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Open Hanjs Msthesis 041808.Pdf The Pennsylvania State University The Graduate School College of Engineering SENSITIVITY STUDY ON THE ENERGY GROUP STRUCTURE FOR HIGH TEMPERATURE REACTOR ANALYSIS A Thesis in Nuclear Engineering by James Sanggene Han Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2008 The thesis of James Sanggene Han was reviewed and approved* by the following: Kostadin N. Ivanov Distinguished Professor of Nuclear Engineering Thesis Advisor Samuel Levine Professor Emeritus of Nuclear Engineering Abderrafi M. Ougouag Nuclear Engineer Idaho National Laboratory Hans Gougar Senior Consultant Pebble Bed Modular Reactor (Pty) Ltd Jack Brenizer J. 'Lee' Everett Professor of Mechanical and Nuclear Engineering Chair of the Nuclear Engineering *Signatures are on file in the Graduate School ii iii ABSTRACT The interactions of neutrons and materials in a core are strongly dependent on the energy of the incoming neutron. A nearly continuous energy dependent cross section data set makes for a challenging usage in computation. Therefore to simplify the computational problem, the cross sections are grouped into energy structures and properties dependent on energy are effectively averaged into energy groups. This thesis is focused on the selection of energy group structures for the reactor analysis of the Pebble Bed Modular Reactor. Energy group structure is simply defined as the discretization of energy into groups by the selection of energy boundaries. Traditional reactor analysis requires a two-step process. The first step utilizes a cross section generation code which takes the material composition and geometry of a particular region and its given conditions, to produce cross sections. This part is sometimes referred to as the cell calculation. The second part of the process is the reactor level calculation and utilizes the computed cross sections from the first step to calculate overall reactor properties. In this study, COMBINE6 was used for the cross section generation code and the Penn State nodal diffusion code NEM was used for the reactor analysis code. To arrive at an optimal group structure, many series of combinations of group structures were tested. Each set of results computed from the two-step process were compared with solution of a method independent of energy discretization, MCNP5, which is a Monte Carlo continuous energy code. MCNP5 is used as a reference because it generates a neutron transport solution using continuous energy cross sections and thus is a better representation of the physical system. From these numerical case studies, an optimal 5, 6, 7, 8, and 9 Group structure has been chosen based on the results that best match MNCP5’s results. In addition to evidence from simulations, the group structures determined can also be justified by arguments in reactor physics. iv TABLE OF CONTENTS LIST OF FIGURES .....................................................................................................vii ACKNOWLEDGEMENTS.........................................................................................xix Chapter 1 Introduction to Gas Cooled Reactors ........................................................1 Chapter 2 Nuclear Engineering and the Fundamentals of Reactor Physics................4 Chapter 3 Research Goals and Motivation .................................................................9 Motivation for Study of Group Structures............................................................10 Chapter 4 Theory: Selection Methodology & Review of Literature ..........................12 4.1 Group Structure General Theoretical Considerations.....................................12 4.2 General Guidelines for Energy Group Structures from Literature .................12 4.4 Fast Energy Group Structure Selection Basis.................................................18 4.5 Thermal Energy Group Selection Basis .........................................................22 4.6 Thermal Cutoff Energy Selection Basis .........................................................24 4.7 Important Isotopes in the Thermal Region .....................................................24 Chapter 5 Computational Methods and Models .........................................................26 5.1 Problem Description and Assumptions ..........................................................26 5.2 Models ............................................................................................................28 5.3 Model Assumptions & Errors.........................................................................29 5.3.1 Low Buckling Assumption...................................................................29 5.3.2 20 Isotope Limitation Per Material.......................................................30 5.3.3 Uniform Temperature Distribution.......................................................31 5.3.4 Homogeneous versus Heterogeneous Material Compositions.............31 Chapter 6 Sources of Error .........................................................................................33 The Diffusion Theory Approximation..................................................................33 Chapter 7 Comparison Methodology..........................................................................35 Chapter 8 Results and Discussion...............................................................................37 8.1 Thermal Cutoff Study.....................................................................................37 8.1.1 Thermal Cut-off Study using 2-Group No Up-scattering.....................38 8.1.2 Thermal Cutoff Study using 2-Group with Up-scattering....................41 8.1.3 Thermal Cutoff Study using Fixed 9-Group Structure.........................44 8.1.4 Thermal Cut-off Study Conclusion ......................................................47 v 8.2 3-Group Study ................................................................................................48 8.2.1 Fission Source Containment.................................................................48 8.2.2 3-Group Conclusion .............................................................................52 8.3 Thermal Group Studies...................................................................................53 8.3.1 Group Structure Abbreviation ..............................................................53 8.3.2 Thermal Studies 1: 5-Group of 2 fast and 3 thermal groups ................54 8.3.3 Thermal Studies 2: 5-Group of 3 fast groups and 2 thermal groups ....60 8.3.4 Thermal Studies 3: 6-Group .................................................................63 8.3.5 Thermal Studies 4: 7-Group .................................................................66 8.3.6 Thermal Studies 5: 8-Group .................................................................69 8.3.7 Thermal Studies Conclusion.................................................................73 8.4 Fast Group Studies..........................................................................................73 8.4.1 Preliminary Assessment of Fast Group Structure and Importance ......73 8.4.3 Fast Studies 2........................................................................................81 8.4.4 Physical Explanations for Partitions: 2.04 keV, 639 keV, 1.74 MeV..83 8.4.5 Fast Studies 3........................................................................................86 8.4.6 Physical Explanations for Partitions: 10 keV.......................................89 8.4.7 Fast Studies 4........................................................................................90 8.4.8 Fast Studies 5........................................................................................94 8.4.9 Fast Studies 6........................................................................................96 8.4.10 Fast Studies Conclusion .....................................................................99 8.4.11 Fast Studies 7: Constant Lethargy Divisions......................................99 8.4.12 Constant Lethargy of Fast Region Conclusion...................................102 8.4.13 Maximum Number of Energy Group Structures................................103 8.5 G&S Studies of Broad Group Structures from LWR and Recommended modifications for HTGR................................................................................107 8.6 Recommended Best Group Structures Subdivided By Number of Groups....111 8.6.1 5 Group Selection.................................................................................112 8.6.1.1 Spatial Shielding Effects in Diffusion Theory without Environment Feedback ...................................................................114 8.6.1.2 k-effective as a Good Indicator ..................................................114 8.6.2 6 Group Selection.................................................................................115 8.6.3 7 Group Selection.................................................................................118 8.6.4 8 Group Selection.................................................................................121 8.6.5 9+ Group Selection...............................................................................124 Chapter 9 Conclusions ................................................................................................127 Chapter 10 Future Work .............................................................................................133 Bibliography ................................................................................................................135
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