Asymptotic Homogenized SP2 Approximations to the Neutron Transport Equation.

Asymptotic;SP2;Diffusion;Homogenized;Transport;Cross Section;Multigroup;Nuclear Engineering and Radiological Sciences;Engineering;Nuclear Engineering and Radiological Sciences

Saller, ThomasMartin, William R ;

University of Michigan

关键词: Asymptotic;    SP2;    Diffusion;    Homogenized;    Transport;    Cross Section;    Multigroup;    Nuclear Engineering and Radiological Sciences;    Engineering;    Nuclear Engineering and Radiological Sciences;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/116754/tgsaller_1.pdf?sequence=1&isAllowed=y

瑞士|英语

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

【 摘 要 】

Many current-generation reactor analysis codes use the diffusion approximation to efficiently calculate neutron fluxes. As a result, there is considerable interest in methods that provide a more accurate diffusion solution without significantly increasing computational costs. In this work, an asymptotic analysis, previously used to derive a homogenized diffusion equation for lattice-geometry systems, is generalized to derive a one-dimensional, one-group homogenized SP2 equation as a more accurate alternative to the standard homogenized diffusion equation. This analysis results in new diffusion coefficients and an improved formula for flux reconstruction. The asymptotic SP2 formulation is compared to standard SP2, asymptotic diffusion, and standard diffusion for several test problems. Both the eigenvalue and reconstructed fluxes are examined. In general, the asymptotic equations are more accurate than the standard equations, and SP2 is more accurate than diffusion theory, especially for optically small systems.The calculation of more accurate multigroup cross sections is considered. Standard multigroup cross sections are designed to preserve both the (multigroup) infinite medium neutron spectrum and eigenvalue; this property still holds if the multigroup cross sections are modified by a multiplicative scaling factor. In this thesis, a formula for the scaling factor is derived that makes the modified multigroup cross sections satisfy the asymptotic diffusion or SP2 limit of the neutron transport equation. Numerical simulations demonstrate that the scaled multigroup cross sections yield more accurate results than unscaled cross sections for multigroup eigenvalue problems in finite media.Finally, the asymptotic analysis is then extended to a hypothesized multigroup, spatially homogenized SP2 equation. The hypothesized equation uses standard homogenized cross section definitions, but leaves the diffusion coefficients undefined. The asymptotic analysis of the multigroup SP2 equation results in a monoenergetic SP2 equation, similar to the one obtained for the continuous energy transport equation. By requiring that the hypothesized multigroup SP2 equation have the same asymptotic limit as the continuous energy transport equation, we establish a condition that the additional multigroup diffusion coefficient, D2g, must satisfy. Two logical definitions for D2g are chosen, but numerical results indicate that they are inconsistent in their accuracy, and are frequently outperformed by standard multigroup diffusion and SP2.