The Pennsylvania State University The Graduate School Department of Mechanical and Nuclear Engineering IMPROVED NEUTRON KINETICS FOR COUPLED THREE-DIMENSIONAL BOILING WATER REACTOR ANALYSIS A Thesis in Nuclear Engineering by Bedirhan Akdeniz © 2007 Bedirhan Akdeniz Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2007 The thesis of Bedirhan Akdeniz was reviewed and approved* by the following: Kostadin N. Ivanov Professor of Nuclear Engineering Thesis Advisor Chair of Committee Lawrence E. Hochreiter Professor of Nuclear Engineering Yousry Y. Azmy Professor of Nuclear Engineering Cengiz Camcı Professor of Aerospace Engineering Erwin Müller Fellow Engineer Westinghouse Electric, Sweden Special Member Dobromir Panayotov Principal Engineer Westinghouse Electric, Sweden Special Member Jack S. Brenizer, Jr. Professor of Nuclear Engineering Chair of Nuclear Engineering Program *Signatures are on file in the Graduate School iii ABSTRACT The need for a more accurate method of modelling cross section variations for off-nominal core conditions is becoming an important issue with the increased use of coupled three-dimensional (3-D) thermal-hydraulics/neutronics simulations. In traditional reactor core analysis, thermal reactor core calculations are customarily performed with 3- D two-group nodal diffusion methods. Steady-state multi-group transport theory calculations on heterogeneous single assembly domains subject to reflective boundary conditions are normally used to prepare the equivalent two-group spatially homogenized nodal parameters. For steady-state applications, the equivalent nodal parameters are theoretically well-defined; but, for transient applications, the definition of the nodal kinetics parameters, in particular, delayed neutron precursor data is somewhat unclear. The fact that delayed neutrons are emitted at considerably lower energies than prompt neutrons and that this difference cannot be accounted for in a two-group representation is of particular concern. To compensate for this inherent deficiency of the two-group model a correction is applied to the nodal values of the delayed neutron fractions; however, the adequacy of this correction has never been tested thoroughly for Boiling Water Reactor (BWR) applications, especially where the instantaneous thermal-hydraulic conditions play an important role on the core neutron kinetics calculations. This thesis proposes a systematic approach to improve the 3-D neutron kinetics modelling in coupled BWR transient calculations by developing, implementing and validating methods for consistent generation of neutron kinetics and delayed neutron data for such coupled thermal- hydraulics/neutronics simulations. iv TABLE OF CONTENTS LIST OF FIGURES .....................................................................................................vi LIST OF TABLES.......................................................................................................ix NOMENCLATURE ....................................................................................................x ACKNOWLEDGEMENTS.........................................................................................xvi Chapter 1 INTRODUCTION......................................................................................1 Chapter 2 BACKGROUND AND SENSITIVITY ANALYSES...............................7 2.1 LITERATURE REVIEW ..............................................................................9 2.1.1 Evaluation of Basic Delayed Neutron Data.........................................10 2.1.2 Evaluation of Delayed Neutron Fractions (β) .....................................15 2.2 CODE DESCRIPTIONS ...............................................................................22 2.2.1 Lattice Physics Code: TransLAT ........................................................23 2.2.2 PARCS Core Simulator.......................................................................26 2.2.3 TRACE/PARCS Coupled Code ..........................................................28 2.3 PRELIMINARY SENSITIVITY STUDIES .................................................30 2.3.1 Peach Bottom Turbine Trip (PBTT) Problem.....................................31 2.3.1.1 PBTT TRACE Thermal-Hydraulics Model ..............................33 2.3.1.2 PBTT PARCS Neutronics Model .............................................36 2.3.1.3 PBTT Sensitivity Results and Discussion.................................37 2.3.2 Numerical Studies Using LMW Benchmark.......................................42 2.3.2.1 LMW Sensitivity Results and Discussion.................................45 2.4 SUMMARY...................................................................................................49 Chapter 3 CONSISTENT GENERATION AND MODELING OF DELAYED NEUTRON DATA ...............................................................................................51 3.1 METHODOLOGIES FOR DELAYED NEUTRON FRACTIONS .............52 3.1.1 Overview on Kinetics Equations.........................................................52 3.1.2 Direct (Physical) Beta..........................................................................54 3.1.3 Adjoint Weighted Beta Effective ........................................................55 3.1.4 k-ratio Beta Effective ..........................................................................57 3.1.5 Importance Factor................................................................................59 3.2 ENHANCING THE ACCURACY OF THE SIMPLIFIED K-RATIO METHOD......................................................................................................60 3.2.1 Methodology Development.................................................................61 3.2.2 Improved Calculation Procedure.........................................................64 3.2.3 Results and Discussion........................................................................66 3.2.4 Conclusion to Proposed k-ratio Method..............................................72 v 3.3 EVALUATION OF THE EFFECT OF STATE PARAMETERS................73 3.3.1 Burnup Effect ......................................................................................77 3.3.2 Moderator Void Feedback...................................................................81 3.3.3 Fuel Temperature (Doppler) Feedback ...............................................86 3.3.4 Control Rod Feedback.........................................................................89 3.3.5 Effect of Different Buckling Options..................................................92 3.3.6 Conclusions to State Parameter Effects...............................................95 3.4 PARAMETERIZATION OF THE DELAYED NEUTRON IMPORTANCE FACTOR ............................................................................97 3.4.1 Description of the Methodology..........................................................99 3.4.2 Results and Discussion........................................................................101 3.4.3 Conclusion on Parameterization of Importance Factor.......................104 3.5 SUMMARY...................................................................................................106 Chapter 4 IMPLEMENTATIONS OF THE METHODS...........................................108 4.1 IMPROVEMENTS TO LATTICE PHYSICS CODE ...................................109 4.2 IMPROVEMENTS TO NEUTRON KINETICS CODE ...............................115 4.3 MINI-CORE TRANSIENT BENCHMARK .................................................118 4.4 VERIFICATION OF THE IMPLEMENTATIONS ......................................119 4.5 SUMMARY....................................................................................................127 Chapter 5 MULTI-GROUP KINETICS CALCULATIONS .....................................129 5.1 INTRODUCTION TO MULTI-GROUP CALCULATIONS.......................130 5.2 SELECTION OF MULTI-GROUP STRUCTURES ....................................132 5.3 3-D THERMAL-HYDRAULICS AND NEUTRONICS COUPLED CALCULATIONS ........................................................................................145 5.4 SUMMARY...................................................................................................152 Chapter 6 SUMMARY AND CONCLUSIONS.........................................................154 References....................................................................................................................160 Appendix 97-Group Neutron Energy Structure in Lattice Calculations.....................164 vi LIST OF FIGURES Figure 1-1: General Overview of the Thesis Organization.........................................6 Figure 2-1: Thermal-Hydraulic 33-Channel Mapping for PBTT ...............................34 Figure 2-2: TRACE Thermal-Hydraulic Nodalization Diagram ................................35 Figure 2-3: PBTT Best Estimate Core Power for All Sets from the Table 2-1...........39 Figure 2-4: PBTT Extreme Case (No Scram) Core Power for All Sets from the Table 2-1...............................................................................................................40 Figure 2-5: LMW Transient Problem Initial Rod Positions (Vertical).......................43 Figure 2-6: LMW Transient Problem Final Rod Positions (Vertical) .......................43 Figure 2-7: LMW Transient Problem (Horizontal Cross Section) ............................44 Figure 2-8: LMW Power Comparison for Different Beta Methods............................46 Figure 2-9: