Novel Resonance Self-Shielding Methods for Nuclear Reactor Analysis

Abstract

In the simulation of the behavior of neutrons in a nuclear reactor, there has long been a dichotomy in solution techniques. One can use Monte Carlo methods, known to be very accurate and problem agnostic but also very costly, or deterministic methods, known to be more computationally efficient but also requiring tuning to a specific application. As designers rely more and more heavily on predictive simulation, higher fidelity and more problem agnostic deterministic methods are desired. This thesis seeks to push these deterministic methods towards that goal of higher fidelity in the context of multigroup cross section generation and resonance self-shielding. This work has two primary objectives: to quantitatively assess the efficacy of current self-shielding approximations and to propose new self-shielding methods. These objectives are cast primarily in the context of mutual self-shielding, the effect of one nuclide's resonances on the neutron reaction rate with another nuclide. The first objective is accomplished through the development of a framework for the evaluation of self-shielding methods. This framework is analogous to a unit test suite in software engineering, in that specific aspects of physics modeled by a self-shielding method are isolated. The framework is used on numerous existing methods, and highlights the successes and failures of these methods on very simple problems. This objective is also accomplished via an analysis of the consequences of neglecting the angular dependence of multigroup cross sections in the solution to the multigroup neutron transport equation. The second objective is accomplished by proposing two new methods: the subgroup method with interference cross sections and ultrafine with simplified scattering. The former uses a fitting method to find the effect of interfering nuclides on the subgroup levels of a primary nuclide, allowing mutual self-shielding effects to be treated natively inside the subgroup method without increasing algorithmic complexity. The latter is a hybrid of the subgroup method and ultrafine methods, using an ultrafine energy mesh on the left hand side of the transport equation with the scatter source of the subgroup method on the right hand side. These two methods are tested in the context of the evaluation framework alongside classical methods. Although it shows promise on some simple problems, the subgroup method with interference cross sections was seen to exhibit shortcomings on problems with many nuclides. Ultrafine with simplified scattering was found to perform very well on all problems in the test suite.