Exact-to-Precision Generalized Perturbation Theory for Nuclear Reactor Analysis.

摘要

This dissertation is devoted to developing a unified framework under the name of exact-to-precision generalized perturbation theory (EPGPT) which combines perturbation theory with reduced basis methods and range finding algorithms for reactor analysis and design calculations. This framework places high premium on reducing the associated computational overhead via the reduced basis methods in order to enable the use of perturbation theory in routine reactor calculations. For this work, EPGPT will be used to evaluate the variations in the neutron flux due to various perturbations such as cross sections perturbations, enrichment variations, poison loading, temperature, etc., at the lattice physics level, often referred to as assembly level calculations. To ensure that the EPGPT predications are robust, range-finding algorithm is utilized to make quantitative bounding statements about the errors in the predications of responses for all possible model perturbations. In contrast to traditional generalized perturbation theory, EPGPT allows one to efficiently calculate higher orders of variations for the responses of interest with very inexpensive computational cost.;The major focus of this research is to develop an efficient computational algorithm employing the EPGPT to address the explosion in dimensionality whether at the input parameter level or at the response level. Although the proposed algorithm is only demonstrated by using radiation diffusion/transport models for the purpose of reactor design analysis, it can be applied to many different problems because of it is generic in nature. By way of examples, these new developments could be employed in core simulation to accurately estimate the few-group cross sections variations resulting from perturbations in neutronics and thermal-hydraulics core conditions. These variations are currently being described using a look-up table approach, where thousands of assembly calculations are performed to capture few-group cross sections variations for the downstream core calculations. Other applications include the efficient evaluation of surrogates for applications that require repeated model runs such as design optimization, inverse studies, uncertainty quantification, and online core monitoring.