Development of high fidelity methods for 3D Monte Carlo transient analysis of nuclear reactors

Abstract

Monte Carlo is increasingly being used to perform high-fidelity, steady-state neutronics analysis of power reactor geometries on today's leadership class supercomputers. Extending Monte Carlo to time dependent problems has proven to be a formidable challenge due to the significant computational resource and data processing requirements. In this thesis, a transient methodology is proposed and implemented to enable accurate and computationally tractable time dependent Monte Carlo analysis. The frequency transform method has been described and implemented in Monte Carlo for the first time. The attractiveness of this method lies in its ability to accurately capture the space and time dependent distribution of the delayed neutron source throughout a transient. Nuances to the algorithmic implementation are described and validated through a series of simple analytical test problems. Comparison with the adiabatic method currently employed for Monte Carlo transient analysis shows significant improvement in the spatial distribution and magnitude of the power for a negative reactivity insertion transient in the 2D and 3D C5G7 geometry. To aid in understanding the effect of statistical uncertainty in the tallied quantities on the time dependent flux solution, a simplified point kinetics model was developed and used for insightful analysis on simple transient test problems. This revealed how the time dependent flux profiles for a series of independent trials can be approximated by a normal distribution at low uncertainties in the tallied reactivity, but deviates from a normal distribution at relatively modest uncertainties in reactivity. Given the compuational constraints of solving large problems, having a simple model that can provide insight on the expected behavior and flux distribution can be very valuable. The frequency transform methodology belongs to a class of indirect space-time factorization methods that perform high-order calculations (e.g. Monte Carlo) over long time steps and low-order, computationally-efficient calculations (e.g. Point Kinetics) over short time steps as an approach to balance performance and accuracy. The coarse mesh finite difference (CMFD) diffusion operator is employed as the low-order solver in Monte Carlo transient analysis for the first time. The CMFD diffusion operator is attractive due to its potential to increase the time step size between the computationally expensive high-order solves. Implementing this methodology is important as continuous energy Monte Carlo is reactor-agnostic and able to treat complex geometries without difficulty, opening up the possibility of solving transients on new experimental geometries for which there is little data.