613 0.098 1141 c/z 0.000 0.000 0.108 $ Coating for ax 4 1142 c/z 0.000 0.409 0.108 1143 c/z 0.000 -0.409 0.108 1144 c/z 0.354 0.204 0.108 1145 c/z 0.354 -0.204 0.108 1146 c/z -0.354 0.204 0.108 1147 c/z -0.354 -0.204 0.108 1148 c/z 0.000 0.817 0.108 1149 c/z 0.000 -0.817 0.108 1150 c/z 0.708 0.409 0.108 1151 c/z 0.708 -0.409 0.108 1152 c/z -0.708 0.409 0.108 1153 c/z -0.708 -0.409 0.108 1154 c/z 0.708 0.000 0.108 1155 c/z -0.708 0.000 0.108 1156 c/z 0.354 0.613 0.108 1157 c/z 0.354 -0.613 0.108 1158 c/z -0.354 0.613 0.108 1159 c/z -0.354 -0.613 0.108 1161 c/z 0.000 0.000 0.098 $ Axial segment 5 1162 c/z 0.000 0.410 0.098 1163 c/z 0.000 -0.410 0.098 1164 c/z 0.355 0.205 0.098 1165 c/z 0.355 -0.205 0.098 1166 c/z -0.355 0.205 0.098 1167 c/z -0.355 -0.205 0.098 1168 c/z 0.000 0.819 0.098 1169 c/z 0.000 -0.819 0.098 1170 c/z 0.709 0.410 0.098 1171 c/z 0.709 -0.410 0.098 1172 c/z -0.709 0.410 0.098 1173 c/z -0.709 -0.410 0.098 1174 c/z 0.709 0.000 0.098 1175 c/z -0.709 0.000 0.098 1176 c/z 0.355 0.614 0.098 1177 c/z 0.355 -0.614 0.098 1178 c/z -0.355 0.614 0.098 1179 c/z -0.355 -0.614 0.098 1181 c/z 0.000 0.000 0.108 $ Coating for ax 5 1182 c/z 0.000 0.410 0.108 1183 c/z 0.000 -0.410 0.108 1184 c/z 0.355 0.205 0.108 1185 c/z 0.355 -0.205 0.108 1186 c/z -0.355 0.205 0.108 1187 c/z -0.355 -0.205 0.108 1188 c/z 0.000 0.819 0.108 1189 c/z 0.000 -0.819 0.108 1190 c/z 0.709 0.410 0.108 1191 c/z 0.709 -0.410 0.108

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193 1192 c/z -0.709 0.410 0.108 1193 c/z -0.709 -0.410 0.108 1194 c/z 0.709 0.000 0.108 1195 c/z -0.709 0.000 0.108 1196 c/z 0.355 0.614 0.108 1197 c/z 0.355 -0.614 0.108 1198 c/z -0.355 0.614 0.108 1199 c/z -0.355 -0.614 0.108 1201 c/z 0.000 0.000 0.098 $ Axial segment 6 1202 c/z 0.000 0.410 0.098 1203 c/z 0.000 -0.410 0.098 1204 c/z 0.355 0.205 0.098 1205 c/z 0.355 -0.205 0.098 1206 c/z -0.355 0.205 0.098 1207 c/z -0.355 -0.205 0.098 1208 c/z 0.000 0.821 0.098 1209 c/z 0.000 -0.821 0.098 1210 c/z 0.711 0.410 0.098 1211 c/z 0.711 -0.410 0.098 1212 c/z -0.711 0.410 0.098 1213 c/z -0.711 -0.410 0.098 1214 c/z 0.711 0.000 0.098 1215 c/z -0.711 0.000 0.098 1216 c/z 0.355 0.616 0.098 1217 c/z 0.355 -0.616 0.098 1218 c/z -0.355 0.616 0.098 1219 c/z -0.355 -0.616 0.098 1221 c/z 0.000 0.000 0.108 $ Coating for ax 6 1222 c/z 0.000 0.410 0.108 1223 c/z 0.000 -0.410 0.108 1224 c/z 0.355 0.205 0.108 1225 c/z 0.355 -0.205 0.108 1226 c/z -0.355 0.205 0.108 1227 c/z -0.355 -0.205 0.108 1228 c/z 0.000 0.821 0.108 1229 c/z 0.000 -0.821 0.108 1230 c/z 0.711 0.410 0.108 1231 c/z 0.711 -0.410 0.108 1232 c/z -0.711 0.410 0.108 1233 c/z -0.711 -0.410 0.108 1234 c/z 0.711 0.000 0.108 1235 c/z -0.711 0.000 0.108 1236 c/z 0.355 0.616 0.108 1237 c/z 0.355 -0.616 0.108 1238 c/z -0.355 0.616 0.108 1239 c/z -0.355 -0.616 0.108 1241 c/z 0.000 0.000 0.098 $ Axial segment 7 1242 c/z 0.000 0.411 0.098 1243 c/z 0.000 -0.411 0.098 1244 c/z 0.356 0.205 0.098 1245 c/z 0.356 -0.205 0.098 1246 c/z -0.356 0.205 0.098 1247 c/z -0.356 -0.205 0.098 1248 c/z 0.000 0.822 0.098 1249 c/z 0.000 -0.822 0.098 1250 c/z 0.712 0.411 0.098

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194 1251 c/z 0.712 -0.411 0.098 1252 c/z -0.712 0.411 0.098 1253 c/z -0.712 -0.411 0.098 1254 c/z 0.712 0.000 0.098 1255 c/z -0.712 0.000 0.098 1256 c/z 0.356 0.616 0.098 1257 c/z 0.356 -0.616 0.098 1258 c/z -0.356 0.616 0.098 1259 c/z -0.356 -0.616 0.098 1261 c/z 0.000 0.000 0.108 $ Coating for ax 7 1262 c/z 0.000 0.411 0.108 1263 c/z 0.000 -0.411 0.108 1264 c/z 0.356 0.205 0.108 1265 c/z 0.356 -0.205 0.108 1266 c/z -0.356 0.205 0.108 1267 c/z -0.356 -0.205 0.108 1268 c/z 0.000 0.822 0.108 1269 c/z 0.000 -0.822 0.108 1270 c/z 0.712 0.411 0.108 1271 c/z 0.712 -0.411 0.108 1272 c/z -0.712 0.411 0.108 1273 c/z -0.712 -0.411 0.108 1274 c/z 0.712 0.000 0.108 1275 c/z -0.712 0.000 0.108 1276 c/z 0.356 0.616 0.108 1277 c/z 0.356 -0.616 0.108 1278 c/z -0.356 0.616 0.108 1279 c/z -0.356 -0.616 0.108 1281 c/z 0.000 0.000 0.098 $ Axial segment 8 1282 c/z 0.000 0.411 0.098 1283 c/z 0.000 -0.411 0.098 1284 c/z 0.356 0.206 0.098 1285 c/z 0.356 -0.206 0.098 1286 c/z -0.356 0.206 0.098 1287 c/z -0.356 -0.206 0.098 1288 c/z 0.000 0.822 0.098 1289 c/z 0.000 -0.822 0.098 1290 c/z 0.712 0.411 0.098 1291 c/z 0.712 -0.411 0.098 1292 c/z -0.712 0.411 0.098 1293 c/z -0.712 -0.411 0.098 1294 c/z 0.712 0.000 0.098 1295 c/z -0.712 0.000 0.098 1296 c/z 0.356 0.617 0.098 1297 c/z 0.356 -0.617 0.098 1298 c/z -0.356 0.617 0.098 1299 c/z -0.356 -0.617 0.098 1301 c/z 0.000 0.000 0.108 $ Coating for ax 8 1302 c/z 0.000 0.411 0.108 1303 c/z 0.000 -0.411 0.108 1304 c/z 0.356 0.206 0.108 1305 c/z 0.356 -0.206 0.108 1306 c/z -0.356 0.206 0.108 1307 c/z -0.356 -0.206 0.108 1308 c/z 0.000 0.822 0.108 1309 c/z 0.000 -0.822 0.108

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195 1310 c/z 0.712 0.411 0.108 1311 c/z 0.712 -0.411 0.108 1312 c/z -0.712 0.411 0.108 1313 c/z -0.712 -0.411 0.108 1314 c/z 0.712 0.000 0.108 1315 c/z -0.712 0.000 0.108 1316 c/z 0.356 0.617 0.108 1317 c/z 0.356 -0.617 0.108 1318 c/z -0.356 0.617 0.108 1319 c/z -0.356 -0.617 0.108 1321 c/z 0.000 0.000 0.098 $ Axial segment 9 1322 c/z 0.000 0.411 0.098 1323 c/z 0.000 -0.411 0.098 1324 c/z 0.356 0.206 0.098 1325 c/z 0.356 -0.206 0.098 1326 c/z -0.356 0.206 0.098 1327 c/z -0.356 -0.206 0.098 1328 c/z 0.000 0.822 0.098 1329 c/z 0.000 -0.822 0.098 1330 c/z 0.712 0.411 0.098 1331 c/z 0.712 -0.411 0.098 1332 c/z -0.712 0.411 0.098 1333 c/z -0.712 -0.411 0.098 1334 c/z 0.712 0.000 0.098 1335 c/z -0.712 0.000 0.098 1336 c/z 0.356 0.617 0.098 1337 c/z 0.356 -0.617 0.098 1338 c/z -0.356 0.617 0.098 1339 c/z -0.356 -0.617 0.098 1341 c/z 0.000 0.000 0.108 $ Coating for ax 9 1342 c/z 0.000 0.411 0.108 1343 c/z 0.000 -0.411 0.108 1344 c/z 0.356 0.206 0.108 1345 c/z 0.356 -0.206 0.108 1346 c/z -0.356 0.206 0.108 1347 c/z -0.356 -0.206 0.108 1348 c/z 0.000 0.822 0.108 1349 c/z 0.000 -0.822 0.108 1350 c/z 0.712 0.411 0.108 1351 c/z 0.712 -0.411 0.108 1352 c/z -0.712 0.411 0.108 1353 c/z -0.712 -0.411 0.108 1354 c/z 0.712 0.000 0.108 1355 c/z -0.712 0.000 0.108 1356 c/z 0.356 0.617 0.108 1357 c/z 0.356 -0.617 0.108 1358 c/z -0.356 0.617 0.108 1359 c/z -0.356 -0.617 0.108 1361 c/z 0.000 0.000 0.098 $ Axial segment 10 1362 c/z 0.000 0.411 0.098 1363 c/z 0.000 -0.411 0.098 1364 c/z 0.356 0.206 0.098 1365 c/z 0.356 -0.206 0.098 1366 c/z -0.356 0.206 0.098 1367 c/z -0.356 -0.206 0.098 1368 c/z 0.000 0.822 0.098

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196 1369 c/z 0.000 -0.822 0.098 1370 c/z 0.712 0.411 0.098 1371 c/z 0.712 -0.411 0.098 1372 c/z -0.712 0.411 0.098 1373 c/z -0.712 -0.411 0.098 1374 c/z 0.712 0.000 0.098 1375 c/z -0.712 0.000 0.098 1376 c/z 0.356 0.617 0.098 1377 c/z 0.356 -0.617 0.098 1378 c/z -0.356 0.617 0.098 1379 c/z -0.356 -0.617 0.098 1381 c/z 0.000 0.000 0.108 $ Coating for ax10 1382 c/z 0.000 0.411 0.108 1383 c/z 0.000 -0.411 0.108 1384 c/z 0.356 0.206 0.108 1385 c/z 0.356 -0.206 0.108 1386 c/z -0.356 0.206 0.108 1387 c/z -0.356 -0.206 0.108 1388 c/z 0.000 0.822 0.108 1389 c/z 0.000 -0.822 0.108 1390 c/z 0.712 0.411 0.108 1391 c/z 0.712 -0.411 0.108 1392 c/z -0.712 0.411 0.108 1393 c/z -0.712 -0.411 0.108 1394 c/z 0.712 0.000 0.108 1395 c/z -0.712 0.000 0.108 1396 c/z 0.356 0.617 0.108 1397 c/z 0.356 -0.617 0.108 1398 c/z -0.356 0.617 0.108 1399 c/z -0.356 -0.617 0.108 c c Tie element, axial segment 1 1800 cz 0.2095 $ Flow 1801 cz 0.2603 $ Tie tube (20.0 mil) 1802 cz 0.5839 $ ZrH (127.5 mil) 1803 cz 0.6779 $ Flow (37.0 mil) 1804 cz 0.6982 $ Tie Tube ( 8.0 mil) 1805 cz 0.8061 $ Insulator (42.5 mil) c c Tie element, axial segment 2 1810 cz 0.2095 $ Flow 1811 cz 0.2603 $ Tie tube (20.0 mil) 1812 cz 0.5839 $ ZrH (127.5 mil) 1813 cz 0.6779 $ Flow (37.0 mil) 1814 cz 0.6982 $ Tie Tube ( 8.0 mil) 1815 cz 0.8061 $ Insulator (42.5 mil) c c Tie element, axial segment 3 1820 cz 0.2095 $ Flow 1821 cz 0.2603 $ Tie tube (20.0 mil) 1822 cz 0.5839 $ ZrH (127.5 mil) 1823 cz 0.6779 $ Flow (37.0 mil) 1824 cz 0.6982 $ Tie Tube ( 8.0 mil) 1825 cz 0.8061 $ Insulator (42.5 mil) c c Tie element, axial segment 4

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197 1830 cz 0.2095 $ Flow 1831 cz 0.2603 $ Tie tube (20.0 mil) 1832 cz 0.5839 $ ZrH (127.5 mil) 1833 cz 0.6779 $ Flow (37.0 mil) 1834 cz 0.6982 $ Tie Tube ( 8.0 mil) 1835 cz 0.8061 $ Insulator (42.5 mil) c c Tie element, axial segment 5 1840 cz 0.2095 $ Flow 1841 cz 0.2603 $ Tie tube (20.0 mil) 1842 cz 0.5839 $ ZrH (127.5 mil) 1843 cz 0.6779 $ Flow (37.0 mil) 1844 cz 0.6982 $ Tie Tube ( 8.0 mil) 1845 cz 0.8061 $ Insulator (42.5 mil) c c Tie element, axial segment 6 1850 cz 0.2095 $ Flow 1851 cz 0.2603 $ Tie tube (20.0 mil) 1852 cz 0.5839 $ ZrH (127.5 mil) 1853 cz 0.6779 $ Flow (37.0 mil) 1854 cz 0.6982 $ Tie Tube ( 8.0 mil) 1855 cz 0.8061 $ Insulator (42.5 mil) c c Tie element, axial segment 7 1860 cz 0.2095 $ Flow 1861 cz 0.2603 $ Tie tube (20.0 mil) 1862 cz 0.5839 $ ZrH (127.5 mil) 1863 cz 0.6779 $ Flow (37.0 mil) 1864 cz 0.6982 $ Tie Tube ( 8.0 mil) 1865 cz 0.8061 $ Insulator (42.5 mil) c c Tie element, axial segment 8 1870 cz 0.2095 $ Flow 1871 cz 0.2603 $ Tie tube (20.0 mil) 1872 cz 0.5839 $ ZrH (127.5 mil) 1873 cz 0.6779 $ Flow (37.0 mil) 1874 cz 0.6982 $ Tie Tube ( 8.0 mil) 1875 cz 0.8061 $ Insulator (42.5 mil) c c Tie element, axial segment 9 1880 cz 0.2095 $ Flow 1881 cz 0.2603 $ Tie tube (20.0 mil) 1882 cz 0.5839 $ ZrH (127.5 mil) 1883 cz 0.6779 $ Flow (37.0 mil) 1884 cz 0.6982 $ Tie Tube ( 8.0 mil) 1885 cz 0.8061 $ Insulator (42.5 mil) c c Tie element, axial segment10 1890 cz 0.2095 $ Flow 1891 cz 0.2603 $ Tie tube (20.0 mil) 1892 cz 0.5839 $ ZrH (127.5 mil) 1893 cz 0.6779 $ Flow (37.0 mil) 1894 cz 0.6982 $ Tie Tube ( 8.0 mil) 1895 cz 0.8061 $ Insulator (42.5 mil) c c Hole in slats (assume 5.0% of slat area is coolant hole)

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198 180 cz 0.2379 181 cz 0.2386 182 cz 0.2392 183 cz 0.2398 184 cz 0.2404 185 cz 0.2409 186 cz 0.2412 187 cz 0.2413 188 cz 0.2414 189 cz 0.2413 c c Control drums 0.00 degree rotation 800 c/z 0.0 48.202 3.71 802 c/z 0.0 48.202 3.51 804 c/z 0.0 48.202 2.71 812 p 1.00000 1 0 48.202 814 p -1.00000 1 0 48.202 c c Axial tally cards 971 pz -46.421 972 pz -34.816 973 pz -23.210 974 pz -11.605 975 pz 0.000 976 pz 11.605 977 pz 23.210 978 pz 34.816 979 pz 46.421 c beginning of material cards c Material Card (number in parens is room temp density to be used) c c 35v/o UCZrC in C (????) c m1 92234.30c 0.0071 92235.30c 0.9300 92238.30c 0.06289 c 6000.30c 2.2 c 40090.30c 0.5145 40091.30c 0.1122 40092.30c 0.1715 c 40094.30c 0.1738 40096.30c 0.028 c c [Comp180/3.49] CTE[6.6,0.,0.,0] m1 92234.30c -0.03692 92235.30c -4.836 92238.30c -0.327028 6000.30c -38.8 40090.30c -28.812 40091.30c -6.2832 40092.30c -9.604 40094.30c -9.7328 40096.30c -1.568 c [Comp399/3.61] CTE[6.6,0.,0.,0] m2 92234.30c -0.07881 92235.30c -10.545 92238.30c -0.69819 6000.30c -36.0 40090.30c -27.011 40091.30c -5.8905 40092.30c -9.004 40094.30c -9.1245 40096.30c -1.47 c [Comp598/3.64] CTE[6.6,0.,0.,0] m3 92234.30c -0.11644 92235.30c -15.58 92238.30c -1.03156 6000.30c -33.6 40090.30c -25.5192 40091.30c -5.5651 40092.30c -8.5064 40094.30c -8.6205 40096.30c -1.3889 c c [ZrC40/8.640] 40v/o ZrC in C m4 6000.30c -2.24605E-01 40090.30c -3.93173E-01 40091.30c -8.669607-02

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199 40092.30c -1.33973E-01 40094.30c -1.38727E-01 40096.30c -2.28260E-02 c m4 6000.30c 2.2 c 40090.30c 0.5145 40091.30c 0.1122 40092.30c 0.1715 c 40094.30c 0.1738 40096.30c 0.028 c c [Inc718/8.18] Inconel718(8.18) m5 5010.30c -1.04165E-05 5011.30c -4.96296E-05 6000.30c -7.99685E-04 13027.30c -5.00094E-03 15031.30c -1.50369E-04 16032.30c -1.49673E-04 22000.30c -8.99863E-03 24050.30c -7.93239E-03 24052.30c -1.59022E-01 24053.30c -1.83764E-02 24054.30c -4.65735E-03 25055.30c -3.50533E-03 26054.30c -9.57669E-03 26056.30c -1.54414E-01 26057.30c -3.60316E-03 26058.30c -4.92188E-04 27059.30c -9.99324E-03 28058.30c -3.52802E-01 28060.30c -1.40580E-01 28061.30c -6.21189E-03 28062.30c -2.01325E-02 28064.30c -5.29817E-03 29063.30c -2.05126E-03 29065.30c -9.45622E-04 41093.30c -5.12410E-02 42000.30c -3.05047E-02 14028.30c -3.21667E-03 14029.30c -1.69170E-04 14030.30c -1.15357E-04 c m5 5010.30c 5.13302E-06 5011.30c 2.22431E-05 6000.30c 3.28513E-04 c 13027.30c 9.14533E-04 15031.30c 2.39541E-05 c 16032.30c 2.30986E-05 22000.30c 9.27365E-04 24050.30c 7.83641E-04 c 24052.30c 1.51065E-02 24053.30c 1.71272E-03 24054.30c 4.26041E-04 c 25055.30c 3.14825E-04 26054.30c 8.76035E-04 26056.30c 1.36213E-02 c 26057.30c 3.12259E-04 26058.30c 4.19196E-05 27059.30c 8.36682E-04 c 28058.30c 3.00470E-02 28060.30c 1.15741E-02 28061.30c 5.03036E-04 c 28062.30c 1.60407E-03 28064.30c 4.08930E-04 29063.30c 1.60835E-04 c 29065.30c 7.18623E-05 41093.30c 2.72136E-03 42000.30c 1.56899E-03 c 14028.30c 5.67310E-04 14029.30c 2.88066E-05 14030.30c 1.89896E-05 c c [Be/1.81] Be TD=1.85 / 98%=1.81 CTE[7.0, 0.,0.,0.] m6 4009.30c -1.0 mt6 be.01t c c [ZrH/5.47] ZrH(5.47g/cc) SNAP-2 ratios i gnoring Hf and Nb m7 1001.30c -2.16180E-02 40090.30c -4.96099E-01 40091.30c -1.09392E-01 40092.30c -1.69046E-01 40094.30c -1.75043E-01 40096.30c -2.88015E-02 mt7 h/zr.01t c m7 1001.30c 2.0 c 40090.30c 0.5145 40091.30c 0.1122 40092.30c 0.1715 c 40094.30c 0.1738 40096.30c 0.028 c mt42 zr/h.01t c c [ZrCLow/0.640] ZrC Low density insulator m8 6000.30c -1.16347E-01 40090.30c -4.48066E-01 40091.30c -9.88003E-02 40092.30c -1.52678E-01 40094.30c -1.58095E-01 40096.30c -2.60129E-02 c m8 6000.30c 1.0 c 40090.30c 0.5145 40091.30c 0.1122 40092.30c 0.1715 c 40094.30c 0.1738 40096.30c 0.028 c c [BorCop/8.8] Borated Copper(8.8) m9 5010.30c -1.18249E-02 5011.30c -6.84296E-04 29063.30c -6.74727E-01 29065.30c -3.12764E-01 c m9 5010.30c .076 5011.30c .004 c 29063.30c .69 29035.30c .31 c c [Al/2.7] Aluminum(2.7) m10 13027.30c -1.0 c [Hyd/0.000614] Hydrogen

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200 m11 1001.30c -1.0 c [B4C/2.2] Boron carbide 95% enr TD=2.3 g/cc m12 5010.30c -7.28046E-01 5011.30c -4.21312E-02 6000.30c -2.29823E-01 c m12 5010.30c .76 5011.30c .04 6000.30c .20 c [Water/1.0] H2O(1.0) m50 1001.30c -1.11915E-01 8016.30c -8.88085E-01 mt50 lwtr.01t c m50 1001.60c 2 8016.60c 1 c c [Wetsand/2.056] (64%quartz at 2.65 g/cc)) m51 1001.30c -1.61499E-02 8016.30c -5.83856E-01 14028.30c -3.67490E-01 14029.30c -1.93260E-02 14030.30c -1.31787E-02 mt51 lwtr.01t c m51 1001.60c 0.2400 c 8016.60c 0.5467 c 14028.60c 0.19673 c 14029.60c 0.009989 c 14030.60c 0.006585 c composite fuel 2 wt pct: 5.2 enric: 0.8523 m301 92234.30c -0.03363 92235.30c -4.42409 92238.30c -0.74228 6000.30c -38.8 40090.30c -28.812 40091.30c -6.2832 40092.30c -9.604 40094.30c -9.7328 40096.30c -1.568 c composite fuel 3 wt pct: 5.2 enric: 0.7811 m302 92234.30c -0.03079 92235.30c -4.05079 92238.30c -1.11842 6000.30c -38.8 40090.30c -28.812 40091.30c -6.2832 40092.30c -9.604 40094.30c -9.7328 40096.30c -1.568 c composite fuel 4 wt pct: 5.2 enric: 0.7158 m303 92234.30c -0.02820 92235.30c -3.70902 92238.30c -1.46278 6000.30c -38.8 40090.30c -28.812 40091.30c -6.2832 40092.30c -9.604 40094.30c -9.7328 40096.30c -1.568 c composite fuel 5 wt pct: 5.2 enric: 0.6560 m304 92234.30c -0.02582 92235.30c -3.39654 92238.30c -1.77764 6000.30c -38.8 40090.30c -28.812 40091.30c -6.2832 40092.30c -9.604 40094.30c -9.7328 40096.30c -1.568 c composite fuel 6 wt pct: 5.2 enric: 0.6012 m305 92234.30c -0.02365 92235.30c -3.11061 92238.30c -2.06574 6000.30c -38.8 40090.30c -28.812 40091.30c -6.2832 40092.30c -9.604 40094.30c -9.7328 40096.30c -1.568 c composite fuel 7 wt pct: 5.2 enric: 0.5510 m306 92234.30c -0.02166 92235.30c -2.84904 92238.30c -2.32930 6000.30c -38.8 40090.30c -28.812 40091.30c -6.2832 40092.30c -9.604 40094.30c -9.7328 40096.30c -1.568 c composite fuel 8 wt pct: 5.2 enric: 0.5050 m307 92234.30c -0.01984 92235.30c -2.60965 92238.30c -2.57052 6000.30c -38.8 40090.30c -28.812 40091.30c -6.2832 40092.30c -9.604 40094.30c -9.7328 40096.30c -1.568 c composite fuel 9 wt pct: 5.2 enric: 0.4628 m308 92234.30c -0.01817 92235.30c -2.39028 92238.30c -2.79155

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201 6000.30c -38.8 40090.30c -28.812 40091.30c -6.2832 40092.30c -9.604 40094.30c -9.7328 40096.30c -1.568 c composite fuel 10 wt pct: 5.2 enric: 0.4241 m309 92234.30c -0.01664 92235.30c -2.18931 92238.30c -2.99405 6000.30c -38.8 40090.30c -28.812 40091.30c -6.2832 40092.30c -9.604 40094.30c -9.7328 40096.30c -1.568 c end of mat cards c print -128 prdmp 110 110 1 1 mode n kcode 4000 1.0 10 410 ksrc 8 -8 0 -8 8 0 9 7 0 -9 -7 0 3 3 5 -3 -3 -5 2 4 -5 -2 -4 5 7 0 10 8 0 -10 -8 0 10 -7 0 -10 5 0 15 6 0 -15 -6 0 15 -5 0 -15 9 4 20 -4 -9 -20 6 -8 25 -6 8 25 c end of deck c Tally cards fc004 Limit: 23 Exp Di 10 f004:n ( 229 < 209 [-23: 23 -23: 23 0:0]< 19) fm004 ( 3.32090 1 -6) sd004 33.65324 f104:n (1091 < 209 [-23: 23 -23: 23 0:0]< 19) fm104 ( 3.32090 301 -6) sd104 33.65324 f204:n (1092 < 209 [-23: 23 -23: 23 0:0]< 19) fm204 ( 3.32090 302 -6) sd204 33.65324 f304:n (1093 < 209 [-23: 23 -23: 23 0:0]< 19) fm304 ( 3.32090 303 -6) sd304 33.65324 f404:n (1094 < 209 [-23: 23 -23: 23 0:0]< 19) fm404 ( 3.32090 304 -6) sd404 33.65324 f504:n (1095 < 209 [-23: 23 -23: 23 0:0]< 19) fm504 ( 3.32090 305 -6) sd504 33.65324 f604:n (1096 < 209 [-23: 23 -23: 23 0:0]< 19) fm604 ( 3.32090 306 -6) sd604 33.65324 f704:n (1097 < 209 [-23: 23 -23: 23 0:0]< 19) fm704 ( 3.32090 307 -6) sd704 33.65324 f804:n (1098 < 209 [-23: 23 -23: 23 0:0]< 19) fm804 ( 3.32090 308 -6) sd804 33.65324 f904:n (1099 < 209 [-23: 23 -23: 23 0:0]< 19) fm904 ( 3.32090 309 -6) sd904 33.65324 f014:n ( 228 < 208 [-23: 23 -23: 23 0:0]< 18) fm014 ( 3.31987 1 -6) sd014 33.66366 f114:n (1081 < 208 [-23: 23 -23: 23 0:0]< 18)

PAGE 214

202 fm114 ( 3.31987 301 -6) sd114 33.66366 f214:n (1082 < 208 [-23: 23 -23: 23 0:0]< 18) fm214 ( 3.31987 302 -6) sd214 33.66366 f314:n (1083 < 208 [-23: 23 -23: 23 0:0]< 18) fm314 ( 3.31987 303 -6) sd314 33.66366 f414:n (1084 < 208 [-23: 23 -23: 23 0:0]< 18) fm414 ( 3.31987 304 -6) sd414 33.66366 f514:n (1085 < 208 [-23: 23 -23: 23 0:0]< 18) fm514 ( 3.31987 305 -6) sd514 33.66366 f614:n (1086 < 208 [-23: 23 -23: 23 0:0]< 18) fm614 ( 3.31987 306 -6) sd614 33.66366 f714:n (1087 < 208 [-23: 23 -23: 23 0:0]< 18) fm714 ( 3.31987 307 -6) sd714 33.66366 f814:n (1088 < 208 [-23: 23 -23: 23 0:0]< 18) fm814 ( 3.31987 308 -6) sd814 33.66366 f914:n (1089 < 208 [-23: 23 -23: 23 0:0]< 18) fm914 ( 3.31987 309 -6) sd914 33.66366 f024:n ( 227 < 207 [-23: 23 -23: 23 0:0]< 17) fm024 ( 3.32095 1 -6) sd024 33.65272 f124:n (1071 < 207 [-23: 23 -23: 23 0:0]< 17) fm124 ( 3.32095 301 -6) sd124 33.65272 f224:n (1072 < 207 [-23: 23 -23: 23 0:0]< 17) fm224 ( 3.32095 302 -6) sd224 33.65272 f324:n (1073 < 207 [-23: 23 -23: 23 0:0]< 17) fm324 ( 3.32095 303 -6) sd324 33.65272 f424:n (1074 < 207 [-23: 23 -23: 23 0:0]< 17) fm424 ( 3.32095 304 -6) sd424 33.65272 f524:n (1075 < 207 [-23: 23 -23: 23 0:0]< 17) fm524 ( 3.32095 305 -6) sd524 33.65272 f624:n (1076 < 207 [-23: 23 -23: 23 0:0]< 17) fm624 ( 3.32095 306 -6) sd624 33.65272 f724:n (1077 < 207 [-23: 23 -23: 23 0:0]< 17) fm724 ( 3.32095 307 -6) sd724 33.65272 f824:n (1078 < 207 [-23: 23 -23: 23 0:0]< 17) fm824 ( 3.32095 308 -6) sd824 33.65272 f924:n (1079 < 207 [-23: 23 -23: 23 0:0]< 17) fm924 ( 3.32095 309 -6) sd924 33.65272

PAGE 215

203 f034:n ( 226 < 206 [-23: 23 -23: 23 0:0]< 16) fm034 ( 3.32741 1 -6) sd034 33.58735 f134:n (1061 < 206 [-23: 23 -23: 23 0:0]< 16) fm134 ( 3.32741 301 -6) sd134 33.58735 f234:n (1062 < 206 [-23: 23 -23: 23 0:0]< 16) fm234 ( 3.32741 302 -6) sd234 33.58735 f334:n (1063 < 206 [-23: 23 -23: 23 0:0]< 16) fm334 ( 3.32741 303 -6) sd334 33.58735 f434:n (1064 < 206 [-23: 23 -23: 23 0:0]< 16) fm434 ( 3.32741 304 -6) sd434 33.58735 f534:n (1065 < 206 [-23: 23 -23: 23 0:0]< 16) fm534 ( 3.32741 305 -6) sd534 33.58735 f634:n (1066 < 206 [-23: 23 -23: 23 0:0]< 16) fm634 ( 3.32741 306 -6) sd634 33.58735 f734:n (1067 < 206 [-23: 23 -23: 23 0:0]< 16) fm734 ( 3.32741 307 -6) sd734 33.58735 f834:n (1068 < 206 [-23: 23 -23: 23 0:0]< 16) fm834 ( 3.32741 308 -6) sd834 33.58735 f934:n (1069 < 206 [-23: 23 -23: 23 0:0]< 16) fm934 ( 3.32741 309 -6) sd934 33.58735 f044:n ( 225 < 205 [-23: 23 -23: 23 0:0]< 15) fm044 ( 3.34060 1 -6) sd044 33.45480 f144:n (1051 < 205 [-23: 23 -23: 23 0:0]< 15) fm144 ( 3.34060 301 -6) sd144 33.45480 f244:n (1052 < 205 [-23: 23 -23: 23 0:0]< 15) fm244 ( 3.34060 302 -6) sd244 33.45480 f344:n (1053 < 205 [-23: 23 -23: 23 0:0]< 15) fm344 ( 3.34060 303 -6) sd344 33.45480 f444:n (1054 < 205 [-23: 23 -23: 23 0:0]< 15) fm444 ( 3.34060 304 -6) sd444 33.45480 f544:n (1055 < 205 [-23: 23 -23: 23 0:0]< 15) fm544 ( 3.34060 305 -6) sd544 33.45480 f644:n (1056 < 205 [-23: 23 -23: 23 0:0]< 15) fm644 ( 3.34060 306 -6) sd644 33.45480 f744:n (1057 < 205 [-23: 23 -23: 23 0:0]< 15) fm744 ( 3.34060 307 -6) sd744 33.45480 f844:n (1058 < 205 [-23: 23 -23: 23 0:0]< 15) fm844 ( 3.34060 308 -6)

PAGE 216

204 sd844 33.45480 f944:n (1059 < 205 [-23: 23 -23: 23 0:0]< 15) fm944 ( 3.34060 309 -6) sd944 33.45480 f054:n ( 224 < 204 [-23: 23 -23: 23 0:0]< 14) fm054 ( 3.36097 1 -6) sd054 33.25204 f154:n (1041 < 204 [-23: 23 -23: 23 0:0]< 14) fm154 ( 3.36097 301 -6) sd154 33.25204 f254:n (1042 < 204 [-23: 23 -23: 23 0:0]< 14) fm254 ( 3.36097 302 -6) sd254 33.25204 f354:n (1043 < 204 [-23: 23 -23: 23 0:0]< 14) fm354 ( 3.36097 303 -6) sd354 33.25204 f454:n (1044 < 204 [-23: 23 -23: 23 0:0]< 14) fm454 ( 3.36097 304 -6) sd454 33.25204 f554:n (1045 < 204 [-23: 23 -23: 23 0:0]< 14) fm554 ( 3.36097 305 -6) sd554 33.25204 f654:n (1046 < 204 [-23: 23 -23: 23 0:0]< 14) fm654 ( 3.36097 306 -6) sd654 33.25204 f754:n (1047 < 204 [-23: 23 -23: 23 0:0]< 14) fm754 ( 3.36097 307 -6) sd754 33.25204 f854:n (1048 < 204 [-23: 23 -23: 23 0:0]< 14) fm854 ( 3.36097 308 -6) sd854 33.25204 f954:n (1049 < 204 [-23: 23 -23: 23 0:0]< 14) fm954 ( 3.36097 309 -6) sd954 33.25204 f064:n ( 223 < 203 [-23: 23 -23: 23 0:0]< 13) fm064 ( 3.38482 1 -6) sd064 33.01768 f164:n (1031 < 203 [-23: 23 -23: 23 0:0]< 13) fm164 ( 3.38482 301 -6) sd164 33.01768 f264:n (1032 < 203 [-23: 23 -23: 23 0:0]< 13) fm264 ( 3.38482 302 -6) sd264 33.01768 f364:n (1033 < 203 [-23: 23 -23: 23 0:0]< 13) fm364 ( 3.38482 303 -6) sd364 33.01768 f464:n (1034 < 203 [-23: 23 -23: 23 0:0]< 13) fm464 ( 3.38482 304 -6) sd464 33.01768 f564:n (1035 < 203 [-23: 23 -23: 23 0:0]< 13) fm564 ( 3.38482 305 -6) sd564 33.01768 f664:n (1036 < 203 [-23: 23 -23: 23 0:0]< 13) fm664 ( 3.38482 306 -6) sd664 33.01768 f764:n (1037 < 203 [-23: 23 -23: 23 0:0]< 13)

PAGE 217

205 fm764 ( 3.38482 307 -6) sd764 33.01768 f864:n (1038 < 203 [-23: 23 -23: 23 0:0]< 13) fm864 ( 3.38482 308 -6) sd864 33.01768 f964:n (1039 < 203 [-23: 23 -23: 23 0:0]< 13) fm964 ( 3.38482 309 -6) sd964 33.01768 f074:n ( 222 < 202 [-23: 23 -23: 23 0:0]< 12) fm074 ( 3.41060 1 -6) sd074 32.76815 f174:n (1021 < 202 [-23: 23 -23: 23 0:0]< 12) fm174 ( 3.41060 301 -6) sd174 32.76815 f274:n (1022 < 202 [-23: 23 -23: 23 0:0]< 12) fm274 ( 3.41060 302 -6) sd274 32.76815 f374:n (1023 < 202 [-23: 23 -23: 23 0:0]< 12) fm374 ( 3.41060 303 -6) sd374 32.76815 f474:n (1024 < 202 [-23: 23 -23: 23 0:0]< 12) fm474 ( 3.41060 304 -6) sd474 32.76815 f574:n (1025 < 202 [-23: 23 -23: 23 0:0]< 12) fm574 ( 3.41060 305 -6) sd574 32.76815 f674:n (1026 < 202 [-23: 23 -23: 23 0:0]< 12) fm674 ( 3.41060 306 -6) sd674 32.76815 f774:n (1027 < 202 [-23: 23 -23: 23 0:0]< 12) fm774 ( 3.41060 307 -6) sd774 32.76815 f874:n (1028 < 202 [-23: 23 -23: 23 0:0]< 12) fm874 ( 3.41060 308 -6) sd874 32.76815 f974:n (1029 < 202 [-23: 23 -23: 23 0:0]< 12) fm974 ( 3.41060 309 -6) sd974 32.76815 f084:n ( 221 < 201 [-23: 23 -23: 23 0:0]< 11) fm084 ( 3.43887 1 -6) sd084 32.49878 f184:n (1011 < 201 [-23: 23 -23: 23 0:0]< 11) fm184 ( 3.43887 301 -6) sd184 32.49878 f284:n (1012 < 201 [-23: 23 -23: 23 0:0]< 11) fm284 ( 3.43887 302 -6) sd284 32.49878 f384:n (1013 < 201 [-23: 23 -23: 23 0:0]< 11) fm384 ( 3.43887 303 -6) sd384 32.49878 f484:n (1014 < 201 [-23: 23 -23: 23 0:0]< 11) fm484 ( 3.43887 304 -6) sd484 32.49878 f584:n (1015 < 201 [-23: 23 -23: 23 0:0]< 11) fm584 ( 3.43887 305 -6) sd584 32.49878

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206 f684:n (1016 < 201 [-23: 23 -23: 23 0:0]< 11) fm684 ( 3.43887 306 -6) sd684 32.49878 f784:n (1017 < 201 [-23: 23 -23: 23 0:0]< 11) fm784 ( 3.43887 307 -6) sd784 32.49878 f884:n (1018 < 201 [-23: 23 -23: 23 0:0]< 11) fm884 ( 3.43887 308 -6) sd884 32.49878 f984:n (1019 < 201 [-23: 23 -23: 23 0:0]< 11) fm984 ( 3.43887 309 -6) sd984 32.49878 f094:n ( 220 < 200 [-23: 23 -23: 23 0:0]< 10) fm094 ( 3.46599 1 -6) sd094 32.24449 f194:n (1001 < 200 [-23: 23 -23: 23 0:0]< 10) fm194 ( 3.46599 301 -6) sd194 32.24449 f294:n (1002 < 200 [-23: 23 -23: 23 0:0]< 10) fm294 ( 3.46599 302 -6) sd294 32.24449 f394:n (1003 < 200 [-23: 23 -23: 23 0:0]< 10) fm394 ( 3.46599 303 -6) sd394 32.24449 f494:n (1004 < 200 [-23: 23 -23: 23 0:0]< 10) fm494 ( 3.46599 304 -6) sd494 32.24449 f594:n (1005 < 200 [-23: 23 -23: 23 0:0]< 10) fm594 ( 3.46599 305 -6) sd594 32.24449 f694:n (1006 < 200 [-23: 23 -23: 23 0:0]< 10) fm694 ( 3.46599 306 -6) sd694 32.24449 f794:n (1007 < 200 [-23: 23 -23: 23 0:0]< 10) fm794 ( 3.46599 307 -6) sd794 32.24449 f894:n (1008 < 200 [-23: 23 -23: 23 0:0]< 10) fm894 ( 3.46599 308 -6) sd894 32.24449 f994:n (1009 < 200 [-23: 23 -23: 23 0:0]< 10) fm994 ( 3.46599 309 -6) sd994 32.24449 c NTRgen Version 0.77 Hot c FuelHexes TieTubes FuelMass FuelVolume CoolArea Diam L/D c 1194 199 1334.402 396160.72 681.67 80.19 1.45 c Core(F+TT) Slats Barrel RR VesFlow Vessel Plat+Cham Rx(Total) c 2001.1 120.2 71.9 487.4 0.0 65.1 109.4 2855.1

PAGE 219

207 LIST OF REFERENCES 1. Watson, Clayton W., Nuclear Rockets: High Perf ormance Propulsion for Mars LA-12784-MS, Los Alamos National Laboratory, Los Alamos (1994) 2. Angelo, Joseph A. and Buden, David, Space Nuclear Power Orbit Book Company, Malabar (1985) 3. Pelowitz, Denise B., ed., MCNPX User’s Manual, Version 2.5.0 LA-CP-05-0369, Los Alamos National Laboratory, Los Alamos (2005) 4. Durham, Franklin P., Nuclear Engine Definition Study, Preliminary Report, Volume I – Engine Description (U) LA-5044-MS, Los Alamos National Laboratory, Los Alamos (1979) 5. Lyon, Luther L., Performance of (U,Zr)C-Graph ite (Composite) and of (U,Zr)C (Carbide) Fuel Elements in the Nuclear Furnace 1 Test Reactor LA-5398-MS, Los Alamos National Laborator y, Los Alamos (1973) 6. Sapir, Joseph L. and Orndoff, John D., Neutronics of the Phoebus-2 Reactor (U) LA-4455, Los Alamos National La boratory, Los Alamos (1970)

PAGE 220

208 BIOGRAPHICAL SKETCH Benjamin W. Amiri was born in St. Loui s, Missouri, in February 1981. He graduated as the salutatorian of Francis Howell High School in 1999. He then went to the University of Missouri-Rolla where he graduated summa cum laude with a Bachelor of Science in nuclear engineering and a minor in mathematics in 2003. From there he went to the University of Florida to pursue hi s Master of Science in nuclear engineering. Benjamin has worked at Los Alamos Nati onal Laboratory and K nolls Atomic Power Laboratory. He is a member of the Ameri can Nuclear Society and hopes to contribute to the exploration of space.


Permanent Link: http://ufdc.ufl.edu/UFE0015744/00001

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Copyright Date: 2008

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Title: Iterative Procedure for Enrichment Zoning of Nuclear Thermal Rockets
Physical Description: Mixed Material
Copyright Date: 2008

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ITERATIVE PROCEDURE FOR ENRICHMENT ZONING
OF NUCLEAR THERMAL ROCKETS


















By

BENJAMIN W. AMIRI


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2006

































Copyright 2006

by

Benjamin W. Amiri

































This document is dedicated to the exploration of space for the betterment of all mankind.















ACKNOWLEDGMENTS

I would like to thank Dr. Samim Anghaie, Dr. Edward Dugan, and Dr. David

Poston for serving on my supervisory committee. Thanks go as well to Richard

Kapemick and Tom Marcille of Los Alamos National Laboratory, and Steve Simpson of

Marshall Space Flight Center for generously sharing their time and expertise.

Finally, thanks go to my family, without whom I would certainly not be where I am

today.
















TABLE OF CONTENTS



A C K N O W L E D G M E N T S ................................................................................................. iv

L IST O F T A B L E S ........ .......................................................... ..................... vii

LIST OF FIGURES ......... ....... .................... .......... ....... ............ ix

ABSTRACT .............. .......................................... xi

CHAPTER

1 IN TR O D U C T IO N ............................................................. .. ......... ...... .....

B benefit of N TR System s ............................................................................... 1
T h e R ov er P program ....................................................... .......... ............ ........ 2
O objectives ............................................................... ..... ...... ......... 3

2 M E T H O D O L O G Y ..................................... ...................................... .................... .... 5

M C N P X ................................................................................................... . 5
T M S S ............................................................................ .7

3 NUCLEAR ROCKET DESIGN.......................................................................10

4 NTRGEN AND NTRFILTER ............ ................................... 16

N T R g en ...................................... ............. .................... ................ 16
Therm al Expansion........... ... .... ... ........... ... .............18
Input Files ............................................. ................. ............ 19
Prim ary input file (xxx.inp)................................... .................................... 20
O their required input files ........................................ ......................... 25
Optional input files..................... ................. .............. 27
N T R F ilter ...................................... ................................................. 2 8

5 R E S U L T S .......................................................................... 3 3

U nzoned C ore C calculations ................................................ .............................. 33
Z oning C alculations........ ....... .................................................... .. .. .... ....... 4 1
906 Fuel H ex Core.................................... ....... .........41
1194 F u el H ex C ore ............... ................................................................44


v









1518 Fuel Hex Core..................... ....................... ........46
1410 Fuel H ex Core.............................................. ......... 48
1770 Fuel Hex Core..................... ...................... ......50
F final D design s ............................................... ...... .......................52

6 C O N C L U SIO N ......... ......................................................................... ......... ........60

APPENDIX

A NTRGEN PRIMARY INPUT FILE...................................... ....... ............... 62

B NTRGEN CELLCARDS INPUT FILE..................................................... ...............64

C NTRGEN MATCARDS INPUT FILE.................................... ........................ 67

D NTRGEN TEMPERATURE INPUT FILE ..............................69

E NTRGEN ZONE INPUT FILE ...........................................................................70

F M CNPX INPU T FILE ............................................................................92

L IST O F R EFER EN CE S ........................................................................... ..............207

B IO G R A PH IC A L SK E T C H ........................................... ...........................................208
















LIST OF TABLES

Table p

2-1. Polynom ials generated by TM SS. ........................................ .......................... 7

4-1. Valid cell identifiers in cellcards..................... ...... ............................ 26

4-2. A sam ple N TRfilter zone structure................................................. ....... ........ 31

4-3. A sample NTRfilter rezoning calculation....... ...............................31

5-1. Dimensions of considered NTR cores. ............................... .. ........................ 37

5-2. Criticality results for unzoned NTR cores............................................ ...........37

5-3. Criticality and runtime comparison for unzoned NTR cores. ...................................38

5-4. Hex peaking factors for unzoned NTR cores. ................................. .................38

5-5. Criticality results for 906 fuel hex core zoning iterations. .......................................42

5-6. Enrichment zone description for 906 fuel hex core zoning iterations......................42

5-7. Hex peaking factor for 906 fuel hex core zoning iterations. .....................................43

5-8. Computation time for 906 fuel hex core zoning iterations ......................................43

5-9. Criticality results for 1194 fuel hex core zoning iterations. ............. ..................45

5-10. Enrichment zone description for 1194 fuel hex core zoning iterations ..................45

5-11. Hex peaking factor for 1194 fuel hex core zoning iterations................................46

5-12. Computation time for 1194 fuel hex core zoning iterations............................... 46

5-13. Criticality results for 1518 fuel hex core zoning iterations. ....................................47

5-14. Enrichment zone description for 1518 fuel hex core zoning iterations ..................47

5-15. Hex peaking factor for 1518 fuel hex core zoning iterations ................................48

5-16. Computation time for 1518 fuel hex core zoning iterations ....................................48









5-17. Criticality results for 1410 fuel hex core zoning iterations. ....................................49

5-18. Enrichment zone description for 1410 fuel hex core zoning iterations ..................49

5-19. Hex peaking factor for 1410 fuel hex core zoning iterations ................................49

5-20. Computation time for 1410 fuel hex core zoning iterations ...................................49

5-21. Criticality results for 1770 fuel hex core zoning iterations. ....................................50

5-22. Enrichment zone description for 1770 fuel hex core zoning iterations....................51

5-23. Hex peaking factor for 1770 fuel hex core zoning iterations .............. ...............51

5-24. Computation time for 1770 fuel hex core zoning iterations............................... 51

5-25. Dimensions and nuclear characteristics of final NTR designs..............................54

5-26. Nuclear characteristic analysis of final NTR designs............... ................56
















LIST OF FIGURES

Figure page

3-1. N TR flow paths. ....................................... .. ........... ......... .... 10

3-2. Axial view of a sample NTR system. ......................................................... 12

3-3. Axial view of flow inlet and outlet manifolds for NTR system .............................12

3-4. Axial view of NTR system exit chamber. ..................................... ............... 13

3-5. Overall layout of N TR core. ...................................................................... 13

3-6. NTR core periphery and control drum. ........................................... ............... 14

3-7. N TR fuel hex and tie tube................................................. .............................. 14

4-1. MCNPX models produced by NTRgen................................. ...............17

4-2. Axial view of expanded core periphery.............................................................19

4-3. C ore periphery. ............. ................ .......... .......... ............. ................. .. 25

4-4. Outline of the NTRgen iterative procedure. ...........................................................32

5-1. Comparison of initial MCNPX runs for 906 fuel hex case. ............. ...................34

5-2. Comparison of initial MCNPX runs for 1194 fuel hex case. ............. .................35

5-3. Comparison of initial MCNPX runs for 1518 fuel hex case. ............. .................35

5-4. Comparison of initial MCNPX runs for 1410 fuel hex case. ................ ...............36

5-5. Comparison of initial MCNPX runs for 1770 fuel hex case. ............. .................36

5-6. Relative fission rate in the unzoned 906 fuel hex core ..........................................39

5-7. Relative fission rate in the unzoned 1194 fuel hex core.......................................39

5-8. Relative fission rate in the unzoned 1518 fuel hex core.......................................40

5-9. Relative fission rate in the unzoned 1410 fuel hex core.......................................40









5-10. Relative fission rate in the unzoned 1770 fuel hex core............... ...................41

5-11. Relative fission rate in the 906 fuel hex core through zoning iterations ...............43

5-12. Radial layout of zoned 906 fuel hex core. .............. ..............................................44

5-13. Detailed view of enrichment zoning in 906 fuel hex core ..................................45

5-14. Relative fission rate in the 1194 fuel hex core through zoning iterations ..............47

5-15. Relative fission rate in the 1518 fuel hex core through zoning iterations .............48

5-16. Relative fission rate in the 1410 fuel hex core through zoning iterations ..............50

5-17. Relative fission rate in the 1770 fuel hex core through zoning iterations ...............52

5-18. Expanded partially homogenized k-eff for zoned NTR cores ..............................53

5-19. Shutdown swing versus height-to-diameter ratio for NTR cores..........................56

5-21. Fission rate distribution for final 1194 fuel hex NTR core design..........................58

5-22. Fission rate distribution for final 1518 fuel hex NTR core design..........................58

5-23. Fission rate distribution for final 1410 fuel hex NTR core design..........................59

5-24. Fission rate distribution for final 1770 fuel hex NTR core design..........................59
















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

ITERATIVE PROCEDURE FOR ENRICHMENT ZONING
OF NUCLEAR THERMAL ROCKETS

By

Benjamin W. Amiri

August 2006

Chair: Samim Anghaie
Major Department: Nuclear and Radiological Engineering

Nuclear thermal rockets were designed and tested during the Rover program, which

lasted from 1955 to 1973. By using hydrogen as the propellant, these systems have the

potential to reach a specific impulse more than twice that of conventional chemical

rockets.

This thesis describes the development and implementation of NTRgen and

NTRfilter, two programs which can be used in concert to design nuclear thermal rocket

cores. NTRgen produces detailed MCNPX decks as well as MCNPX decks which

include partial homogenization of some core components to accelerate the calculation.

NTRgen accounts for axially varying thermal expansion of the core as well as providing a

core mass estimate. NTRfilter reads fission rate tallies which are written by NTRgen and

run with MCNPX. Based on these tallies NTRfilter will produce an enrichment zone

map to reduce the core radial peaking factor. This zone map can subsequently be read by









NTRgen to produce MCNPX models of a zoned core. By iterating between NTRgen and

NTRfilter one can arrive at a core design with a radial peaking factor less than 1.15.

The final design chosen in this study contains 1194 fuel hexes arranged in a

hexagonal lattice and has a reactor mass of 2855.2 kg. The hex peaking factor calculated

for this core is 1.10737 using the partially homogenized expanded MCNPX model.














CHAPTER 1
INTRODUCTION

As the exploration of space progresses, more ambitious missions will be planned

requiring systems that produce more power and can provide faster transit times than

traditional chemical systems. Nuclear fission is a logical successor to these chemical

systems, as fission is an established technology for terrestrial power applications and has

the potential to meet the more demanding system requirements. Nuclear fission power

can be utilized in space to provide propulsion via nuclear electric propulsion (NEP) or

nuclear thermal propulsion (NTP). An NEP system uses the heat from fission to produce

electricity, which powers a propulsion drive (often an ion thruster). The focus of this

study is NTP, which uses the heat from fission to heat a fluid which is then ejected from

the core to provide thrust. An NTP system of this type is referred to as a nuclear thermal

rocket (NTR).

Benefit of NTR Systems

The performance of a rocket can be expressed in terms of specific impulse (Ip).

The formula for specific impulse is given below:

F T
I, = oc -


In this equation, specific impulse, Isp, is equal to F, the thrust (the force imparted

upon the rocket by the exiting propellant) over the propellant mass flow rate. Specific

impulse is proportional to the square root of the exiting propellant temperature, T, over

the molecular weight of the propellant, M. For a given propellant mass flow rate, a









system with a higher Ip will get more thrust from the propellant than a system with a

lower I,. Similarly, for a given thrust level the higher I, system will require less

propellant mass to achieve the same thrust level as a lower I, system. Chemical rocket

systems combine hydrogen (H2) and oxygen (02) to form H20 with a molecular weight of

-18 to be used as propellant. Nuclear thermal rockets use H2 which has been heated from

fission as the propellant. Since H2 has a molecular weight of-2 we would expect an

NTR system operating with the same propellant exit temperature as a chemical system to

have a specific impulse greater than the chemical system by about a factor of 3 (I /18/2).

In practice, the exit propellant temperature is lower for NTR systems than for chemical

systems, resulting in a specific impulse of solid-core rockets about twice as large as that

of chemical rockets (9600 m/s for NTR systems vs. 4400 m/s for chemical rockets) [1].

A higher specific impulse system for a manned mission (i.e., to Mars) implies that

the craft will be able to travel faster, thus reducing transit time and minimizing astronaut

exposure to cosmic radiation. For an unmanned mission, the higher specific impulse

system will be able to devote more of its mass allotment to cargo and/or science

equipment.

The Rover Program

Significant development and testing of NTR systems was done during the Rover

program, which lasted from 1955 to 1973. The Rover program began as a research

program to develop new means of deploying large-scale weapons. However, decreases in

the weight of weapons systems as well as improvements in the capabilities of chemical

rockets led to a shift in focus of the Rover program from weapons deployment to space

exploration. Nineteen major nuclear tests were performed in support of the Rover









program. These tests began with the Kiwi series of reactors, whose purpose was to

demonstrate the feasibility of NTR technology. After the successful Kiwi tests was the

NRX series, followed by the Phoebus series. Later NTR tests included the XE, Peewee

and finally Nuclear Furnace in 1972. Among the records set by these tests were the

highest steady-state power level ever achieved in a reactor (over 4,000 MW in the June

1968 Phoebus-2A test) as well as the highest operating temperature and average power

density (2,550 K and 2,340 MW/m3 in the December 1968 Peewee test) [2].

The Rover program demonstrated the viability of NTR systems by designing,

building, testing and operating these reactors. The integration of knowledge obtained

during this program led to the small engine design. Unfortunately, though a technical

success, changing national priorities eventually led to cancellation of the Rover program

before small engine could be built and tested. The small engine design is the starting

point for the NTR systems considered in this study, and will be discussed in Chapter 3.

Objectives

The objective of this task was to develop the process and tools with which one

could arrive at a neutronically feasible NTR design. MCNPX was to be used as the

primary neutronic analysis code. There are three standard modes by which reactivity can

be affected throughout the life of a nuclear rocket: thermal expansion (increased

dimensions and corresponding density reduction), temperature-dependent cross-section

effects (Doppler broadening), and core burnup. NTRgen accounts for thermal expansion

explicitly, and the other effects are assumed to be no more than 2.5%. Thus, to ensure

that the core can operate through its designed life the beginning-of-life thermally

expanded k-eff should be above 1.025. As this approximation becomes more refined

only incidental changes in the overall design process will be required. The beginning-of-









life shutdown k-eff (i.e., all control drums turned in) should be below 0.985 to ensure

pre-launch subcriticality. A summary of objectives is given below:

* Create a program that can generate neutronic (MCNPX) models of NTR cores.
This program should do the following: thermally expand the core, write tallies
necessary to determine peaking factors, partially homogenize the core to accelerate
the calculation with a minimal loss in accuracy, provide a mass estimate of the
reactor system.

* Calculate and implement an enrichment zoning scheme to reduce the hex peaking
factor.

* Use these tools to arrive at a design with a radial peaking factor below 1.15, a
beginning-of-life thermally expanded k-eff above 1.025 and beginning-of-life
shutdown k-eff below 0.985.














CHAPTER 2
METHODOLOGY

Two codes which played a major rule in execution of this study were MCNPX and

TMSS (Thermal-Mechanical SpreadSheet). MCNPX is used to analyze the neutronic

characteristics of a system, while TMSS performs thermal analysis.

MCNPX

Neutronic analysis of the NTR cores was performed with MCNPX, a widely used

Monte Carlo transport code developed and maintained at Los Alamos National

Laboratory. The Monte Carlo method is a technique which allows one to simulate any

process for which one has probabilistic data. MCNPX allows one to simulate a detailed

geometry and to essentially conduct a "numerical experiment" by tracking the behavior

of simulated particles through the system. Since the Monte Carlo method is by nature a

stochastic process, statistical errors will inevitably exist [3].

The first step in the Monte Carlo method is to determine the probability density

function (pdf), p(x), of the process being considered. The pdf has the characteristic that

integrating over its entire range (in this case from xL to xu) yields 1.

Jup(x)dx = 1

The cumulative distribution function (CDF), P(x) is then given by

P(x) = J p(x')dx'


One can then simulate this statistical process by setting the CDF equal to a random

number between 0 and 1, E, and sampling.









E = P(x) ; x = P '(x)

In the case of a neutron traveling through a medium, the pdf for the distance the

neutron travels in the medium without collision is given as

p(x)dx = Ee- Xdx

This equation is indeed a valid pdf, as it satisfies the criteria of integrating to 1 over

its range (in the case of a traveling particle its range is from 0 to oo). We then obtain the

CDF following the procedure given above.

P(x) = ,e',Xdx' = E ; 1- e -, =

By then solving for x, the sampled flight distance, one can generate a series of

random numbers, E, and statistically simulate the free-flight neutron distance.

x_ ln(l E) ln(g)
Y, Y,

MCNPX employs this technique not just for neutron flight, but for all statistical

processes that make up a fission system. By tracking particle histories the overall

neutronic behavior of the system, including multiplication factor, reaction rates and flux

profiles, can be ascertained. Running more particle histories decreases the statistical

uncertainty of the calculation.

The Monte Carlo method has the disadvantage that it tends to be relatively time

consuming compared to deterministic techniques. However, one can simulate complex

geometries readily and use continuous energy cross-sections. The cross-sections used in

this study were generated from the Evaluated Nuclear Data Files library ENDF/B-VI.

The ENDF/B-VI files were processed using the NJOY Nuclear Data Processing System.









TMSS

TMSS is a thermal-mechanical analysis tool developed for nuclear thermal rockets

by Richard Kapernick of Los Alamos National Laboratory. TMSS has the ability to

generate polynomials for fuel hex pitch (the flat-to-flat distance of an individual hex) and

coolant channel diameter as a function of the core height. The coolant channel diameter

is set such that the pressure drop through the core does not exceed 2.6 MPa. Fuel hex

pitch is set so that maximum fuel centerline temperature is 3050 K. Core exit coolant

temperature is fixed at 2700 K. TMSS also calculates the necessary thermal power in the

core, which for these designs is 1608.84 MW. It should be noted that these cores are

designed to operate for 10 full-power hours.

The polynomials are given in Table 2-1, where the polynomial fit for each

dimension follows the formula d = AO + Al 1 h + A2 h2, where dis the dimension of

interest (fuel pitch or coolant diameter, given in cm) and h is core height in cm. The

polynomials are shown in Figure 2-1 and 2-2.

Table 2-1. Polynomials generated by TMSS.
Fuel Fuel pitch Coolant diameter
hexes AO A] A2 AO A] A2
906 -1.1039e0 3.2853e-2 -8.5073e-5 1.9209e-1 4.5098e-4 -6.2840e-7
1194 8.0749e-1 5.7636e-3 4.2062e-5 1.6708e-1 5.1683e-4 -9.9251e-7
1518 3.8015e-1 1.5681e-2 2.7919e-5 1.5075e-1 5.2037e-4 -1.0894e-6
1410 4.2688e-1 1.4214e-2 2.3639e-5 1.5331e-1 5.7035e-4 -1.3457e-6
1770 6.3551e-1 8.8134e-3 1.1355e-4 1.3869e-1 5.9786e-4 -1.6937e-6

These dimensions are set by the limiting fuel hex, i.e., the fuel hex that produces

the most power. Since the maximum power hex in effect drives the design, it is

advantageous to have as uniform a power distribution as possible, hence the importance

of enrichment zoning.













2.100




2.000




1.900

-906
S/ / --1194
0.1.800 1518
x
S1410
S/ / ( -1770
U-

1.700




1.600




1.500
60.00 80.00 100.00 120.00 140.00 160.00
Core height (cm)

Figure 2-1. Fuel hex pitch polynomial generated by TMSS.

0.2500


0.2400


0.2300


E 0.2200


S0.2100 -906

'a -m-1194
S0.2000 1518
1410
5 0.1900-- -- -i-1770


o 0.1800


0.1700


0.1600


0.1500
60.00 80.00 100.00 120.00 140.00 160.00
Core height (cm)

Figure 2-2. Coolant diameter polynomial generated by TMSS.






9


There are other means by which the effect of maximum power hexes can be offset,

such as controlling the flow distribution through the core using variable size orifices, but

this method tends to increase pressure drop.

The TMSS polynomials serve to ensure that the final core design is not attractive

simply from a neutronic standpoint, but that the design is thermally feasible as well.

While the TMSS polynomials were employed for this study, they are not necessary to the

link between NTRgen and NTRfilter which will be described in Chapter 4.





























CHAPTER 3

NUCLEAR ROCKET DESIGN



The NTR system examined in this study is similar to those developed during the




Rover program. The small engine flow cycle, fuel form, and dimensions were used as a




starting point in arriving at a new design. A simplified flow diagram is given in




Figure 3-1 [4].


TANK




I
I
I


I
I
I
I
I
I
I
I
I

---~
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I


Flow manifolds


Core -


Reflector


Exit chamber


Flow paths:
4 --- Tank feed

4--- Fuel

S--- Tie tube

- --- Nozzle/reflector


Nozzle


Figure 3-1. NTR flow paths.











Liquid hydrogen is pumped out of the propellant tank (not shown to scale) at which

point the flow is split between two paths. A portion of the hydrogen flows down through

the center of the tie tubes and up through the outer portion of the tie tubes. This flow

serves to cool the tie tubes, and the heated hydrogen then flows through a turbine which

powers the pump. After exiting the turbine, the hydrogen flows through the fuel where it

is heated before exiting through the nozzle as propellant. The hydrogen that does not

enter the tie tubes is used to cool the nozzle. After cooling the nozzle, this hydrogen

flows up through the reflector where it mixes with hydrogen exiting the turbine before

entering the core through the fuel coolant manifold, then flowing through the core and

exiting the nozzle as heated propellant. An axial view of the MCNPX model is given in

Figure 3-2. Figure 3-3 shows the flow control manifolds while Figure 3-4 shows the core

exit chamber.

Reactivity is controlled through the use of rotating drums in the radial reflector.

These drums contain a beryllium oxide (BeO) neutron reflector and a boron carbide

(B4C) neutron poison. By rotating the drums such that the poison is nearest to the core,

reactivity can be decreased and the core shut down. The overall radial core layout is

given in Figure 3-5, while a more detailed view of a control drum in the most reactive

position (poison turned out) is given in Figure 3-6.

The reactor core is made up of fuel hexes and tie tubes. These components are

shown in Figures 3-6 and 3-7. The fuel form used in this study is a (U,Zr)-C graphite

composite which was studied and tested during the Rover program [5]. This fuel consists

of 5.2% uranium (by weight), 56.0% zirconium, and 38.8% carbon.












Closeup in
Figure 3-3


















Closeup in
Figure 3-4


Axial view of a sample NTR system.


Shield


Top interface plate -

Bottom interf. plate -


Support plate


Fuel coolant inlet


Tie tube coolant inlet (down pass)

Tie tube coolant outlet (up pass)


Control drum









I Expansion gap Tie tube
Radial reflector Fuel hexes
Drum poison
Vessel coolant
Outer vessel

Figure 3-3. Axial view of flow inlet and outlet manifolds for NTR system.


...i

4**









4**











4*


Figure 3-2.


Flow inlet and outlet
manifolds









Reactor core












Exit chamber


I-









Fuel coolant Tie tube coolant


-- Exit chamber



Figure 3-4. Axial view of NTR system exit chamber.






/ -




I /





Figure 3-5. Overall layout of NTR core.

Each fuel hex contains 19 hydrogen coolant channels. Each coolant channel is

coated with a thin layer of zirconium carbide (ZrC) coating to prevent interaction

between the hot flowing hydrogen and the fuel. The tie tube provides structural support

for the core. The tie tube structural material is Inconel-718. The tie tube also contains a

zirconium hydride (ZrH) moderator to soften the neutron spectrum. The tie tube insulator

(low density zirconium carbide, ZrC) provides thermal insulation between the high

temperature fuel and the tie tube moderator. The tie tube matrix is composed of ZrC at a

density of 8.64 g/cc, whereas the low density ZrC insulator is at 0.64 g/cc.





















Control dimin .

Drumpoioii (



Radial icllccioi-


Vessel cooLilim \ '1

Outer vcI --

Figure 3-6. NTR core periphery and control drum.





Fuel


Fuel coolant












Fuel coating


Tie tube






Fuel hex









Reflector slat













- Tie tube coolant (down pass)


- Tie tube structure


- Tie tube moderator


Tie tube coolant (up pass)

Tie tube structure

Tie tube insulation

Tie tube matrix


Figure 3-7. NTR fuel hex and tie tube.









The focus of this study is the use of NTRgen and NTRfilter to flatten the power

distribution in the core for the reasons described in Chapter 2. This issue arose during the

Rover program and was addressed by varying the fuel loading through the core. During

the Phoebus tests, four loading zones were used initially but were found to be

insufficient. A subsequent test contained over twenty loading zones and achieved a

significantly more uniform power distribution [6]. The goal of this study was to

determine the effectiveness of using variable fuel enrichment as a means of power

shaping as opposed to variable fuel loading.














CHAPTER 4
NTRGEN AND NTRFILTER

NTRgen and NTRfilter are codes which were developed to facilitate the generation

of robust MCNPX NTR models and to quickly analyze produced data, respectively.

NTRgen

NTRgen is a Fortran 90 code used to generate MCNPX models of nuclear thermal

rockets within the preconceived design space described in Chapter 3. NTRgen allows

one to readily modify parameters such as core dimensions, materials, drum rotation

angle, temperatures, etc. NTRgen also calculates the mass of the modeled system,

including the fuel, tie tubes, radial reflector, pressure vessel, nozzle, flow manifolds, and

internal shield.

NTRgen produces several MCNPX decks for each scenario specified by the user.

These decks include a fully discrete model, a partially discrete model, and a homogenized

model. A comparison of how the fueled core is represented in each of the three models is

given in Figure 4-1. As this figure shows, in the fully discrete model each individual

coolant channel is explicitly modeled, as is each component of the tie tube. In the

partially discrete model, the fuel hex is composed of a homogeneous mixture of fuel,

coolant and coating. The tie tube is explicitly modeled in the example given in

Figure 4-1B, but the user has the option of employing a homogenized model of the tie

tube in the partially discrete model as well. The mass of each component of the hex will

be calculated, a new MCNPX material card will be written based on this calculation, and

that homogenized material will be placed in the hex. The partially discrete model has the









advantage of using far fewer surfaces than the fully discrete model, thus reducing the

MCNPX computation time. Figure 4-1C shows the fully homogenized model, in which

each ring of hexes is modeled as a homogenized cylinder. The center ring consists of one

homogenized tie tube, the next ring consists of six homogenized fuel hexes, and so on.

While this model uses the fewest surfaces of all models generated, it also employs more

geometric assumptions than the other models. The homogenized model is incapable of

accounting for radial variations, limiting its usefulness in calculating peaking factors.

Due to these limitations, the homogenized model was used sparingly in this study.













.;I B0


Figure 4-1. MCNPX models produced by NTRgen. A) fully discrete. B) partially
discrete. C) fully homogenized.









Thermal Expansion

The user has the option of producing MCNPX decks that represent a thermally

expanded NTR core. To activate this option, the user must input the system temperatures

in either the primary input file or in a separate temperature file, as will be discussed in the

following sections. Since temperatures in a NTR can vary axially by over 2000 K

NTRgen does not expand the core by a single average axial expansion, but allows the

user to expand up to ten axial core regions independently. Thermal expansion is dictated

by the following equation, where hold is an unexpanded core dimension such as radius or

height, hhot is the expanded core dimension, a is the temperature-dependent coefficient of

thermal expansion (CTE), Tis the temperature of the material, and To is room

temperature (assumed to be 293 K).

hhot h cold ( (T T

Similarly, density is reduced by the following equation, where cold is an

unexpanded material density and phot is the expanded material density.

Pcold
Phot 3
(o a(T). (T To))

All fuel material in a given axial level is expanded uniformly based on the axial

fuel temperature profile and fuel CTE (i.e., no radial expansion variation). Tie tube

materials at each axial level are expanded using an average tie tube temperature and the

fuel CTE. An axial closeup of an expanded core periphery is given in Figure 4-2. In this

figure, hydrogen is heated while flowing from core inlet (top) to exit (bottom). Since

axial core temperature variation is modeled whereas radial reflector temperature is treated

as uniform, the expansion gap decreases axially. Reflector thermal expansion is assumed










to be dictated by the radial reflector meat CTE at the radial reflector temperature given on

the primary input file.

I---<--





--------- Expansion gap



Axial expansion region











Control Drum Core

Radial Reflector


Figure 4-2. Axial view of expanded core periphery.

Input Files

The primary input file for NTRgen must have a ".inp" extension. For example, a

case with the root name "test" would have a primary input file named "test.inp". Two

other required input files are named "cellcards" and "matcards". In addition to the

required input files, there are two optional input files: the temperature file with a ".tmp"

extension (in this case test.tmp), and the zone map with a ".zon" extension (giving

test.zon).









Primary input file (xxx.inp)

The primary input file must be ordered exactly as described below. The input file

line number is given, followed by the variable name, the variable type (real, integer, or

character), and a brief description of the variable. The primary input file is the file with

which the user has the most direct interaction. A sample NTRgen primary input file is

given in Appendix A.

1. difltt a real variable, inner flow diameter of the tie tubes, given in cm

2. titt real, thickness of the inner tie tube structure, given in cm

3. tmott real, thickness of the tie tube moderator, given in cm

4. tofltt real, thickness of the outer tie tube flow, given in cm

5. tott real, thickness of the outer tie tube structure, given in cm

6. tinstt real, thickness of tie tube insulation, given in cm

7. nrfflw an integer variable, number of coolant channel rows in the fuel (1, 2, or 3).
1 = 1 coolant channel, 2 = 7 coolant channels, 3 = 19 coolant channels.

8. dflfh real, diameter of the fuel coolant channels, given in cm

9. tcotmin real, thickness of the fuel coolant channel coating at core inlet, given in
cm

10. tcotmax real, thickness of the fuel coolant channel coating at core outlet, given in
cm. If tcotmax and tcotmin are the same the coating thickness will be uniform
axially at beginning-of-life. The user has the option of increasing coating thickness
axially in which case the coating thickness will be uniform in each axial region, but
increase linearly throughout the core.

11. pflwsl real, diameter of the slat hex coolant channel, given in cm (if positive) OR
fraction of the slat hex area used for coolant, given in percent (if negative)

12. nttrmax,ncut OR tslhex two integer variables, the number of rows of modules and
the number of modules cut at the edge OR one real variable, the minimum
thickness of slats at the edge, given in cm (if negative). Number of modules cut at
edge is shown in Figure 4-3. A module is defined as a tie tube surrounded by the
appropriate number of hexes (this number is set by nftrat, entry # 14).

13. pitch real, the flat-to-flat distance of the fuel hexes, given in cm









14. nftrat -integer, ratio of fuel hexes to tie tubes, (0, 2, 3, or 6). The "0" option
indicates no tie tubes in the core.

15. blank line delimiter

16. dcore real, diameter of the core (fuel, tie tubes, slats), given in cm

17. texgap real, thickness of the expansion gap between the core and the reflector,
given in cm. Note that if this dimension is insufficient to accommodate thermal
expansion it will automatically be resized.

18. tbarl real, thickness of the core barrel, given in cm

19. trr real, thickness of the radial reflector, given in cm

20. tvcgap real, thickness of the coolant gap between the radial reflector and the
pressure vessel, given in cm

21. tves real, thickness of the pressure vessel, given in cm

22. zcore real, core height, given in cm

23. nrr integer, number of control drums

24. ddrum real, diameter of the control drums, given in cm

25. tdrgap real, thickness of the gap between the drum and the radial reflector, given
in cm

26. tdrpoi real, thickness of control drum poison, given in cm

27. angdrp real, angle transcended by the control drum poison, given in degrees

28. angrot real, angle at which the drums are rotated, given in degrees, 0 being the
most reactive (drums turned out), 180 being the least reactive (drums turned in)

29. blank line delimiter

30. naxcol integer, number of axial coolant regions. Coolant density changes axially
due to the large temperature and pressure gradients throughout the core. This
variable indicates how many regions should be used to represent that axial
variation. This number also dictates how many axial regions will be used for
axially varying thermal expansion.

31. tinlet real, coolant temperature at core inlet, given in K

32. toutlet real, coolant temperature at core outlet, given in K

33. pinlet real, coolant pressure at core inlet, given in MPa









34. pdrop real, coolant pressure drop through the core, given in MPa. If no
temperature input file is given then tinlet, toutlet, pinlet, and pdrop will be used to
determine the axially varying hydrogen coolant density using the ideal gas law.
Temperature will be assumed to increase from tinlet to toutlet with a cosine
distribution, while pressure is assumed to drop linearly from pinlet to
(pinlet pdrop) linearly.

35. tintt real, coolant temperature at tie tube inlet, given in K

36. toutt real, coolant temperature at tie tube outlet, given in K

37. pintt real, coolant pressure at tie tube inlet, given in MPa

38. pdroptt real, coolant pressure drop through the tie tube, given in MPa

39. tempref real, temperature of the radial reflector, given in K

40. zspgap real, thickness of the gap between the top of the core and the support
plate, given in cm

41. zsplat real, thickness of the support plate, given in cm

42. zttupm real, thickness of the tie tube up-flow manifold, given in cm

43. zbipl real, thickness of the bottom interface plate, given in cm

44. zttdnm real, thickness of the tie tube down-flow manifold, given in cm

45. ztipl real, thickness of the top interface plate, given in cm

46. zfcinm real, thickness of the fuel coolant inlet manifold, given in cm

47. zshld real, thickness of the internal shield, given in cm

48. dttipl real, diameter of tie tube down-flow through interface plates, given in cm

49. tchnl real, thickness of structure separating tie tube down-flow from tie tube
up-flow in interface plates, given in cm

50. ttopl real, thickness of tie tube up-flow region through interface plates, given in
cm

51. dfcpl real, diameter of fuel coolant flow through interface plates, given in cm

52. ttupm, pttupm two real variables, the tie tube up-flow manifold coolant
temperature given in K, and pressure given in MPa

53. ttdnm, pttdnm two real variables, the tie tube down-flow manifold coolant
temperature given in K, and pressure given in MPa









54. tfcinm, pfcinm two real variables, the fuel coolant manifold inlet temperature
given in K, and pressure given in MPa

55. zcham real, length of the exit chamber, given in cm

56. tcham real, thickness of the exit chamber, given in cm

57. ihom integer (0, 1, or 2), if ihom=0 the core region (fuel hexes and tie tubes) will
be modeled as one region and the radial reflector will be modeled using R-Z
geometry in the homogenized case, if ihom=l the core region will be homogenized
by row and the radial reflector will be modeled using R-Z geometry in the
homogenized case, if ihom=2 the the core region will be homogenized by row and
the radial reflector will be discretely modeled in the homogenized case.

58. ipar integer (0 or 1), ifipar=0 the tie tube hex will be homogenized in the
partially discrete case, if par=l the tie tube will be discretely modeled in the
partially discrete case.

59. ntal integer, number of axial tally regions. Only used in the cold, fully discrete
model and should be equal to naxcol in most cases.

60. talline character, type of tallies to be performed. "0" for none, "Peak" for peaking
factor tallies based on fission rate

61. itmpex integer, "0" for no thermal expansion, "1" for thermally expanded system

62. itmpxs integer, "0" for no temperature-dependent cross-sections, "1" for
temperature-dependent cross-sections

63. blank line delimiter

64. marr(0) character, fuel material identifier. The following entries make up the
material array, marr. This array is filled with character identifiers corresponding to
identifiers found for each MCNPX material in the matcards file, which will be
discussed shortly.

65. marr(l) character, fuel coating identifier

66. marr(2) character, tie tube structure identifer

67. marr(3) character, tie tube moderator identifier

68. marr(4) character, tie tube insulation identifier

69. marr(5) character, tie tube matrix identifier

70. marr(6) character, slat material identifier

71. marr(7) character, core barrel identifier









72. marr(8) character, radial reflector identifier

73. marr(9) character, drum poison identifier

74. marr(10) character, pressure vessel identifier

75. marr(1 1) character, coolant identifier

76. marr(13) character, support plates identifier

77. marr(14) character, shield material identifier

78. marr(15) character, chamber identifier

79. blank line delimiter

80. nacc integer, number of additional scenarios to be generated. This option allows
one to produce multiple MCNPX decks representing various conditions with a
single execution of NTRgen. If nacc=0 the input file stops at this line. If nacc>0,
then the following nine variables must be supplied for each of the additional
scenarios:

81. dcomm character, a text description of the scenario being described. The first
letter given will be the character identifier for this scenario. For example, if
dcomm is given as "b drums at 90 deg" and the input file is called test.inp, the
detailed MCNPX deck will be named testb.

82. talline same as talline described at line 60, but applied to the additional scenario

83. angrot same as angrot described at line 28, but applied to the additional scenario

84. itmpex same as itmpex described at line 61, but applied to the additional scenario

85. itmpxs same as itmpex described at line 62, but applied to the additional scenario

86. marr(17) character, identifier for material to fill in-core coolant channels

87. marr(18) character, identifier for material to fill vessel coolant channel

88. marr(19) character, identifier for material to fill expansion gap and control drum
gap

89. marr(20) character, identifier for material surrounding the reactor



















0 *
SA B

Figure 4-3. Core periphery. A) 2 rows cut at edge. B) 3 rows cut at edge.

Other required input files

The other input files required for execution ofNTRgen are the matcards and

cellcards files. These input files rarely need to be altered when producing an NTR

design. The cellcards file provides the basic framework of the MCNPX cell cards (an

example cellcards file is given in Appendix B). Where a standard MCNPX cell card

would have a material number and density, however, the cellcards file has an NTRgen

cell identifier indicating what type of cell the card represents. Table 4-1 gives a list of

valid cell identifiers in cellcards as well as which element in the material array

corresponds to that identifier. Note that not all cell types can be filled with a void, and

that some of the material regions can be altered using the nacc option on the primary

input file.

The matcards file contains the material cards to be used in generating the MCNPX

decks (an example matcards file is given in Appendix C). An NTRgen identifier must

precede each material card. A sample NTRgen identifier is given below:

c [Be/1.81] Be TD=1.85/98%=1.81 CTE[7.0,.,,0.,.]









Table 4-1. Valid cell identifiers in cellcards
Identifier Material array Description
Fuelmat 0 Fuel
Fuelcot 1 Coating between fuel and coolant
Fuelout 1 Coating on outside of fuel hex
TTstrui 2 Inner tie tube structure
TTstruo 2 Outer tie tube structure
TTmod 3 Tie tube moderator
TTinsu 4 Tie tube insulation
TTmatrx 5 Tie tube matrix
Slatmat 6 Inner reflector slats
Barrel 7 Core barrel
RRref 8 Radial reflector and control drum meat
RRpois 9 Control drum poison
Vessel 10 Outer pressure vessel
Fuelflw 11 or 17* Fuel coolant channels**
Slatflw 11 or 17* Slat coolant channels**
Coregap 19 Gap between reflector slats and core barrel **
RRgap 19 Gap between control drum and radial reflector **
TTflowi 11 or 17* Inner tie tube down-flow **
TTflowo 11 or 17* Outer tie tube up-flow **
Vescool 12 or 18* Vessel coolant **
TTDn 11 Tie tube down-flow coolant manifold
TTUp 11 Tie tube up-flow coolant manifold
FCMan 11 Fuel coolant manifold
FCCham 11 Fuel coolant exit chamber
Plate 13 Interface plates
Shield 14 Internal shield
Extcore 20 Exterior to core**
Corelat 0 Core lattice, calls a lattice filling subroutine
0 0 Void
*For the first case generated the first material array entry is used, for subsequent cases the
second material array entry is used
**Void may be placed in these cells

The first character must be "c" followed by a space (thus the NTRgen identifier

becomes a comment in the MCNPX deck). The character identifier and the density (in

g/cc) are placed inside brackets, separated by "/", in this case Be at 1.81 g/cc. The

character identifier can be up to 7 characters long and corresponds to the identifier filled

in the material array of the primary input file as discussed in the previous section. If

thermal expansion is to be performed using this material, the coefficients must be entered

inside brackets preceded by the characters "CTE". The four values in brackets, [a,b,c,d],









where a, b, c, and d are real values, give coefficient of thermal expansion, a ,according to

the following correlation, where Tis temperature given in Kelvin:

a(T)=(a+b.T+c.T2 +d3).10-6

The CTE information is optional, and need only be provided for the fuel and

reflector meat as these materials are assumed to dictate all thermal expansion. Note that

the other characters in the identifier are comments which do not affect NTRgen.

Optional input files

The temperature file (xxx.tmp) gives an axial profile of the core temperature and

fuel coolant density. A sample temperature file is given in Appendix D. Each line of the

temperature file simply consists of a temperature given in Kelvin and a fuel coolant

density given in mg/cc. The core inlet is listed on the first line, and the number of entries

must equal the number of axial coolant levels being considered (naxcol, line 30 of the

primary input file). If no temperature file is provided, core temperature will be assumed

to increase following a cosine distribution, where the core inlet temperature and outlet

temperature given on the primary input file (tinlet and toutlet, lines 32 and 33 of the

primary input file). In the absence of a temperature file, fuel coolant density is estimated

using the ideal gas law, where pressure drops linearly from inlet to outlet based on the

given inlet pressure and core pressure drop (pinlet and pdrop, lines 34 and 35 of the

primary input file).

The other optional input file is the zone map (xxx.zon) which tells NTRgen what

the enrichment of each fuel hex should be to reduce radial peaking. A zone map is

produced by NTRfilter based on tallies written by NTRgen and executed by MCNPX. A

sample zone map is given in Appendix E. The first entry in the zone map indicates how









many zones are being described in the map (integer variable named izlim, 10 for the case

given in Appendix E). Following this entry are the enrichments to be implemented in the

map. The number of enrichments listed should be equal to izlim, the first entry. NTRgen

uses this initial data to create the appropriate MCNPX fuel material cards for the various

enrichments. Following the initial data block in the zone file is the enrichment map. The

enrichment map consists of the MCNPX hex indices for each fuel element, followed by

the peaking factor and the enrichment calculated by NTRfilter to flatten the radial fission

rate distribution and reduce radial peaking factors (this calculation is discussed in the

following section). When NTRgen is filling in the core lattice, it searches the zone file

for the appropriate enrichment and applies that enrichment to the corresponding hex. A

sample zone file entry is given below:

15 -20 1.12 0.7093

In this entry, the MCNPX lattice indices are (15,-20), the peaking factor in this hex is

1.12, and the hex should be filled with 70.93% enriched fuel.

NTRgen processes the information in each of the input files and produces MCNPX

decks. A sample MCNPX deck which was generated by NTRgen is provided in

Appendix F.

NTRFilter

The zone file is produced using NTRFilter, a filter program which sorts through

MCNPX tally data to produce an enrichment map that minimizes the radial peaking

factor. NTRfilter analyzes an MCNPX metal file, which contains a concise summary of

tally data produced during the run. The metal file also contains a comment line which is

inserted by NTRgen to instruct NTRfilter as to how many fuel elements and how many

axial levels are represented.









A sample comment line is reproduced below:

Limit: 23 Cold PD 10

This comment indicates the maximum index of any tallied element is 23, and that

the case run was with a cold, partially discrete geometry using 10 axial levels. Since this

comment is automatically inserted by NTRgen and read by NTRfilter, the user need not

interact with the contents of the metal file. NTRfilter will produce a hex peaking factor

(HPFmax), defined as the maximum fission rate in any fuel hex divided by the fission rate

in an average fuel hex, as well as the indices of this maximum fission rate hex. NTRfilter

will produce a hex minimum factor (HPFmin), defined as the minimum fission rate in any

fuel hex divided by the fission rate in an average fuel hex, as well as the indices of this

minimum fission rate hex. NTRfilter will also produce a total peaking factor (TPF),

defined as the maximum fission rate in any fuel segment divided by the fission rate in an

average fuel segment, as well as the indices of this maximum fission rate segment.

If the metal file being analyzed was produced using a zone map (generated from a

previous run) this previous zone map should be renamed zones.old before executing

NTRfilter if a new zone enrichment map is desired. To rezone the core, NTRfilter first

takes the tally value for each fuel segment and divides by the fuel enrichment in that

segment (found in zones.old, if present) to arrive at an approximation of what the fission

rate distribution would look like if the core enrichment were uniform. This technique

assumes that fission rate is directly proportional to fuel enrichment, and that the flux

distribution is unperturbed by altering fuel enrichment. While these assumptions are

invalid when starting with either an unzoned or poorly zoned enrichment scheme, as the

iterations progress these assumptions become valid and one can arrive at an optimum









enrichment zoning. In this equation, UPFmn, is the unzoned hex minimum factor and

UPFmax is the unzoned hex peaking factor. These quantities are similar to HPFmax and

HPFmin, with the difference being that the effect of varying enrichment has been removed

from UPFmax and UPFmin by dividing out fuel enrichment in each hex as described. NZ is

the total number of zones desired, i is the individual zone number (between 1 and NZ),

and UPFbound(i) is the upper bound of zone i. Thus, hexes with UPF between

UPFbound(i-1) and UPFbound(i) would fall into zone i.


(UPFm J
UPFbOUfd (i) = UPFmin UPF 2m"n


The representative unzoned peaking factor of each zone, UPFmid(i) is given below.


UPFm Nz
UPFmld (i) = UPFm ax
dmmn UP^mi)


The appropriate enrichment for each zone is calculated using the following equation,

where enrich(i) is the enrichment for each zone and enrmax is the maximum enrichment to

be used. In this scheme, those zones with the highest unzoned peaking factor are

assigned the lowest enrichment which is appropriate given the assumption that those

regions with a higher fission rate should require less enrichment to achieve a uniform

fission rate distribution.

L UPFmrd(1)2
enrich(i) = enrmax UPFd(i)
UPFmnd

An example zone structure is given in Table 4-2, where the unzoned hex peaking

factor is 1.3660, the unzoned hex minimum factor is 0.5344, the maximum enrichment to

be used is 93% and 3 zones are desired.









Table 4-2. A sample NTRfilter zone structure.
Zone Lower UPF bound Upper UPF bound Representative Enrichment
UPF
1 0.7101 0.9637 0.8272 93.00%
2 0.9637 1.3079 1.1227 68.52%
3 1.3079 1.7751 1.5237 50.49%

Table 4-3 goes through a sample calculation using the zoning scheme from Table

4-2. New fission rate is calculated by multiplying the old fission rate by the ratio of the

new enrichment to the old enrichment. For example, region 5 gives 0.95*(68.52/56) =

1.1624. In this example the original enrichment zoning is quite poor, considering that

some drastic changes must be made (i.e., enrichment in region 2 goes from 93% to

50.49%, enrichment in region 6 goes from 80% to 50.49%). Changes such as these limit

the validity of the stated assumptions, but as the iterations progress and new enrichment

schemes are implemented the assumptions will become valid and one will approach the

optimized enrichment map.

Table 4-3. A sample NTRfilter rezoning calculation.
Region Fisson Peaking Enrich. Unzoned Zone New New New
rate factor peaking enrich, fission peaking
factor rate factor
1 1.1 0.7811 93% 0.8399 1 93.00% 1.1000 0.9562
2 2.3 1.6331 93% 1.7561 3 50.49% 1.2486 1.0854
3 1.4 0.9941 56% 1.7751 3 50.49% 1.2622 1.0972
4 0.8 0.5680 80% 0.7101 1 93.00% 0.9300 0.8084
5 0.95 0.6476 56% 1.2046 2 68.52% 1.1624 1.0105
6 1.9 1.3491 80% 1.6864 3 50.49% 1.1991 1.0423

Figure 4-4 gives a general description of the interaction between NTRgen, MCNPX

and NTRfilter.






32



cellcards


9 use previous zone--
file (if present)
I









X metal file


use previous zone
--' file (if present) I


I--------........


Figure 4-4. Outline of the NTRgen iterative procedure.














CHAPTER 5
RESULTS

By employing NTRgen and NTRfilter in concert, one can start with an unzoned

core and systematically arrive at an enrichment scheme which suits the reactor layout of

interest. The five core layouts that were considered in this study come from the

polynomials generated by TMSS which were presented at the end of Chapter 2. These

initial runs are for unzoned cores with a uniform enrichment of 93%.

Unzoned Core Calculations

The partially homogenized (PH) cases generally ran in about 30% of the runtime of

the fully discrete (FD) models (average of about 3.6 minutes for partially homogenized

vs. 11.5 for the fully discrete). All computation times listed in this document are for a

2.4-GHz Optiron processor. Results from the initial runs are given in Figures 5-1 through

5-5. The numbers in parentheses in the figure titles are the number of rows of modules

and the number of rows cut at the edge given in entry 12 of the primary input file, as

described in the primary input file section of Chapter 4. A core with 8 total rows of

hexes and 2 rows cut at the edge, for example, would result in 906 fuel hexes. A second-

order polynomial was fit to each of these curves to determine which core dimensions will

yield a beginning-of-life expanded k-eff of about 1.03. The target value of 1.03 was

chosen because the subsequent rezoning will necessarily reduce the average enrichment

of the core, as 93% is the maximum enrichment to be loaded in any hex. These initial

runs were run to standard deviation of about 0.003, as they are only used to determine











dimensions of the core with which to begin zoning. No consideration was given to


shutdown conditions at this point in the process.


Once the dimensions for a core expected to yield a BOL expanded k-eff of about


1.03 were determined, that case was run to higher fidelity with fission rate tallies to


determine the hex peaking factor in the core. The dimensions of these cases are given in


Table 5-1, while the criticality results for these unzoned cores are given in Table 5-2. In


Table 5-2, the standard deviation is reported in parentheses below the criticality result.


Note that in all tables and figures "hot" refers to the MCNPX run employing the


thermally expanded geometry and does not account for temperature dependence in the


cross sections.


906 Fuel Hexes (8,2)

1.10000


1.05000 IE


1.00000
0 BOL Cold PH
BOL Hot PH
S050 A Shutdown PH
S.9 BOL Cold FD
x BOL Hot FD
I *Shutdown FD
0.90000


0.85000


0.80000
130.00 135.00 140.00 145.00 150.00 155.00 160.00 165.00
Height (cm)

Figure 5-1. Comparison of initial MCNPX runs for 906 fuel hex case.













1194 Fuel Hexes (9,2)


1.15000



1.10000



1.05000



S1.00000



0.95000



0.90000



0.85000


95.00 100.00 105.00 110.00 115.00 120.00


Height (cm)

Figure 5-2. Comparison of initial MCNPX runs for 1194 fuel hex case.


1518 Fuel Hexes (10,2)


80.00 85.00
Height (cm)


90.00


* BOL Cold PH
* BOL Hot PH
A Shutdown PH
BOL Cold FD
x BOL Hot FD
* Shutdown FD


95.00


Figure 5-3. Comparison of initial MCNPX runs for 1518 fuel hex case.


* BOL Cold PH
* BOL Hot PH
A Shutdown PH
BOL Cold FD
x BOL Hot FD
* Shutdown FD


I

II




I

- I


I


90.00


1.10000




1.05000




1.00000




0.95000




0.90000




0.85000
7(


I



+



i


i


i4


0.00


75.00













1410 Fuel Hexes (10,3)


1.10000




1.05000




1.00000




0.95000




0.90000




0.85000
75


95.00


* BOL Cold PH
* BOL Hot PH
A Shutdown PH
BOL Cold FD
x BOL Hot FD
*Shutdown FD


100.00


Height (cm)

Figure 5-4. Comparison of initial MCNPX runs for 1410 fuel hex case.


1770 Fuel Hexes (11,3)


* BOL Cold PH
* BOL Hot PH
A Shutdown PH
BOL Cold FD
* BOL Hot FD
*Shutdown FD


62.00 64.00 66.00 68.00 70.00 72.00 74.00 76.00 78.00 80.00
Height (cm)


Figure 5-5. Comparison of initial MCNPX runs for 1770 fuel hex case.


90.00


I
I
I



Ib
I

I


II


5.00


80.00


85.00


1.05000





1.00000





9 0.95000





0.90000


0.85000
6(


I
^


I I












I
i
T
oJ


0.00









Table 5-1. Dimensions of considered NTR cores.
Fuel Total Rows Height Pitch Cool RR Outer Fuel Mass
hexes rows cut (cm) (cm) diam thick diam. Vol. (kg)
(cm) (cm) (cm) (cc)
906 8 2 155.73 1.949 0.2471 8.00 71.00 326114 2729.0
1194 9 2 106.28 1.895 0.2108 8.00 79.00 302210 2324.9
1518 10 2 84.50 1.905 0.1869 8.00 89.00 327850 2361.3
1410 10 3 89.59 1.890 0.1963 8.00 86.00 311900 2315.3
1770 11 3 76.14 1.963 0.1744 8.00 99.00 379450 2640.5

Table 5-2. Criticality results for unzoned NTR cores.
Fuel hexes BOL cold BOL cold BOL expnd BOL hot Shutdown Shutdown
FD k-eff PH k-eff FD k-eff PH k-eff FD k-eff PH k-eff
906 1.04438 1.04502 1.03364 1.03428 0.93441 0.93664
(0.00060) (0.00059) (0.00060) (0.00059) (0.00057) (0.00059)
1194 1.05108 1.05227 1.03899 1.03831 0.97241 0.97312
(0.00061) (0.00058) (0.00060) (0.00057) (0.00061) (0.00058)
1518 1.04366 1.04493 1.02996 1.03128 0.98942 0.99088
(0.00053) (0.00061) (0.00057) (0.00059) (0.00059) (0.00059)
1410 1.05088 1.05056 1.03707 1.03825 0.98989 0.99132
(0.00062) (0.00056) (0.00056) (0.00061) (0.00056) (0.00058)
1770 1.04373 1.04523 1.02955 1.03191 1.00380 1.00409
(0.00060) (0.00056) (0.00058) (0.00057) (0.00061) (0.00062)

Table 5-3 gives a comparison of the criticality results given in Table 5-2. For each

condition, the difference between partially homogenized and fully discrete k-eff are

given. Also provided in this table are the fully discrete and partially homogenized

runtimes for each case. For example, in the 906 fuel hex case the BOL cold fully discrete

model took 1370 minutes whereas the BOL cold partially homogenized model took 596

minutes. The hex peaking factor for each one of these unzoned cores is given in Table 5-

4 (the standard deviation of each peaking factor is reported in parentheses). Note that the

shutdown criticality runs took dramatically less time because no peaking factor tallies

were performed. Figures 5-6 through 5-10 are a comparison of the fission rate

distribution in the each of the core layouts using cold and expanded geometry with both

fully discrete and partially homogenized models. In addition to the average fission rate at

each radial location are the maximum and minimum fission rates (the dotted lines above









and below each solid line). Note that the maximum relative fission rate in each one of the

curves corresponds to the peaking factors found in Table 5-4. In many cases, the k-eff

and hex peaking factor determined using the partially homogenized model is within the

standard deviation of the fully discrete model. In some cases the difference is greater

than the standard deviation, but this is to be expected due to the both the statistical nature

of the simulation and the fact that some geometrical approximations have been made.

Given the strong general agreement between fully discrete and partially homogenized

models in both criticality and peaking factor results (Tables 5-3 and 5-4) and the

agreement in fission rate distribution (Figures 5-6 through 5-10) it becomes clear that the

advantage in runtime using the partially homogenized models (a reduction of 50% or

more in some tallied cases) outweighs any loss in accuracy.

Table 5-3. Criticality and runtime comparison for unzoned NTR cores.
Fuel hexes BOL cold BOL hot Shutdown BOL cold BOL hot Shutdown
k-eff diff, k-eff diff, k-eff diff, runtimes runtimes runtimes
PH FD PH FD PH FD FD & PH FD & PH FD & PH
(minutes) (minutes) (minutes)
906 0.00064 0.00064 0.00223 1370, 596 1358, 585 195, 49
1194 0.00119 -0.00068 0.00071 1754, 775 1526, 796 182, 51
1518 0.00127 0.00132 0.00146 1966, 1009 1932, 1000 170, 53
1410 -0.00032 0.00118 0.00143 1824,978 1817,873 173,53
1770 0.00150 0.00236 0.00029 1999, 1179 2249, 1176 161,52

Table 5-4. Hex peaking factors for unzoned NTR cores.
Fuel hexes BOL cold FD BOL cold PH BOL hot FD BOL hot PH
906 1.65400 (0.00613) 1.65628 (0.00615) 1.67678 (0.00608) 1.67140 (0.00612)
1194 1.65540 (0.00704) 1.63262 (0.00686) 1.62037 (0.00691) 1.63005 (0.00688)
1518 1.54465 (0.00763) 1.53860 (0.00765) 1.56310 (0.00765) 1.56745 (0.00768)
1410 1.74392 (0.00782) 1.73470 (0.00781) 1.75460 (0.00789) 1.74926 (0.00803)
1770 1.64281 (0.00896) 1.66858 (0.00880) 1.72717 (0.00904) 1.69125 (0.00869)






















o 1.3

S1.2
1 2----------------.---------------/ /
a) i
1.1




0.9 -


0.8
0 5 10 15 20 25 30
Distance from center (cm)

Figure 5-6. Relative fission rate in the unzoned 906 fuel hex core.


1.7

1.6


1.5

1.4


1.3

A













Distance from center (cm)

Figure 5-7. Relative fission rate in the unzoned 1194 fuel hex core.
.1 ^----------------------------? -


0 ";











Figure 5-7. Relative fission rate in the unzoned 1194 fuel hex core.


-Cold FD
Hot FD
-Cold PH
-Hot PH


























-Cold FD
Hot FD
-Cold PH
-Hot PH


























o. 1.2
(A

| 1.1
F1S
n-:


0 5 10 15 20 25 30 35 40 45
Distance from center (cm)

Figure 5-8. Relative fission rate in the unzoned 1518 fuel hex core.





1.7-
./


1.5




2 1.3















0.7
0 5 10 15 20 25 30 35 40
Distance from center (cm)

Figure 5-9. Relative fission rate in the unzoned 1410 fuel hex core.


-Cold FD

Hot FD

-Cold PH

-Hot PH


-Cold FD

Hot FD

-Cold PH

-Hot PH



















S1.3 I -Cold FD
2 1.3
0 .Hot FD
S1.2 -Cold PH
-Hot PH
1.1



0.9

0.8 ----.---

0.7
0 5 10 15 20 25 30 35 40 45 50
Distance from center (cm)

Figure 5-10. Relative fission rate in the unzoned 1770 fuel hex core.

Zoning Calculations

Starting with the core layouts just described, three zoning iterations were

performed on each core in an effort to reduce the hex peaking factor. Each zoning

iteration consisted of running MCNPX to produce fission rate tallies, running NTRfilter

on the tally data to produce an enrichment zoning map, running NTRgen using this

zoning map to produce new MCNPX decks, then repeating the process. Ten enrichment

zones were employed for each iteration.

906 Fuel Hex Core

Criticality results for the 906 fuel hex core as a function of zoning iteration are

given in Table 5-5. The trend is as one would expect the largest drop in k-effis from

the unzoned core to the first zoning scheme. As the zoning iterations progress, the

assumptions used by NTRfilter in calculating the zoning scheme become more valid









(flux profile unchanged by rezoning, fission rate proportional to enrichment). A

description of each zoning scheme is given in Table 5-6. This table summarizes the

enrichment of each zone, and how many fuel hexes of each zone are present in the core.

Table 5-7 contains the hex peaking factor at each iteration. Table 5-8 lists the

computation times for the MCNPX runs. The radial fission rate distribution as a function

of zoning iteration is given in Figure 5-11. These fission rate distributions were

generated using the expanded, partially homogenized models. Note that the relative

fission rate given in Figure 5-11 does not correspond to the hex peaking factor listed in

Table 5-7. The key distinction is that the values found in Figure 5-11 are an average of

the fission rates of all fuel hexes at a particular radius, whereas the hex peaking factor

considers the maximum fission rate found in any individual fuel hex.

Table 5-5. Criticality results for 906 fuel hex core zoning iterations.
Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH Average
k-eff k-eff k-eff k-eff Enrichment
(%)
0 (unzoned) 1.04438 1.04502 1.03364 1.03428 93.00
(0.00060) (0.00059) (0.00060) (0.00059)
1 1.01539 1.01688 1.00552 1.00504 82.87
(0.00055) (0.00059) (0.00056) (0.00055)
2 1.00797 1.00995 0.99728 0.99776 79.85
(0.00056) (0.00060) (0.00059) (0.00058)
3 1.00741 1.00885 0.99657 0.99698 79.22
(0.00056) (0.00056) (0.00058) (0.00053)

Table 5-6. Enrichment zone description for 906 fuel hex core zoning iterations.
Zone Iteration 1 Iteration 2 Iteration 3
Enrich (%) # Enrich (%) # Enrich (%) #
1 93.00 256 93.00 260 93.00 274
2 86.85 258 85.34 230 85.07 209
3 81.10 190 78.30 159 77.81 159
4 75.73 70 71.85 119 71.17 114
5 70.72 32 65.93 16 65.10 19
6 66.04 30 60.50 44 59.54 41
7 61.67 21 55.51 18 54.46 24
8 57.59 13 50.94 24 49.82 30
9 53.78 16 46.74 14 45.57 14
10 50.22 20 42.89 22 41.68 22












Table 5-7. Hex peaking factor for 906 fuel hex core zoning iterations.
Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH
0 1.65400 (0.00613) 1.65628 (0.00615) 1.67680 (0.00608) 1.67140 (0.00612)
1 1.16916 (0.00441) 1.18487 (0.00442) 1.18695 (0.00439) 1.16607 (0.00428)
2 1.08512 (0.00403) 1.09498 (0.00388) 1.08938 (0.00388) 1.09765 (0.00384)
3 1.07997 (0.00395) 1.08485 (0.00325) 1.07836 (0.00393) 1.08618 (0.00402)


Table 5-8. Computation time for 906 fuel hex core zoning iterations.
Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH
(minutes) (minutes) (minutes) (minutes)
0 1370 596 1359 585
1 1356 591 1435 645
2 1362 616 1441 638
3 1391 621 1399 620


1.6


1.5


1.4


| 1.3

.0
A 1)


w
]c
0)
a,


1.1





0.9


- Unzoned
Zone 1
-Zone 2
-Zone 3


0 5 10 15 20 25 30 35
Distance from center (cm)

Figure 5-11. Relative fission rate in the 906 fuel hex core through zoning iterations.

Tables 5-5 through 5-8 and Figure 5-11 indicate that by the third zoning iteration


the criticality results, zoning scheme, and fission rate have approached the point that


subsequent zoning iterations would not produce significant enough perturbations to


justify the additional computation time. A radial view of the 906 fuel hex core with the









third zoning iteration is given in Figure 5-12. Notice that there is some asymmetry due to

statistical variations in the tallies. Figure 5-13 gives a more detailed view of the zone

layout indicating how the enrichment zones (zones 1-10, given in Table 5-6) are

distributed in the core.








I* .6^ ,.
...-( } .O




















Figure 5-12. Radial layout of zoned 906 fuel hex core.
from 1.63005 to 1.11039 using the expanded partially homogenized model.
.1: i

0 ., "[ "" 'I T .^' i ^^rT''- ^ ^ '"'- i








Figure 5-12. Radial layout of zoned 906 fuel hex core.
r<^',TJ.B.iTiiiL* .AI" -rB.. s-'
*'^ ^-rr^.^^ (r. /

( .aj~.^ii.~^~j^

























from 1.63005 to 1.11039 using the expanded partially homogenized model.












"~Ij


Figure 5-13. Detailed view of enrichment zoning in 906 fuel hex core.

Table 5-9. Criticality results for 1194 fuel hex core zoning iterations.
Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH Average
k-eff k-eff k-eff k-eff Enrichment
(%)
0 (unzoned) 1.05108 1.05227 1.03899 1.03831 93.00
(0.00061) (0.00058) (0.00060) (0.00057)
1 1.01694 1.01572 1.00404 1.00422 81.22
(0.00061) (0.00058) (0.00059) (0.00057)
2 1.00944 1.00851 0.99552 0.99588 78.25
(0.00057) (0.00057) (0.00061) (0.00058)
3 1.00533 1.00504 0.99309 0.99404 77.24
(0.00060) (0.00059) (0.00059) (0.00059)

The radial fission rate at each zoning iteration is given in Figure 5-14. The trend

observed is similar to that found for the 906 fuel hex core. There is a dramatic

improvement in the uniformity of fission rate from the unzoned core to the first zoning

scheme. Subsequent iterations are less dramatic, with the third zoning iteration providing

a nearly flat radial fission rate distribution.











Table 5-10. Enrichment zone description for 1194 fuel hex core zoning iterations.
Zone Iteration 1 Iteration 2 Iteration 3
Enrich (%) # Enrich (%) # Enrich (%) #
1 93.00 250 93.00 307 93.00 324
2 86.91 330 85.38 256 85.17 228
3 81.22 209 78.38 178 77.99 160
4 75.90 158 71.95 170 71.42 163
5 70.93 127 66.05 128 65.41 122
6 66.29 31 60.64 63 59.90 87
7 61.95 31 55.67 24 54.85 32
8 57.89 10 51.11 30 50.23 32
9 54.10 25 46.92 15 46.00 16
10 50.56 23 43.07 23 42.13 30

Table 5-11. Hex peaking factor for 1194 fuel hex core zoning iterations.
Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH
0 1.65540 (0.00704) 1.63262 (0.00686) 1.62037 (0.00691) 1.63005 (0.00688)
1 1.17338 (0.00510) 1.18481 (0.00498) 1.17969 (0.00506) 1.17111 (0.00500)
2 1.10349 (0.00464) 1.10615 (0.00459) 1.10651 (0.00366) 1.11001 (0.00457)
3 1.10241 (0.00473) 1.09559 (0.00446) 1.09288 (0.00366) 1.11039 (0.00466)

Table 5-12. Computation time for 1194 fuel hex core zoning iterations.
Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH
(minutes) (minutes) (minutes) (minutes)
0 1754 775 1526 796
1 1667 810 1689 805
2 1745 822 1694 811
3 1723 826 1657 825

1518 Fuel Hex Core

Criticality data for the 1518 fuel hex core is given in Table 5-13. Tables 5-14

though 5-16 contain enrichment zone data, hex peaking factors, and computation times.

Again, the zoning method performs well, reducing the hex peaking factor from 1.56745

to 1.10907 in three iterations. Figure 5-15 shows radial fission rate for the 1518 fuel hex


core.











16








0
.12

S1 2 -
i 1 --- -----------------




09 -

08
0 5 10 15 20 25
Distance from center (cm)


Figure 5-14

Table 5-13.


-Unzoned
Zone 1
-Zone 2
-Zone 3


30 35 40


Relative fission rate in the 1194 fuel hex core through zoning iterations.

Criticality results for 1518 fuel hex core zoning iterations.


Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH Average
k-eff k-eff k-eff k-eff Enrichment
(%)
0 (unzoned) 1.04366 1.04493 1.02996 1.03128 93.00
(0.00053) (0.00061) (0.00057) (0.00059)
1 1.00151 1.00096 0.98712 0.98857 79.27
(0.00061) (0.00057) (0.00058) (0.00058)
2 0.98969 0.98857 0.97463 0.97627 75.29
(0.00054) (0.00060) (0.00057) (0.00056)
3 0.98442 0.98533 0.97255 0.97302 73.99
(0.00058) (0.00057) (0.00059) (0.00056)

Table 5-14. Enrichment zone description for 1518 fuel hex core zoning iterations.
Zone Iteration 1 Iteration 2 Iteration 3
Enrich (%) # Enrich (%) # Enrich (%) #
1 93.00 272 93.00 292 93.00 323
2 87.04 345 85.55 314 85.38 266
3 81.45 236 78.71 197 78.38 177
4 76.23 178 72.40 183 71.96 177
5 71.34 179 66.61 145 66.06 134
6 66.77 188 61.28 170 60.64 138
7 62.49 45 56.37 122 55.67 143
8 58.48 16 51.86 36 51.11 98
9 54.73 35 47.71 28 46.92 26
10 51.22 24 43.89 31 43.07 36











Hex peaking factor for 1518 fuel hex core zoning iterations.
BOL cold FD BOL cold PH BOL hot FD E
1.54465 (0.00763) 1.53860 (0.00765) 1.56310 (0.00765) 1
1.16592 (0.00419) 1.18619 (0.00448) 1.18589 (0.00591) 1
1.12827 (0.00418) 1.12928 (0.00415) 1.12504 (0.00540) 1
1.12862 (0.00424) 1.11567 (0.00408) 1.10932 (0.00541) 1


1OL hot PH
.56745 (0.00768)
.18210 (0.00585)
.11116 (0.00417)
.10907 (0.00523)


Table 5-16. Computation time for 1518 fuel hex core zoning iterations.
Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH
(minutes) (minutes) (minutes) (minutes)
0 1966 1009 1932 1000
1 2027 1037 1963 1034
2 1932 993 2040 1076
3 1951 1004 1889 1093


-Unzoned
Zone 1
-Zone 2
-Zone 3


0 5 10 15 20 25 30 35 40 45
Distance from center (cm)


Figure 5-15. Relative fission rate in the 1518 fuel hex core through zoning iterations.

1410 Fuel Hex Core

Table 5-9 gives criticality results for the 1410 fuel hex core, while Table 5-10 gives

the enrichment zone descriptions. Table 5-11 contains the hex peaking factors and Table

5-12 lists the computation times. Hex peaking factor in the 1410 core was reduced from


Table 5-15
Iteration
0
1
2
3









1.74926 to 1.13030 in the expanded partially homogenized model after three iterations.

The radial fission rate distribution is shown in Figure 5-16.


Table 5-17.


Criticality results for 1410 fuel hex core zoning iterations.


Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH Average
k-eff k-eff k-eff k-eff Enrichment
(%)
0 (unzoned) 1.05088 1.05056 1.03707 1.03825 93.00
(0.00062) (0.00056) (0.00056) (0.00061)
1 1.00459 1.00634 0.99299 0.99332 78.00
(0.00060) (0.00060) (0.00058) (0.00056)
2 0.99449 0.99550 0.98248 0.98323 74.26
(0.00058) (0.00059) (0.00059) (0.00060)
3 0.98851 0.99012 0.97675 0.97918 72.40
(0.00059) (0.00059) (0.00056) (0.00055)

Table 5-18. Enrichment zone description for 1410 fuel hex core zoning iterations.
Zone Iteration 1 Iteration 2 Iteration 3
Enrich (%) # Enrich (%) # Enrich (%) #
1 93.00 159 93.00 198 93.00 178
2 85.89 408 84.17 376 83.80 375
3 79.32 290 76.18 251 75.50 219
4 73.25 218 68.95 192 68.03 187
5 67.65 212 62.41 193 61.30 186
6 62.48 46 56.49 104 55.23 154
7 57.70 23 51.12 36 49.76 51
8 53.29 14 46.27 21 44.84 17
9 49.21 21 41.88 19 40.40 20
10 45.45 19 37.97 20 36.40 23

Table 5-19. Hex peaking factor for 1410 fuel hex core zoning iterations.
Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH
0 1.74392 (0.00782) 1.73470 (0.00781) 1.75460 (0.00789) 1.74926 (0.00803)
1 1.19466 (0.00572) 1.17743 (0.00541) 1.20741 (0.00547) 1.19103 (0.00533)
2 1.12627 (0.00410) 1.14848 (0.00397) 1.14219 (0.00413) 1.11824 (0.00398)
3 1.10699 (0.00396) 1.10449 (0.00404) 1.13613 (0.00535) 1.13030 (0.00494)

Table 5-20. Computation time for 1410 fuel hex core zoning iterations.
Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH
(minutes) (minutes) (minutes) (minutes)
0 1824 978 1817 873
1 1939 1000 1757 914
2 2024 917 1773 950
3 1885 957 1826 964



















S1.3 Unzoned
SZone 1
A 1.2- -Zone 2
S--Zone 3
1.1




0.9


0.8
0 5 10 15 20 25 30 35 40
Distance from center (cm)

Figure 5-16. Relative fission rate in the 1410 fuel hex core through zoning iterations.

1770 Fuel Hex Core

Tables 5-21 though 5-24 contain enrichment zone data, hex peaking factors, and

computation times for the 1770 fuel hex core. The decreased computation times listed

for the third iteration in Table 5-24 arise from fewer particle histories being tracked

(hence the larger standard deviations for the third iteration in Tables 5-21 and 5-23). The

relative fission rate distribution in this core is presented in Figure 5-17.

Table 5-21. Criticality results for 1770 fuel hex core zoning iterations.
Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH Average
k-eff k-eff k-eff k-eff Enrichment
(%)
0 (unzoned) 1.04373 1.04523 1.02955 1.03191 93.00
(0.00060) (0.00056) (0.00058) (0.00057)
1 0.98912 0.98997 0.97544 0.97680 75.79
(0.00059) (0.00056) (0.00059) (0.00056)
2 0.97256 0.97253 0.95823 0.95890 70.31
(0.00060) (0.00058) (0.00060) (0.00060)
3 0.96462 0.96455 0.95188 0.95254 67.95
(0.00091) (0.00091) (0.00092) (0.00091)











Table 5-22. Enrichment zone description for 1770 fuel hex core zoning iterations.
Zone Iteration 1 Iteration 2 Iteration 3
Enrich (%) # Enrich (%) # Enrich (%) #
1 93.00 220 93.00 174 93.00 175
2 85.91 422 84.07 419 83.59 380
3 79.36 275 76.01 269 75.14 259
4 73.31 224 68.71 199 67.53 202
5 67.72 249 62.12 199 60.70 187
6 62.56 246 56.15 238 54.56 200
7 57.79 75 50.77 205 49.04 199
8 53.38 20 45.89 23 44.08 122
9 49.31 19 41.49 21 39.62 22
10 45.55 20 37.51 23 35.61 24

Table 5-23. Hex peaking factor for 1770 fuel hex core zoning iterations.
Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH
0 1.64281 (0.00896) 1.66858 (0.00880) 1.72717 (0.00904) 1.69125 (0.00869)
1 1.20616 (0.00481) 1.19692 (0.00648) 1.18488 (0.00469) 1.19305 (0.00465)
2 1.14281 (0.00450) 1.15529 (0.00448) 1.14676 (0.00578) 1.13789 (0.00462)
3 1.15388 (0.00995) 1.12414 (0.00696) 1.15586 (0.00979) 1.15675 (0.00750)

Table 5-24. Computation time for 1770 fuel hex core zoning iterations.
Iteration BOL cold FD BOL cold PH BOL hot FD BOL hot PH
(minutes) (minutes) (minutes) (minutes)
0 1999 1179 2249 1176
1 2187 1244 2155 1175
2 2156 1240 2259 1222
3 848 489 887 489

Note that the final peaking factor (1.15675 in the expanded partially homogenized

model) in this core is the highest found out of all considered core layouts. One reason is

that this core is larger (radially) than the others. The effective radius of the core is the

radius of an equivalent circle having the same area as all the tie tubes and fuel hexes

combined. The effective radius of the 1770 fuel hex core is 93.67 cm, whereas the next

largest core is the 1518 fuel hex core with an effective radius of 84.18 cm. The larger

radius implies that more fluctuations in the radial neutron flux distribution may occur

from iteration to iteration, thus taking more time for the assumptions made by NTRfilter

during rezoning to become valid. The implicit assumption in this statement is that the











neutron mean free path is the same for each of the cores. Each of the cores contains the

same materials in roughly the same quantities, so one would expect the neutron spectrum

(and therefore the mean free path) to be similar as well.


1.5


1.4


1.3

S ~- Unzoned
1.2 f- Zone 1
S/ --Zone 2
1.1 -Zone 3
11





0.9


0.8
0 5 10 15 20 25 30 35 40 45 50
Distance from center (cm)

Figure 5-17. Relative fission rate in the 1770 fuel hex core through zoning iterations.

Final Designs

The previous calculations resulted in the production of an enrichment zoning map

specific to each core layout. These zoning maps were then used to produce a neutronic

core design that met both the TMSS criteria given at the end of Chapter 2 (following the

polynomials for coolant diameter and hex pitch) and the criticality conditions at the end

of Chapter 1 (expanded BOL k-eff greater than 1.025, shutdown k-eff less than 0.985).

Again, one could perform the iteration procedure without the TMSS polynomials and

arrive at a zoned core design. The TMSS analysis serves to ensure that temperature and

pressure drop limits are consistent from design to design, giving a more realistic picture







53


of how the designs compare to one another. Similar curves to those presented in Figures

5-1 through 5-5 were generated for the zoned cores. The parameter of interest is

expanded k-eff due to the criticality criteria, and this value is given for each of the core

layouts as a function of core height in Figure 5-18. By interpolating from this figure, one

can determine the appropriate core size for each layout and zoning scheme such that

expanded k-eff is greater than 1.025.


1.08000

1.06000

1.04000

1.02000

1.00000 -*-906
I/ ---1194
S0.98000 1518

0.96000 -1770

0.94000

0.92000

0.90000

0.88000
60.00 80.00 100.00 120.00 140.00 160.00 180.00
Core height (cm)

Figure 5-18. Expanded partially homogenized k-eff for zoned NTR cores.

Once the core size was determined, each design was run to higher fidelity using the

zoning enrichment map to determine its nuclear characteristics. The results of these

calculations are presented in Table 5-25.











Table 5-25. Dimensions and nuclear characteristics of final NTR designs.
Fuel hexes: 906 1194 1518 1410 1770
Hex pitch (cm) 2.050 2.022 2.170 2.090 2.431
Cool channel diam (cm) 0.2526 0.2133 0.1911 0.1970 0.1796
Core height (cm) 178.48 114.69 97.29 100.29 92.87
Effective diameter (cm) 69.99 79.25 95.89 89.01 116.00
Height/diameter 2.55 1.45 1.01 1.13 0.80
Fuel volume (cm3) 423119 382350 510735 442718 748387
Average enrichment (%) 78.72 77.07 73.60 71.55 64.16
Bumup (%) 1.2 1.4 1.1 1.3 0.9%
Reactor mass (kg) 3440.5 2855.2 3451.8 3181.9 4957.5

BOL cold FD k-eff 1.03797 1.03585 1.03596 1.03549 1.03509
(0.00079) (0.00074) (0.00069) (0.00072) (0.00072)
BOL hot FD k-eff 1.02446 1.02366 1.02529 1.02531 1.02386
(0.00071) (0.00070) (0.00074) (0.00069) (0.00069)
Shutdown FD k-eff 0.93613 0.96309 0.98887 0.98260 1.00536
(0.00071) (0.00074) (0.00073) (0.00074) (0.00072)
BOL cold PH k-eff 1.03796 1.03736 1.03763 1.03708 1.03609
(0.00072) (0.00071) (0.00077) (0.00068) (0.00070)
BOL hot PH k-eff 1.02798 1.02479 1.02535 1.02473 1.02596
(0.00069) (0.00076) (0.00075) (0.00072) (0.00072)
Shutdown PH k-eff 0.93687 0.96763 0.98993 0.98460 1.00616
(0.00068) (0.00069) (0.00072) (0.00072) (0.00070)

BOL cold FD peaking factor 1.08491 1.11252 1.14991 1.14045 1.22706
(0.00442) (0.00484) (0.00533) (0.00502) (0.00838)
BOL hot FD peaking factor 1.08485 1.09713 1.15369 1.14311 1.23446
(0.00511) (0.00480) (0.00703) (0.00654) (0.00812)
BOL cold PH peaking factor 1.08745 1.10721 1.12453 1.14159 1.23029
(0.00059) (0.00494) (0.00517) (0.00516) (0.00795)
BOL hot PH peaking factor 1.08625 1.10737 1.14290 1.13744 1.22166
(0.00514) (0.00465) (0.00713) (0.00634) (0.00080)

BOL cold FD runtime (min) 853.90 1077.27 1188.75 1112.25 1432.43
BOL hot FD runtime (min) 846.00 1106.56 1389.18 1261.72 1263.92
Shutdown FD runtime (min) 128.20 119.94 107.38 111.90 95.52
BOL cold PH runtime (min) 389.84 545.85 732.39 615.58 904.64
BOL hot PH runtime (min) 391.78 540.11 741.03 635.15 792.88
Shutdown PH runtime (min) 34.27 36.45 36.83 35.20 38.02

Based on the values presented in Table 5-25, three of the core layouts considered

meet the shutdown criticality design criteria. The 906, 1194, and 1410 fuel hex cores all

have a k-eff of less and 0.985 in the shutdown state. These reactors were designed using

interpolation from the preliminary runs given in Figure 5-18, so all the reactors are at or









near the expanded k-eff criteria of 1.025. All the core designs meet the hex peaking

factor limit of 1.15 except for the 1770 fuel hex case which has a peaking factor of

1.22166 (in the expanded, partially homogenized case). As was discussed earlier, this

larger core might benefit from another zoning iteration to reduce the hex peaking factor.

However, considering that the shutdown k-eff is greater than 1, and that the mass of this

design is already over 1000 kg heavier than the next heaviest design, there is probably not

much benefit to considering this design further.

Table 5-26 compares some of the values presented in Table 5-25. The largest

difference in k-eff between a fully discrete model and a partially homogenized model was

0.00454 in the shutdown case of the 1194 fuel hex core. The runtimes of the partially

homogenized decks were between 45% and 64% that of the fully discrete models for

cases with tallies, and between 26% and 40% that of the fully discrete models for cases

with no tallies.

Thermal expansion had a negative effect on reactivity in all the core designs

considered. The extent of this negative effect ranged from 0.00998 to 0.01351. The

1770 fuel hex core had the smallest shutdown swing of 0.01980. This small swing is

largely due to the fact that this core has a height to diameter ratio (H/D) of 0.80, which is

the smallest of all cores considered. In the taller designs (those with larger H/D) more

poison can be placed near the core when the control drums are rotated in. The trend of

larger H/D corresponding to larger shutdown swing is shown in Figure 5-19.







56


Table 5-26. Nuclear characteristic analysis of final NTR designs.
Fuel hexes: 906 1194 1518 1410 1770
BOL cold k-eff difference -0.00001 0.00151 0.00167 0.00159 0.00100
(PH minus FD)
BOL hot k-eff difference 0.00352 0.00113 0.00006 -0.00058 0.00210
(PH minus FD)
Shutdown k-eff difference 0.00074 0.00454 0.00106 0.00200 0.00080
(PH minus FD)
BOL cold time ratio 0.4565 0.5067 0.6161 0.5535 0.6315
(PH runtime over FD runtime)
BOL hot time ratio 0.4631 0.4881 0.5334 0.5034 0.6273
(PH runtime over FD runtime)
Shutdown time ratio 0.2673 0.3039 0.3430 0.3146 0.3980
(PH runtime over FD runtime)

Expansion reactivity effect FD -0.01351 -0.01219 -0.01067 -0.01018 -0.01123
(hot minus cold k-eff)
Expansion reactivity effect PH -0.00998 -0.01257 -0.01228 -0.01235 -0.01013
(hot minus cold k-eff)
Shutdown k-eff swing FD 0.08833 0.06057 0.03642 0.04271 0.01850
(hot minus shutdown k-eff)
Shutdown k-eff swing PH 0.09111 0.05716 0.03542 0.04013 0.01980
(hot minus shutdown k-eff)


0 0.5


* Fully discrete
* Partially homogenized


1.5
Height to diameter (HID)


Figure 5-19. Shutdown swing versus height-to-diameter ratio for NTR cores.


rU







57


Figures 5-20 through 5-24 show the radial fission rate distribution in each of the


final core design layouts at cold and expanded geometries, using fully discrete and


partially homogenized models. The initial fission rate in the unzoned core designs is also


shown for comparison purposes. Note that these fission rates are plotted as a function of


number of hexes out from center as opposed to distance from center which was used in


Figures 5-6 though 5-10. The hex pitch used in the initial core designs is different than


that used for the final core designs, so plotting as a function of number of hexes


facilitates an easier comparison of the fission rate distributions.


1.7


1.6

1.5


1.4
w -Cold FD Final

1.3 Hot FD Final

-Cold PH Final
1.2 -
1 Hot PH Final

1.1 Hot PH
-- .. ---- Unzoned




0.9

0.8
0 2 4 6 8 10 12 14 16 18
Number of hexes out from center

Figure 5-20. Fission rate distribution for final 906 fuel hex NTR core design.

























-Cold FD Final

Hot FD Final

-Cold PH Final

-Hot PH Final

Hot PH
Unzoned


0 5 10 15 20
Number of hexes out from center

Figure 5-21. Fission rate distribution for final 1194 fuel hex NTR core design.



1.6


1.5


1.4


1.3
a Cold FD Final

c Hot FD Final
o. 1.2
Cold PH Final
11 .... .
";- Hot PH Final

1 -Hot PHe
1 -~--L _1__ Unzoned


0 5 10 15 20 25
Number of hexes out from center

Figure 5-22. Fission rate distribution for final 1518 fuel hex NTR core design.


''
I-


~~c' -----;_--~
-i

























-Cold FD Final

Hot FD Final

-Cold PH Final

-Hot PH Final

Hot PH
Unzoned


0 5 10 15 20
Number of hexes out from center

Figure 5-23. Fission rate distribution for final 1410 fuel hex NTR core design.



1.7


1.6


1.5


1 A


-Cold FD Final

Hot FD Final

-Cold PH Final

-Hot PH Final

Hot PH
Unzoned


0.7 I
0 5 10 15 20 25
Number of hexes out from center

Figure 5-24. Fission rate distribution for final 1770 fuel hex NTR core design.


.2 1.3


A

1.1


2 1.3
c

S1.2


- 11


1


-A \


"
~5 i---~


I














CHAPTER 6
CONCLUSION

The goal of this study was to develop and implement tools to aid the neutronic

design of nuclear thermal rockets. Five nuclear rocket cores were systematically zoned in

an effort to reduce the hex peaking factor. Reducing the hex peaking factor is important

in NTR design because the maximum power hex must meet thermal criteria such as limits

on peak fuel temperature and pressure drop. These criteria will demand smaller fuel

hexes (to lower peak fuel temperature) and larger coolant channels (to meet pressure drop

requirements) both of which serve to decrease the amount of fuel, thus requiring a larger

(i.e. more massive) core to meet criticality conditions. Minimizing mass is a significant

part of any space reactor design (and rockets are no exception), so there is a benefit to

reducing the hex peaking factor.

The partially homogenized MCNPX models proved to be a valuable tool in

reducing computation time. In most cases the partially homogenized models ran in less

than 60% the runtime of the fully discrete models. While there are some differences in

both criticality in fission rate when employing the partially discrete model, NTRgen

produces the fully discrete model as well, allowing the user to determine whether the

potential loss in accuracy is worth the savings in runtime.

Of the three core layouts considered in this study, three met the conditions for

criticality and hex peaking factor. The 906, 1194, and 1410 fuel hex cores can meet BOL

hot k-eff of greater than 1.025 and shutdown less than 0.985 with a hex peaking factor

less than 1.15. Of the three successful designs, the 1194 fuel hex core had the smallest









mass at 2855 kg, making it the most attractive option. The 1518 and 1770 fuel hex cores

did not have enough shutdown swing to satisfy the shutdown criteria, largely because of

the smaller H/D ratio of these designs.

There is ample possibility for future work building on this study. While NTRgen is

a robust and capable tool, improvements such as modeling axial variation in the tie tube

(similar to what is done with the fuel) could be made. NTRfilter currently treats each

individual fuel hex, resulting in some asymmetrical zoning schemes. NTRfilter could be

altered to take advantage of core symmetry when calculating zoning schemes and

peaking factors.
















APPENDIX A
NTRGEN PRIMARY INPUT FILE

0.4192 $ Diameter of inner tie tube flow (cm)
0.0508 $ Thickness of inner tie tube (cm)
0.3238 $ Thickness of tie tube moderator (cm)
0.0940 $ Thickness of outer tie tube flow (cm)
0.0203 $ Thickness of outer tie tube (cm)
0.1080 $ Thickness of tie tube insulator (cm)
3 $ Row of flow channels in fuel hex, center-to-edge
0.2133 $ Diameter of flow channels (cm)- negative is percent of fuel hex as flow (%)
0.010 $ Thickness of coating at inlet (cm)
0.010 $ Thickness of coating at outlet (cm)
5. $ Percent of hex as coolant hole in slat hex (%)
9,2 $ Min thickness of slat hexes at core perimeter (cm)
2.022 $ Hex pitch (cm)
6 $ Ratio of fuel hexes to tie tubes (0, 2, 3, or 6)

84.000 $ Core diameter (cm)
0.762 $ Expansion gap thickness (cm)
1.27 $ Barrel thickness (cm)
8.0 $ Radial reflector region thickness (cm)
0.318 $ Vessel coolant gap thickness (cm)
0.635 $ Vessel thickness (cm)
114.69 $ Core height (cm)
18 $ Number of control drums
7.0 $ Drum diameter (cm)
0.2 $ Drum gap (cm)
0.8 $ Drum poison thickness (cm)
90. $ Poison angle (degrees)
0. $ Drum rotation angle (degrees 0 is most reactive, 180 is least reactive)

10 $ Number of axial coolant regions
287. $ Core inlet temperature (K)
2700.0 $ Core outlet temperature (K)
4.65 $ Core inlet pressure (MPa)
1.1 $ Core pressure drop (MPa)
20.3 $ Tie tube inlet temperature (K)
428.9 $ Tie tube outlet temperature (K)
5.722 $ Tie tube inlet pressure (MPa)
0.701 $ Tie tube pressure drop (MPa)
800. $ Reflector temperature
0.1 $ Gap between core and support plate (cm)
10.6 $ Support plate thickness (cm)
1.65 $ TT up-pass manifold thickness (cm)
1.0 $ Bottom interface plate thickness (cm)
1.65 $ TT down-pass manifold thickness (cm)
1.0 $ Top interface plate thickness (cm)
2.65 $ Fuel coolant manifold thickness (cm)
1.0 $ Shield thickness (cm)










1.575 $ Diameter of inner tie tube flow in plates (cm)
0.025 $ Channel thickness (cm)
0.1375 $ Thickness of outer tie tube flow in plates (cm)
1.6 $ Diameter of fuel coolant channel in plates (cm)
500,6.89 $ TT up-pass manifold Temperature (K) and Pressure (MPa)
30,9.65 $ TT down-pass manifold Temperature (K) and Pressure (MPa)
300,5.03 $ Fuel coolant manifold Temperature (K) and Pressure (MPa)
25.4 $ Length of chamber (cm)
0.1 $ Thickness of chamber wall (cm)
2 $ ihomcards=0 for one core region, 1 for homogenization by row
1 $ 0 for homogenized TT in partially discrete, 1 for discrete TT in PD
10 $ Number of axial tally regions
Peak $ Type of tallies to be performed (0 for none, Peak and/or Energy)
0 $ =0 for no thermal expansion, =1 for thermal expansion approximation
0 $ =0 for no temp-dependent XS in fuel, =1 for temp XS in fuel

Comp 180 $ Fuel matrix
ZrC40 $ Fuel/Coolant channel coating
Inc718 $ Tie tube structure
ZrH $ Tie tube moderator
ZrCLow $ Tie tube insulation
ZrC40 $ Tie tube matrix
Be $ Slat reflector material
Be $ Core Barrel
Be $ Radial reflector
B4C $ Control drum poison
Al $ Outer vessel
Hyd $ Coolant
Al $ Plates
Al $ Shield
Al $ Chamber Wall
-----------Accident Cases
2 $ Number of accident cases to generate
b Hot
Peak $ Tallies desired (0 for none, Peak and/or Energy)
0. $ Drum rotation angle (degrees)
1 $ =0 for no thermal expansion, =1 for thermal expansion approximation
0 $ =0 for no temp-dependent XS in fuel, =1 for temp XS in fuel
Hyd $ In-core flow fuel hexes and tie tubes
Hyd $ Outer-core flow vessel coolant
0 $ Void gaps expansion gap and RR gap
0 $ External to core, surrounding material
c Shutdown
0 $ Tallies desired (0 for none, Peak and/or Energy)
180. $ Drum rotation angle (degrees)
0 $ =0 for no thermal expansion, =1 for thermal expansion approximation
0 $ =0 for no temp-dependent XS in fuel, =1 for temp XS in fuel
Hyd $ In-core flow fuel hexes and tie tubes
Hyd $ Outer-core flow vessel coolant
0 $ Void gaps expansion gap and RR gap
0 $ External to core, surrounding material

















APPENDIX B
NTRGEN CELLCARDS INPUT FILE


NTRa2 small engine NTR
c


c
Corfill 10 0
c
30 Coregap
c
104 Barrel
105 RRref
106 Vescool
110 Vessel


-10-152 148 fill=1 imp:n=l $ Core

10-112-152 148 imp:n=l $ExpansionGap

112-114-152 148 imp:n=l $Beryllium Barrel
114-117-152 148
117-118-152 148 imp:n=l $ Vessel Coolant Gap
118-120-152 148 imp:n=l $ Aluminum vessel


c Flood areas
186 Extcore
187 Extcore
188 Extcore
189 Extcore
190 0


-120-890 146 imp:n=l $ voidbelow core
10 -120 920 -928 imp:n=l $ above core inner radial void
120-122-154 146 imp:n=l $radialvoid
29 -120 890 -900 imp:n=l $ below core inner radial void
122:154:-146 imp:n=0


Hex and Pins (or empty hexes) for inner section
Corelat uses latfill subroutine to write core lattice


Fuelmat
Fuelcot
Fuelflw
Fuelout


(401 402 etc auto fill) u=1,4,7,10,... imp:n=l $ Fuel
auto fill
(-401:-402:etc auto fill) u= 1,4,7,10,... imp:n=1 $ Flow
auto fill


c
370 TTflowi
372 TTstrui
374 TTmod
376 TTflowo
378 TTstruo
380 TTinsu
382 TTmatrx
c
500 Slatflw
502 Slatmat


-160
160 -162
162 -164
164 -166
166 -168
168 -170
170

-180
180


u=2 imp:n=l $TTflow
u=2 imp:n=l $TTInconel
u=2 imp:n=l $TTZrH
u=2 imp:n=l $TTflow
u=2 imp:n=l $TTInconel
u=2 imp:n=l $ TT insulation
u=2 imp:n=l $ TT matrix

u=9 imp:n=l $ Coolant hole in slats
u=9 imp:n=l $Be slats


c
c Control Drums
Refdrum
c
c Plates, Hydrogen flow manifolds, chamber exit flow
600 0 920 -921 -10 fill=150 imp:n=l $ Support plate gap
602 0 921 -922 -10 fill=151 imp:n=l $ Support plate
604 0 922 -923 -10 fill=152 imp:n=l $ TT Up pass Manifold
606 0 923-924 -10 fill=153 imp:n=l $ Bottom Interf plate











0 924 -925 -10 fill=154 imp:n=l $ TT Downpass Manifold
0 925 -926 -10 fill=155 imp:n=l $ Top Interf plate
FCMan 926 -927 -10 imp:n=l $ Fuel coolant manifold
Shield 927-928 -10 imp:n=l $ Shield
FCCham 890 -900 -108 imp:n=l $ Coolant exiting core
Plate 890-900 108-29 imp:n=l $ Chamber wall


u=61 imp:n=l $ Fuel coolant in-flow


u=61 imp:n=
u=61 imp:n=
u=62 imp:n=l
u=62 imp:n=l
u=62 imp:n=
u=62 imp:n 1
u=62 imp:n=l
u=62 imp:n=
u=63 imp:n=
u=63 imp:n=


$ Fuel coolant channel
$ Gap b/n core & Sup Plate
$ TT Downflow
$ TT flow separation
1 $ TT Upflow
$ TT Upflow channel
$ Gap b/n core & Sup Plate
$ Gap b/n core & Sup Plate
$ Gap b/n core & Sup Plate


c
620 FCMan
621 Plate
622 Extcore
623 TTDn
624 Plate
625 TTUp
626 Plate
627 Extcore
628 Extcore
629 Extcore
c
630 FCMan
631 Plate
632 Plate
633 TTDn
634 Plate
635 TTUp
636 Plate
637 Plate
638 Plate
c
640 FCMan
641 Plate
642 TTUp
643 TTDn
644 Plate
645 TTUp
646 TTUp
647 TTUp
648 TTUp
c
650 FCMan
651 Plate
652 Plate
653 TTDn
654 Plate
655 Plate
657 Plate
658 Plate
c
660 FCMan
661 Plate
662 TTDn
663 TTDn
664 TTDn
667 TTDn
668 TTDn
c
670 FCMan


-600
600 -601
601
-605
605 -606
606 -607
607 -608
608
-600
600

-600
600 -601
601
-605
605 -606
606 -607
607
-600
600

-600
600 -601
601
-605
605 -606
606 -607
607
-600
600

-600
600 -601
601
-605
605 -606
606
-600
600

-600
600 -601
601
-605
605
-600
600


imp:n=l $ Fuel coolant in-flow
imp:n=l $ Fuel coolant channel
imp:n=l $ TT Up-pass Manifold
imp:n=l $ TT Downflow
imp:n=l $ TT flow separation
8 imp:n=l $TT Upflow
imp:n=l $ TT Up-pass Manifold
imp:n=l $ TT Up-pass Manifold
imp:n=l $ TT Up-pass Manifold

imp:n=l $ Fuel coolant in-flow
imp:n=l $ Fuel coolant channel
imp:n=l $ Bottom Interface Plate
imp:n=l $ TT Downflow
imp:n=l $ TT flow separation


ii
ii
ii


np:n=l
mp:n=l
np:n=l


$ Bottom Interface Plate
$ Bottom Interface Plate
$ Bottom Interface Plate


imp:n=l $ Fuel coolant in-flow
imp:n=l $ Fuel coolant channel
imp:n=l $ TT Down-pass Manifold
imp:n=l $ TT Downflow
imp:n=l $ TT Down-pass Manifold
imp:n=l $ TT Down-pass Manifold
imp:n=l $ TT Down-pass Manifold


u=76 imp:n=l $ Fuel coolant in-flow


u=64 imp:n=l $ Fuel coolant in-flow
u=64 imp:n=l $ Fuel coolant channel
u=64 imp:n=l $ Support Plate
u=65 imp:n=l $ TT Downflow
u=65 imp:n=l $ TT flow separation
u=65 imp:n=l $ TT Upflow
u=65 imp:n=l $ Support Plate
u=66 imp:n=l $ Support Plate
u=66 imp:n=l $ Support Plate


u=67
u=67
u=67
u=68
u=68
u=6
u=68
u=69
u=69

u=70
u=70
u=70
u=71
u=71
u=71
u=72
u=72

u=73
u=73
u=73
u=74
u=74
u=75
u=75











671 P1
672 P1
673 P1
674 P1
677 P1
678 P1
c
680 0


682 0


684 0


686 0


688 0


690 0


ate
ate
ate
ate
ate
ate


600 -601
601
-605
605
-600
600


u=76
u=76
u=77
u=77
u=78
u=78


-201 202-203 204-205
lat=2 u=150 imp:n=l
spgfill
-201 202-203 204-205
lat=2 u=151 imp:n=l
spfill
-201 202-203 204-205
lat=2 u=152 imp:n=l
ttufill
-201 202-203 204-205
lat=2 u=153 imp:n=l
bipfill


imp:n=l $ Fuel coolant channel
imp:n=l $ Top Interface Plate
imp:n=l $ Top Interface Plate
imp:n=l $ Top Interface Plate
imp:n=l $ Top Interface Plate
imp:n=l $ Top Interface Plate


206 $ Support plate gap


206 $ Support plate


206 $ TT UpPass Manifold


206 $ Bottom Interf Plate


-201 202 -203 204 -205 206 $ TT DownPass Manifold
lat=2 u=154 imp:n=l
ttdfill
-201 202-203 204-205 206 $ Top InterfPlate


lat=2 u=155 imp:n=l
tipfill
c end of cell cards

















APPENDIX C
NTRGEN MATCARDS INPUT FILE

c beginning of material cards
c Material Card (number in parents is room temp density to be used)
c [Compl80/3.49] CTE[6.6,0.,0.,0]
ml 92234.30c-0.03692 92235.30c-4.836 92238.30c-0.327028
6000.30c -38.8
40090.30c-28.812 40091.30c-6.2832 40092.30c-9.604
40094.30c-9.7328 40096.30c-1.568
c [Comp399/3.61] CTE[6.6,0.,0.,0]
m2 92234.30c-0.07881 92235.30c-10.545 92238.30c-0.69819
6000.30c -36.0
40090.30c -27.011 40091.30c -5.8905 40092.30c -9.004
40094.30c -9.1245 40096.30c -1.47
c [Comp598/3.64] CTE[6.6,0.,0.,0]
m3 92234.30c-0.11644 92235.30c-15.58 92238.30c-1.03156
6000.30c -33.6
40090.30c-25.5192 40091.30c-5.5651 40092.30c-8.5064
40094.30c -8.6205 40096.30c -1.3889
c
c [ZrC40/8.640] 40v/o ZrC in C
m4 6000.30c -2.24605E-01 40090.30c -3.93173E-01 40091.30c -8.669607-02
40092.30c -1.33973E-01 40094.30c -1.38727E-01 40096.30c -2.28260E-02

c [Inc718/8.18] Inconel718(8.18)
m5 5010.30c -1.04165E-05 5011.30c -4.96296E-05 6000.30c -7.99685E-04
13027.30c -5.00094E-03 15031.30c -1.50369E-04 16032.30c -1.49673E-04
22000.30c -8.99863E-03 24050.30c -7.93239E-03 24052.30c -1.59022E-01
24053.30c -1.83764E-02 24054.30c -4.65735E-03 25055.30c -3.50533E-03
26054.30c -9.57669E-03 26056.30c -1.54414E-01 26057.30c -3.60316E-03
26058.30c -4.92188E-04 27059.30c -9.99324E-03 28058.30c -3.52802E-01
28060.30c -1.40580E-01 28061.30c -6.21189E-03 28062.30c -2.01325E-02
28064.30c -5.29817E-03 29063.30c -2.05126E-03 29065.30c -9.45622E-04
41093.30c -5.12410E-02 42000.30c -3.05047E-02 14028.30c -3.21667E-03
14029.30c -1.69170E-04 14030.30c -1.15357E-04

c [Be/1.81] Be TD=1.85 / 98%=1.81 CTE[7.0,0.,0.,0.]
m6 4009.30c -1.0
mt6 be.0lt
c
c [ZrH/5.47] ZrH(5.47g/cc) SNAP-2 ratios ignoring Hf and Nb
m7 1001.30c-2.16180E-02 40090.30c-4.96099E-01 40091.30c-1.09392E-01
40092.30c -1.69046E-01 40094.30c -1.75043E-01 40096.30c -2.88015E-02
mt7 h/zr.0lt
c [ZrC Lo\\ 111,40] ZrC Low density insulator
m8 6000.30c-1.16347E-01 40090.30c-4.48066E-01 40091.30c-9.88003E-02
40092.30c -1.52678E-01 40094.30c -1.58095E-01 40096.30c -2.60129E-02
c [BorCop/8.8] Borated Copper(8.8)
m9 5010.30c -1.18249E-02 5011.30c -6.84296E-04











29063.30c -6.74727E-01 29065.30c -3.12764E-01
c [A1/2.7] Aluminum(2.7)
ml0 13027.30c -1.0
c [Hyd/0.000614] Hydrogen
mll 1001.30c -1.0
c [B4C/2.2] Boron carbide 95% enr TD=2.3 g/cc
m12 5010.30c -7.28046E-01 5011.30c -4.21312E-02
6000.30c -2.29823E-01
cml2 5010.30c .76 5011.30c .04 6000.30c .20
c [Water/1.0] H20(1.0)
m50 1001.30c-1.11915E-01 8016.30c-8.88085E-01
mt50 lwtr.0lt
cm50 1001.60c 2 8016.60c 1
c
c [Wetsand/2.056] (64%quartz at 2.65 g/cc))
m51 1001.30c -1.61499E-02 8016.30c -5.83856E-01
14028.30c -3.67490E-01 14029.30c -1.93260E-02 14030.30c -1.31787E-02
mt51 lwtr.0lt
c end of mat cards
c
print -128
prdmp 110 110 1 1
mode n
kcode 4000 1.0 10 410
ksrc 8-8 0 -8 8 0 9 7 0 -9-7 0
3 3 5 -3-3 -5 2 4 -5 -2-4 5
7 0 10 8 0-10 -8 0 10 -7 0-10
5 0 15 6 0-15 -6 0 15 -5 0-15
9 4 20 -4-9-20 6-8 25 -6 8 25
c end of deck

















APPENDIX D
NTRGEN TEMPERATURE INPUT FILE

642.1 4.964
1040.3 4.884
1459.8 3.850
1846.4 2.617
2207.7 1.773
2518.9 1.368
2721.7 1.141
2821.5 0.924
2838.2 0.731
2822.3 0.613

















APPENDIX E
NTRGEN ZONE INPUT FILE

10
0.9300
0.8523
0.7811
0.7158
0.6560
0.6012
0.5510
0.5050
0.4628
0.4241
10 -23 2.35 0.4241
11 -23 2.36 0.4241
7-22 2.04 0.5050
8 -22 1.94 0.5050
9-22 1.83 0.5510
11 -22 1.95 0.5050
14 -22 2.33 0.4241
15 -22 2.45 0.4241
4-21 2.03 0.5050
5-21 1.85 0.5510
6-21 1.64 0.6012
8-21 1.47 0.6560
9-21 1.49 0.6560
10-21 1.51 0.6560
11 -21 1.62 0.6012
12 -21 1.74 0.5510
13 -21 1.79 0.5510
15 -21 1.95 0.5050
18 -21 2.29 0.4241
19 -21 2.36 0.4241
1-20 2.12 0.4628
2-20 1.83 0.5510
3 -20 1.64 0.6012
5-20 1.36 0.7158
6-20 1.29 0.7811
7-20 1.24 0.7811
8-20 1.25 0.7811
9-20 1.30 0.7811
10-20 1.30 0.7811
12 -20 1.40 0.7158
13 -20 1.41 0.7158
14 -20 1.46 0.6560
15 -20 1.61 0.6012
16 -20 1.70 0.6012
17 -20 1.75 0.5510
19 -20 2.00 0.5050











-2 -19
-1 -19
0 -19
2 -19
3 -19
4 -19
5 -19
6 -19
7 -19
9 -19
10 -19
11 -19
12 -19
13 -19
14 -19
16 -19
17 -19
18 -19
19 -19
20 -19
-3 -18
-1 -18
0 -18
1-18
2 -18
3 -18
4 -18
6 -18
7 -18
8 -18
9 -18
10 -18
11 -18
13 -18
14 -18
15 -18
16 -18
17 -18
18 -18
20 -18
-3 -17
-2 -17
-1 -17
0 -17
1-17
3 -17
4 -17
5 -17
6 -17
7 -17
8 -17
10 -17
11 -17
12 -17
13 -17
14 -17


2.44
2.05
1.77
1.38
1.29
1.22
1.17
1.14
1.13
1.15
1.13
1.19
1.20
1.27
1.32
1.37
1.40
1.52
1.80
2.14
2.35
1.56
1.36
1.25
1.18
1.11
1.09
1.08
1.06
1.06
1.07
1.09
1.09
1.14
1.16
1.17
1.19
1.29
1.40
1.89
1.78
1.48
1.29
1.17
1.10
1.06
1.05
1.05
1.06
1.06
1.04
1.07
1.07
1.06
1.10
1.12


0.4241
0.5050
0.5510
0.7158
0.7811
0.8523
0.8523
0.8523
0.8523
0.8523
0.8523
0.8523
0.8523
0.7811
0.7811
0.7158
0.7158
0.6560
0.5510
0.4628
0.4241
0.6560
0.7158
0.7811
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.8523
0.8523
0.8523
0.7811
0.7158
0.5510
0.5510
0.6560
0.7811
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523











15 -17
17 -17
18 -17
19 -17
20 -17
21 -17
-4 -16
-3 -16
-2 -16
0 -16
1-16
2 -16
3 -16
4 -16
5 -16
7 -16
8 -16
9 -16
10 -16
11 -16
12 -16
14 -16
15 -16
16 -16
17 -16
18 -16
19 -16
21 -16
-7 -15
-6 -15
-5 -15
-3 -15
-2 -15
-1 -15
0 -15
1-15
2 -15
4 -15
5 -15
6 -15
7 -15
8 -15
9 -15
11 -15
12 -15
13 -15
14 -15
15 -15
16 -15
18 -15
19 -15
20 -15
21 -15
22 -15
-8 -14
-6 -14


1.08
1.20
1.24
1.41
1.69
2.12
1.75
1.43
1.24
1.10
1.06
1.06
1.03
1.06
1.04
1.06
1.05
1.08
1.06
1.07
1.07
1.09
1.09
1.09
1.13
1.20
1.31
1.93
2.43
1.99
1.67
1.20
1.12
1.07
1.04
1.07
1.07
1.06
1.07
1.07
1.09
1.07
1.09
1.07
1.04
1.05
1.06
1.04
1.06
1.16
1.26
1.45
1.71
2.10
2.36
1.50


0.9300
0.8523
0.7811
0.7158
0.6012
0.4628
0.5510
0.7158
0.7811
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.8523
0.7811
0.5050
0.4241
0.5050
0.6012
0.8523
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.7811
0.7158
0.6012
0.4628
0.4241
0.6560











-5 -14
-4 -14
-3 -14
-2 -14
-1 -14
1-14
2 -14
3 -14
4 -14
5 -14
6 -14
8 -14
9 -14
10 -14
11-14
12 -14
13 -14
15 -14
16 -14
17 -14
18 -14
19 -14
20 -14
22 -14
-8 -13
-7 -13
-6 -13
-5 -13
-4 -13
-2 -13
-1 -13
0 -13
1-13
2 -13
3 -13
5 -13
6 -13
7 -13
8 -13
9 -13
10 -13
12 -13
13 -13
14 -13
15 -13
16 -13
17 -13
19 -13
20 -13
21 -13
22 -13
23 -13
-9 -12
-8 -12
-7 -12
-5 -12


1.33
1.17
1.10
1.07
1.05
1.06
1.09
1.09
1.11
1.13
1.10
1.14
1.11
1.11
1.08
1.08
1.09
1.05
1.03
1.06
1.11
1.21
1.34
1.97
1.79
1.43
1.27
1.20
1.10
1.07
1.06
1.08
1.11
1.14
1.15
1.19
1.17
1.16
1.19
1.16
1.14
1.12
1.10
1.06
1.04
1.03
1.07
1.15
1.23
1.46
1.82
2.27
1.78
1.42
1.21
1.09


0.7811
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.9300
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.7158
0.5050
0.5510
0.7158
0.7811
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.8523
0.8523
0.8523
0.8523
0.8523
0.8523
0.8523
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.7811
0.6560
0.5510
0.4241
0.5510
0.7158
0.8523
0.9300











-4 -12
-3 -12
-2 -12
-1 -12
0 -12
2 -12
3 -12
4 -12
5 -12
6 -12
7 -12
9 -12
10 -12
11-12
12 -12
13 -12
14 -12
16 -12
17 -12
18 -12
19 -12
20 -12
21 -12
23 -12
-12-11
-11 -11
-10-11
-8 -11
-7 -11
-6 -11
-5 -11
-4 -11
-3 -11
-1 -11
0 -11
1 -11
2-11
3 -11
4-11
6-11
7-11
8-11
9-11
10 -11
11 -11
13 -11
14 -11
15 -11
16 -11
17 -11
18 -11
20 -11
21 -11
22 -11
-13 -10
-11-10


1.06
1.10
1.11
1.13
1.14
1.20
1.21
1.24
1.22
1.25
1.26
1.20
1.19
1.18
1.15
1.11
1.08
1.04
1.04
1.06
1.12
1.23
1.39
2.33
2.38
1.97
1.65
1.18
1.11
1.08
1.06
1.09
1.11
1.18
1.19
1.23
1.26
1.28
1.29
1.33
1.31
1.31
1.28
1.23
1.21
1.13
1.09
1.06
1.05
1.04
1.04
1.24
1.44
2.00
2.35
1.47


0.9300
0.9300
0.9300
0.8523
0.8523
0.8523
0.8523
0.7811
0.8523
0.7811
0.7811
0.8523
0.8523
0.8523
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.7811
0.7158
0.4241
0.4241
0.5050
0.6012
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.8523
0.7811
0.7811
0.7811
0.7811
0.7811
0.7811
0.7811
0.7811
0.7811
0.8523
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.7811
0.7158
0.5050
0.4241
0.6560











-10 -10
-9 -10
-8 -10
-7 -10
-6 -10
-4 -10
-3 -10
-2 -10
-1 -10
0 -10
1-10
3 -10
4 -10
5 -10
6 -10
7 -10
8 -10
10 -10
11-10
12 -10
13 -10
14 -10
15 -10
17 -10
18 -10
19 -10
20 -10
21 -10
-13 -9
-12 -9
-11 -9
-10 -9
-9 -9
-7 -9
-6 -9
-5 -9
-4 -9
-3 -9
-2 -9
0 -9
1 -9
2 -9
3 -9
4 -9
5 -9
7 -9
8 -9
9 -9
10 -9
11 -9
12 -9
14 -9
15 -9
16 -9
17 -9
18 -9


1.27
1.16
1.10
1.08
1.08
1.16
1.18
1.21
1.24
1.27
1.30
1.37
1.38
1.37
1.36
1.35
1.36
1.28
1.24
1.20
1.16
1.11
1.08
1.05
1.04
1.17
1.31
1.59
1.81
1.46
1.28
1.15
1.12
1.07
1.11
1.15
1.18
1.22
1.27
1.33
1.37
1.37
1.43
1.45
1.44
1.42
1.40
1.35
1.30
1.27
1.22
1.13
1.10
1.07
1.06
1.08


0.7811
0.8523
0.9300
0.9300
0.9300
0.8523
0.8523
0.8523
0.7811
0.7811
0.7811
0.7158
0.7158
0.7158
0.7158
0.7158
0.7158
0.7811
0.7811
0.8523
0.8523
0.9300
0.9300
0.9300
0.9300
0.8523
0.7811
0.6012
0.5510
0.6560
0.7811
0.8523
0.9300
0.9300
0.9300
0.8523
0.8523
0.8523
0.7811
0.7811
0.7158
0.7158
0.7158
0.7158
0.7158
0.7158
0.7158
0.7158
0.7811
0.7811
0.8523
0.8523
0.9300
0.9300
0.9300
0.9300











19 -9
21 -9
-14 -8
-13 -8
-12 -8
-10 -8
-9 -8
-8 -8
-7 -8
-6 -8
-5 -8
-3 -8
-2 -8
-1 -8
0 -8
1 -8
2 -8
4 -8
5 -8
6 -8
7 -8
8 -8
9 -8
11 -8
12 -8
13 -8
14 -8
15 -8
16 -8
18 -8
19 -8
20 -8
21 -8
22 -8
-15 -7
-13 -7
-12 -7
-11 -7
-10 -7
-9 -7
-8 -7
-6 -7
-5 -7
-4 -7
-3 -7
-2 -7
-1 -7
1 -7
2 -7
3 -7
4 -7
5 -7
6 -7
8 -7
9 -7
10 -7


1.17
1.75
1.93
1.50
1.29
1.07
1.08
1.07
1.10
1.15
1.18
1.28
1.33
1.35
1.39
1.42
1.45
1.49
1.52
1.50
1.48
1.43
1.40
1.29
1.25
1.20
1.16
1.10
1.09
1.12
1.18
1.38
1.79
2.33
2.12
1.25
1.12
1.06
1.06
1.06
1.10
1.19
1.25
1.28
1.36
1.39
1.45
1.50
1.54
1.56
1.56
1.56
1.55
1.46
1.45
1.33


0.8523
0.5510
0.5050
0.6560
0.7811
0.9300
0.9300
0.9300
0.9300
0.8523
0.8523
0.7811
0.7811
0.7158
0.7158
0.7158
0.7158
0.6560
0.6560
0.6560
0.6560
0.7158
0.7158
0.7811
0.7811
0.8523
0.8523
0.9300
0.9300
0.8523
0.8523
0.7158
0.5510
0.4241
0.4628
0.7811
0.8523
0.9300
0.9300
0.9300
0.9300
0.8523
0.7811
0.7811
0.7158
0.7158
0.7158
0.6560
0.6560
0.6560
0.6560
0.6560
0.6560
0.6560
0.7158
0.7811











11 -7
12 -7
13 -7
15 -7
16 -7
17 -7
18 -7
19 -7
20 -7
22 -7
-15 -6
-14 -6
-13 -6
-12 -6
-11 -6
-9 -6
-8 -6
-7 -6
-6 -6
-5 -6
-4 -6
-2 -6
-1 -6
0 -6
1 -6
2 -6
3 -6
5 -6
6 -6
7 -6
8 -6
9 -6
10 -6
12 -6
13 -6
14 -6
15 -6
16 -6
17 -6
19 -6
20 -6
21 -6
-16 -5
-15 -5
-14 -5
-12 -5
-11 -5
-10 -5
-9 -5
-8 -5
-7 -5
-5 -5
-4 -5
-3 -5
-2 -5
-1 -5


1.29
1.26
1.21
1.10
1.07
1.08
1.11
1.24
1.43
2.43
1.67
1.32
1.17
1.04
1.04
1.09
1.13
1.17
1.24
1.30
1.37
1.47
1.51
1.53
1.55
1.61
1.61
1.59
1.56
1.51
1.51
1.41
1.37
1.26
1.20
1.15
1.11
1.07
1.08
1.28
1.55
1.98
1.88
1.42
1.19
1.04
1.06
1.10
1.12
1.18
1.26
1.35
1.43
1.48
1.52
1.55


0.7811
0.7811
0.8523
0.9300
0.9300
0.9300
0.9300
0.7811
0.7158
0.4241
0.6012
0.7811
0.8523
0.9300
0.9300
0.9300
0.8523
0.8523
0.7811
0.7811
0.7158
0.6560
0.6560
0.6560
0.6560
0.6012
0.6012
0.6012
0.6560
0.6560
0.6560
0.7158
0.7158
0.7811
0.8523
0.8523
0.9300
0.9300
0.9300
0.7811
0.6560
0.5050
0.5510
0.7158
0.8523
0.9300
0.9300
0.9300
0.8523
0.8523
0.7811
0.7158
0.7158
0.6560
0.6560
0.6560











0 -5
2 -5
3 -5
4 -5
5 -5
6 -5
7 -5
9 -5
10 -5
11 -5
12 -5
13 -5
14 -5
16 -5
17 -5
18 -5
19 -5
20 -5
-17 -4
-15 -4
-14 -4
-13 -4
-12 -4
-11 -4
-10 -4
-8 -4
-7 -4
-6 -4
-5 -4
-4 -4
-3 -4
-1 -4
0 -4
1 -4
2 -4
3 -4
4 -4
6 -4
7 -4
8 -4
9 -4
10 -4
11 -4
13 -4
14 -4
15 -4
16 -4
17 -4
18 -4
20 -4
-17 -3
-16 -3
-15 -3
-14 -3
-13 -3
-11 -3


1.57
1.63
1.61
1.62
1.61
1.57
1.55
1.40
1.35
1.31
1.28
1.20
1.15
1.06
1.08
1.17
1.35
1.64
2.14
1.25
1.10
1.03
1.04
1.08
1.13
1.24
1.31
1.34
1.42
1.47
1.54
1.60
1.65
1.66
1.68
1.66
1.65
1.56
1.51
1.47
1.40
1.36
1.29
1.18
1.12
1.10
1.06
1.10
1.16
1.73
1.69
1.30
1.16
1.07
1.04
1.11


0.6560
0.6012
0.6012
0.6012
0.6012
0.6560
0.6560
0.7158
0.7158
0.7811
0.7811
0.8523
0.8523
0.9300
0.9300
0.8523
0.7158
0.6012
0.4628
0.7811
0.9300
0.9300
0.9300
0.9300
0.8523
0.7811
0.7811
0.7158
0.7158
0.6560
0.6560
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6560
0.6560
0.6560
0.7158
0.7158
0.7811
0.8523
0.9300
0.9300
0.9300
0.9300
0.8523
0.6012
0.6012
0.7811
0.8523
0.9300
0.9300
0.9300











-10 -3
-9 -3
-8 -3
-7 -3
-6 -3
-4 -3
-3 -3
-2 -3
-1 -3
0 -3
1 -3
3 -3
4 -3
5 -3
6 -3
7 -3
8 -3
10 -3
11 -3
12 -3
13 -3
14 -3
15 -3
17 -3
18 -3
19 -3
20 -3
21 -3
-18 -2
-17 -2
-16 -2
-14 -2
-13 -2
-12 -2
-11 -2
-10 -2
-9 -2
-7 -2
-6 -2
-5 -2
-4 -2
-3 -2
-2 -2
0 -2
1 -2
2 -2
3 -2
4 -2
5 -2
7 -2
8 -2
9 -2
10 -2
11 -2
12 -2
14 -2


1.16
1.23
1.28
1.36
1.42
1.55
1.57
1.61
1.65
1.70
1.70
1.69
1.63
1.61
1.55
1.50
1.45
1.34
1.27
1.22
1.16
1.11
1.07
1.09
1.18
1.40
1.71
2.26
1.88
1.43
1.21
1.05
1.06
1.09
1.15
1.20
1.24
1.38
1.46
1.53
1.57
1.59
1.64
1.74
1.74
1.71
1.70
1.63
1.60
1.48
1.43
1.37
1.31
1.24
1.20
1.09


0.8523
0.7811
0.7811
0.7158
0.7158
0.6560
0.6560
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6560
0.6560
0.7158
0.7158
0.7811
0.8523
0.8523
0.9300
0.9300
0.9300
0.8523
0.7158
0.6012
0.4241
0.5510
0.7158
0.8523
0.9300
0.9300
0.9300
0.8523
0.8523
0.7811
0.7158
0.6560
0.6560
0.6560
0.6012
0.6012
0.5510
0.5510
0.6012
0.6012
0.6012
0.6012
0.6560
0.7158
0.7158
0.7811
0.7811
0.8523
0.9300











15 -2
16 -2
17 -2
18 -2
19 -2
21 -2
-19 -1
-17 -1
-16 -1
-15 -1
-14 -1
-13 -1
-12 -1
-10 -1
-9 -1
-8 -1
-7 -1
-6 -1
-5 -1
-3 -1
-2 -1
-1 -1
0 -1
1 -1
2 -1
4 -1
5 -1
6 -1
7 -1
8 -1
9 -1
11 -1
12 -1
13 -1
14 -1
15 -1
16 -1
18 -1
19 -1
20 -1
-19 0
-18 0
-17 0
-16 0
-15 0
-13 0
-12 0
-11 0
-10 0
-9 0
-8 0
-6 0
-5 0
-4 0
-3 0
-2 0


1.06
1.06
1.12
1.21
1.38
2.37
2.15
1.26
1.10
1.04
1.06
1.08
1.10
1.22
1.29
1.39
1.46
1.54
1.55
1.64
1.69
1.68
1.72
1.72
1.70
1.64
1.59
1.53
1.48
1.42
1.36
1.23
1.17
1.08
1.07
1.05
1.05
1.24
1.50
2.02
1.79
1.36
1.18
1.07
1.05
1.07
1.15
1.20
1.27
1.32
1.41
1.56
1.58
1.61
1.67
1.70


0.9300
0.9300
0.9300
0.8523
0.7158
0.4241
0.4628
0.7811
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.7811
0.7158
0.6560
0.6560
0.6560
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6560
0.6560
0.6560
0.7158
0.7158
0.7811
0.8523
0.9300
0.9300
0.9300
0.9300
0.7811
0.6560
0.5050
0.5510
0.7158
0.8523
0.9300
0.9300
0.9300
0.8523
0.8523
0.7811
0.7811
0.7158
0.6560
0.6560
0.6012
0.6012
0.6012











1.68
1.73
1.73
1.67
1.62
1.57
1.51
1.39
1.35
1.29
1.21
1.13
1.08
1.06
1.09
1.14
1.36
1.73
2.01
1.57
1.26
1.07
1.07
1.09
1.11
1.16
1.24
1.34
1.42
1.50
1.56
1.61
1.66
1.67
1.69
1.73
1.70
1.69
1.64
1.56
1.50
1.43
1.38
1.33
1.22
1.09
1.08
1.04
1.06
1.12
1.23
2.07
2.41
1.42
1.24
1.11


0.6012
0.6012
0.6012
0.6012
0.6012
0.6560
0.6560
0.7158
0.7158
0.7811
0.8523
0.8523
0.9300
0.9300
0.9300
0.8523
0.7158
0.6012
0.5050
0.6560
0.7811
0.9300
0.9300
0.9300
0.9300
0.8523
0.7811
0.7158
0.7158
0.6560
0.6560
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6560
0.6560
0.7158
0.7158
0.7811
0.7811
0.9300
0.9300
0.9300
0.9300
0.8523
0.7811
0.4628
0.4241
0.7158
0.7811
0.9300











1.06
1.07
1.11
1.19
1.27
1.33
1.37
1.46
1.52
1.63
1.66
1.70
1.69
1.71
1.72
1.68
1.63
1.58
1.55
1.49
1.40
1.24
1.20
1.12
1.07
1.05
1.04
1.19
1.39
1.83
2.32
1.76
1.38
1.20
1.09
1.05
1.12
1.17
1.21
1.29
1.34
1.47
1.54
1.60
1.63
1.66
1.69
1.70
1.69
1.69
1.65
1.58
1.54
1.42
1.34
1.27


0.9300
0.9300
0.9300
0.8523
0.7811
0.7811
0.7158
0.6560
0.6560
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6560
0.6560
0.6560
0.7158
0.7811
0.8523
0.9300
0.9300
0.9300
0.9300
0.8523
0.7158
0.5510
0.4241
0.5510
0.7158
0.8523
0.9300
0.9300
0.8523
0.8523
0.8523
0.7811
0.7158
0.6560
0.6560
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6012
0.6560
0.6560
0.7158
0.7158
0.7811











9 3 1.22 0.8523
10 3 1.15 0.8523
11 3 1.10 0.9300
13 3 1.03 0.9300
14 3 1.04 0.9300
15 3 1.11 0.9300
16 3 1.29 0.7811
17 3 1.64 0.6012
-20 4 1.67 0.6012
-18 4 1.15 0.8523
-17 4 1.09 0.9300
-16 4 1.07 0.9300
-15 4 1.10 0.9300
-14 4 1.13 0.8523
-13 4 1.18 0.8523
-11 4 1.29 0.7811
-10 4 1.35 0.7158
-9 4 1.43 0.7158
-8 4 1.49 0.6560
-7 4 1.51 0.6560
-6 4 1.57 0.6560
-4 4 1.63 0.6012
-3 4 1.64 0.6012
-2 4 1.68 0.6012
-1 4 1.69 0.6012
0 4 1.64 0.6012
1 4 1.63 0.6012
3 4 1.56 0.6560
4 4 1.50 0.6560
5 4 1.42 0.7158
6 4 1.36 0.7158
7 4 1.28 0.7811
8 4 1.22 0.7811
10 4 1.13 0.8523
11 4 1.08 0.9300
12 4 1.05 0.9300
13 4 1.04 0.9300
14 4 1.10 0.9300
15 4 1.22 0.7811
17 4 2.05 0.5050
-20 5 1.62 0.6012
-19 5 1.28 0.7811
-18 5 1.13 0.8523
-17 5 1.06 0.9300
-16 5 1.04 0.9300
-14 5 1.15 0.8523
-13 5 1.17 0.8523
-12 5 1.25 0.7811
-11 5 1.31 0.7811
-10 5 1.41 0.7158
-9 5 1.45 0.7158
-7 5 1.50 0.6560
-6 5 1.53 0.6560
-5 5 1.58 0.6560
-4 5 1.59 0.6560
-3 5 1.60 0.6012











1.62
1.57
1.55
1.53
1.45
1.43
1.36
1.24
1.20
1.13
1.09
1.05
1.03
1.19
1.41
1.86
1.97
1.46
1.25
1.03
1.06
1.11
1.13
1.16
1.26
1.36
1.45
1.49
1.48
1.53
1.54
1.56
1.58
1.55
1.52
1.49
1.47
1.37
1.32
1.24
1.18
1.15
1.09
1.06
1.08
1.14
1.28
1.65
2.39
1.40
1.23
1.10
1.06
1.08
1.07
1.18


0.6012
0.6560
0.6560
0.6560
0.7158
0.7158
0.7158
0.7811
0.8523
0.8523
0.9300
0.9300
0.9300
0.8523
0.7158
0.5510
0.5050
0.6560
0.7811
0.9300
0.9300
0.9300
0.8523
0.8523
0.7811
0.7158
0.7158
0.6560
0.6560
0.6560
0.6560
0.6560
0.6560
0.6560
0.6560
0.6560
0.6560
0.7158
0.7811
0.7811
0.8523
0.8523
0.9300
0.9300
0.9300
0.8523
0.7811
0.6012
0.4241
0.7158
0.7811
0.9300
0.9300
0.9300
0.9300
0.8523











1.24
1.29
1.37
1.41
1.42
1.52
1.52
1.50
1.52
1.53
1.51
1.40
1.39
1.37
1.32
1.22
1.19
1.10
1.06
1.04
1.04
1.09
1.22
2.06
2.35
1.77
1.41
1.18
1.08
1.06
1.09
1.14
1.16
1.25
1.28
1.38
1.39
1.43
1.46
1.47
1.45
1.47
1.44
1.39
1.39
1.36
1.29
1.16
1.15
1.09
1.05
1.04
1.04
1.22
1.43
1.92


0.7811
0.7811
0.7158
0.7158
0.7158
0.6560
0.6560
0.6560
0.6560
0.6560
0.6560
0.7158
0.7158
0.7158
0.7811
0.8523
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.7811
0.5050
0.4241
0.5510
0.7158
0.8523
0.9300
0.9300
0.9300
0.8523
0.8523
0.7811
0.7811
0.7158
0.7158
0.7158
0.6560
0.6560
0.7158
0.6560
0.7158
0.7158
0.7158
0.7158
0.7811
0.8523
0.8523
0.9300
0.9300
0.9300
0.9300
0.8523
0.7158
0.5050











-21 9
-19 9
-18 9
-17 9
-16 9
-15 9
-14 9
-12 9
-11 9
-10 9
-9 9
-8 9
-7 9
-5 9
-4 9
-3 9
-2 9
-1 9
0 9
2 9
3 9
4 9
5 9
6 9
7 9
9 9
10 9
11 9
12 9
13 9
-21 10
-20 10
-19 10
-18 10
-17 10
-15 10
-14 10
-13 10
-12 10
-11 10
-10 10
-8 10
-7 10
-6 10
-5 10
-4 10
-3 10
-1 10
0 10
1 10
2 10
3 10
4 10
6 10
7 10
8 10


1.72 0.6012
1.15 0.8523
1.05 0.9300
1.04 0.9300
1.06 0.9300
1.08 0.9300
1.14 0.8523
1.23 0.7811
1.26 0.7811
1.33 0.7811
1.36 0.7158
1.37 0.7158
1.42 0.7158
1.40 0.7158
1.44 0.7158
1.40 0.7158
1.39 0.7158
1.35 0.7158
1.34 0.7158
1.28 0.7811
1.20 0.8523
1.18 0.8523
1.14 0.8523
1.08 0.9300
1.05 0.9300
1.06 0.9300
1.09 0.9300
1.20 0.8523
1.39 0.7158
1.78 0.5510
1.64 0.6012
1.30 0.7811
1.12 0.8523
1.06 0.9300
1.05 0.9300
1.08 0.9300
1.14 0.8523
1.17 0.8523
1.23 0.7811
1.25 0.7811
1.30 0.7811
1.34 0.7158
1.36 0.7158
1.36 0.7158
1.37 0.7158
1.35 0.7158
1.34 0.7158
1.32 0.7811
1.27 0.7811
1.23 0.7811
1.18 0.8523
1.15 0.8523
1.11 0.9300
1.08 0.9300
1.06 0.9300
1.08 0.9300











9 10
10 10
11 10
13 10
-22 11
-21 11
-20 11
-18 11
-17 11
-16 11
-15 11
-14 11
-13 11
-11 11
-10 11
-9 11
-8 11
-7 11
-6 11
-4 11
-3 11
-2 11
-1 11
0 11
1 11
3 11
4 11
5 11
6 11
7 11
8 11
10 11
11 11
12 11
-23 12
-21 12
-20 12
-19 12
-18 12
-17 12
-16 12
-14 12
-13 12
-12 12
-11 12
-10 12
-9 12
-7 12
-6 12
-5 12
-4 12
-3 12
-2 12
0 12
1 12
2 12


1.15
1.28
1.45
2.28
1.94
1.50
1.23
1.06
1.03
1.05
1.05
1.12
1.16
1.22
1.28
1.29
1.27
1.30
1.30
1.29
1.29
1.24
1.23
1.18
1.16
1.10
1.08
1.06
1.10
1.10
1.16
1.59
1.90
2.30
2.36
1.43
1.25
1.12
1.08
1.04
1.03
1.08
1.13
1.16
1.20
1.23
1.21
1.23
1.27
1.24
1.23
1.21
1.17
1.15
1.11
1.09


0.8523
0.7811
0.7158
0.4241
0.5050
0.6560
0.7811
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.7811
0.7811
0.7811
0.7811
0.7811
0.7811
0.7811
0.7811
0.7811
0.7811
0.8523
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.6560
0.5050
0.4241
0.4241
0.7158
0.7811
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.8523
0.8523
0.7811
0.8523
0.7811
0.7811
0.7811
0.7811
0.8523
0.8523
0.8523
0.9300
0.9300











3 12
4 12
5 12
7 12
8 12
9 12
-23 13
-22 13
-21 13
-20 13
-19 13
-17 13
-16 13
-15 13
-14 13
-13 13
-12 13
-10 13
-9 13
-8 13
-7 13
-6 13
-5 13
-3 13
-2 13
-1 13
0 13
1 13
2 13
4 13
5 13
6 13
7 13
8 13
-22 14
-20 14
-19 14
-18 14
-17 14
-16 14
-15 14
-13 14
-12 14
-11 14
-10 14
-9 14
-8 14
-6 14
-5 14
-4 14
-3 14
-2 14
-1 14
1 14
2 14
3 14


1.05
1.05
1.07
1.21
1.39
1.71
2.29
1.79
1.44
1.23
1.15
1.05
1.05
1.07
1.09
1.13
1.13
1.16
1.17
1.20
1.21
1.19
1.20
1.13
1.13
1.10
1.09
1.07
1.06
1.08
1.15
1.27
1.42
1.75
1.93
1.32
1.21
1.11
1.08
1.07
1.07
1.08
1.11
1.11
1.12
1.12
1.16
1.14
1.12
1.14
1.11
1.09
1.05
1.05
1.05
1.06


0.9300
0.9300
0.9300
0.8523
0.7158
0.6012
0.4241
0.5510
0.7158
0.7811
0.8523
0.9300
0.9300
0.9300
0.9300
0.8523
0.8523
0.8523
0.8523
0.8523
0.8523
0.8523
0.8523
0.8523
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.7811
0.7158
0.5510
0.5050
0.7811
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300
0.8523
0.8523
0.8523
0.8523
0.9300
0.9300
0.9300
0.9300
0.9300
0.9300