Simplified Treatments of Anisotropic Scattering in LWR Core Calculations

Abstract

The validity of various simplified treatments of anisotropic scattering is investigated in typical LWR configurations that simulate PWR, BWR, and APWR. In addition to the explicit treatment of anisotropic scattering, the diagonal approximation of anisotropic scattering matrixes and the transport corrected cross section with the assumption of isotropic scattering are also tested. Calculation results indicate that the anisotropic scattering matrix of the P1 component would be explicitly treated to obtain accurate results in the present calculations. The P2 or higher order anisotropic scattering matrix could be approximated by the diagonal approximation while maintaining the calculation accuracy. In addition to the above investigation, the physical meaning of the transport corrected cross section used in a transport calculation is discussed through a simple one-group fixed-source benchmark problem with anisotropic scattering. Though the transport corrected cross section is usually used to consider the P1 scattering cross section, the calculation results and discussion clarify that the transport corrected cross section is not mathematically consistent with the consideration of the P1 scattering cross section. The transport corrected cross section always implicitly includes an infinite order of anisotropic scattering cross sections when it is used in a transport calculation. Since the higher order anisotropic scattering component tends to reduce neutron leakage from a core, the calculated k-effective with the transport corrected cross section would be overestimated. This suggests the cause of the overestimation of k-effective by transport calculation with the transport corrected cross section obtained by in-scatter approximation.

MPACT 4.4 Theory Manual

“…For many applications, a suitable approximation is applied that replaces a linearly anisotropic scattering operator by an isotropic scattering operator with approximate transport-corrected cross sections. One such approximation is the outscatter method [157]. In the outscatter method, the quantity μ0 Σ s is subtracted from the total scattering cross section Σ s and the diagonal elements of the G × G scattering matrix.…”

Gas-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model

“…The nine energy groups structure is provided in Table 6. The isotope transport cross sections are based on a "flux-limited" approximation [18] or in-scatter approximation with scalar flux as a weighting function [19]:…”

Fluoride-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model

“…There are important limitations to the approach herein since the neutron leakage in this reactor significantly affects the local spectrum [10] The isotope transport cross sections are based on a "flux-limited" approximation [11] or inscatter approximation with scalar flux as a weighting function [12]:…”