Transient Methods for Pin-Resolved Whole Core Transport

Three-dimensional, full core modeling with pin-resolved detail has become the state of the art in computational simulation for nuclear reactors. The primary objective of this dissertation is to develop a set of advanced algorithms to accurately and efficiently solve the time-dependent neutron transport equations with pin-resolved detail. The 2D/1D approach is used to reduce the computational burden of the direct 3D calculation of the neutron transport equation. The radial 2D solver utilizes the 2D Method of Characteristics (MOC) solution, and the 1D solver utilizes a 1D nodal solution. The 2D and 1D solutions are coupled using transverse leakages. In addition, a multi-group matrix (MGM) CMFD method is implemented, where the whole 3D matrix is formed and solved to significantly accelerate convergence and to reduce the computational burden for practical applications. The significant and original element of this thesis is the extension of the 2D-1D method to time-dependent transport applications using a Transient Multi-Level (TML) method. The TML method significantly reduces the number of high order transport calculations, and the Predictor-Corrector Quasi-Static Method (PCQM) iteration scheme couples the 3D-Transport/3D-CMFD level and the 3D-CMFD/EPKE level. This research also addresses a potential problem with the TML method, which is the potential for negative flux/precursor number density, because of the large time steps used for the MOC solver with the Backward Euler discretization scheme. The numerical stability issue was studied using the Point Kinetics Equations (PKEs), and an exponential transformation method was implemented to insure stability of the TML algorithm for all applications. A Fourier analysis technique was also applied to investigate the convergence behavior of the time-dependent neutron transport equation. The theoretical results show good agreement with the numerical results. Finally, numerical results are presented to verify and validate the transient algorithms developed in this work. The results for the SPERT III test 86 and test 60 RIA test cases are provided, and the results of MPACT are in reasonable agreement with the experimental data. Finally, a Watts Bar super prompt transient is performed to show the capability to perform large scale PWR simulations, which is the ultimate objective of the work here.PhDNuclear Engineering and Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133353/1/angzhu_1.pd