An Asymptotic, Homogenized, Anisotropic, Multigroup Diffusion Approximation to the Neutron Transport Equation.

Homogenization;Multigroup Diffusion;Discontinuity Factors;Asymptotic Analysis;Variational Analysis;Anisotropic Diffusion;Nuclear Engineering and Radiological Sciences;Engineering;Nuclear Engineering & Radiological Sciences

Trahan, Travis JohnMartin, William R. ;

University of Michigan

关键词: Homogenization;    Multigroup Diffusion;    Discontinuity Factors;    Asymptotic Analysis;    Variational Analysis;    Anisotropic Diffusion;    Nuclear Engineering and Radiological Sciences;    Engineering;    Nuclear Engineering & Radiological Sciences;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/107152/tjtrahan_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Due to its relatively low computational cost, the neutron diffusion approximation remains one of the most commonly-used computational tools for reactor analysis. Although diffusion requires more approximations than higher-order ;;transport;; methods such as SN and Monte Carlo, the computational cost of these methods prohibits their widespread general use. It has long been known that diffusion is anisotropic in heterogeneous reactors, i.e., neutrons diffuse more rapidly in some directions than others. While in many reactors the anisotropic diffusion effects are negligible, in lattices containing voided or optically-thin channels these effects are significant. It is therefore desirable that the homogenized diffusion coefficient be a tensor.In this thesis, a multigroup, homogenized, anisotropic diffusion equation is derived asymptotically from the exact Boltzmann transport equation for large, 3-D, multiplying systems with a periodic lattice structure. The primary mathematical assumption is that the system is a large, periodic lattice, and that the length scale of a lattice element is small relative to the total system size. The leading-order term of the asymptotic flux has a standard form, i.e., it is the product of a homogenized diffusion solution and a transport solution for an infinite, periodic system. The first-order correction term significantly improves the accuracy of the reconstructed fluxes.The goal of this research is to derive a complete homogenized, multigroup diffusion theory using rigorous mathematical analyses, rather than using ad hoc approximations, as have typically been done previously. Specifically, we use an asymptotic method to derive the homogenized diffusion equation, and we use a variational analysis to obtain ;;Marshak;;- and ``variational;;;;-like boundary conditions specifically for lattice geometries, and interface conditions that include flux and current discontinuity factors.We also provide extensive numerical simulations that demonstrate the high accuracy of the asymptotic method. Our results indicate that when the assumptions of the asymptotic analysis are met, the use of the asymptotic diffusion coefficient can lead to significantly improved estimates of the reactor eigenvalue and the neutron flux, otherwise it is comparable in accuracy. The asymptotic flux reconstruction is significantly more accurate than the standard flux reconstruction, especially near the outer regions of the reactor core.