Environment Insensitive Reflector Homogenization Through a Response Matrix Equivalence Method Based on the Relaxed Flux Continuity Equation

A novel approach to modeling the response of a homogenized region has been applied for reflector calculations. This method was developed and tested in the DRAGON5/DONJON5 version 5 environment coupled to the BRISINGR nodal diffusion solver and the open-source NSSF module.This method leads to the introduction of a discontinuity matrix, called the F matrix, which contains parameters that are analogous to discontinuity factors (DFs). The matrix relaxes the flux continuity equation between nodes by introducing new free parameters. This work introduces the linear equivalent reflector method, which proceeds in two steps: (1) The F matrix is calculated from the results of a simplified one-dimensional or two-dimensional (2D) fuel-reflector geometry calculated in transport theory, and (2) the matrix is introduced into full-core calculations in diffusion theory using the nodal expansion method (NEM) or the analytic nodal method (ANM).In this case of the first step, two-group response matrices are obtained so as to preserve the net currents and reaction rates of the reference transport calculation over the macrogeometry with two different sets of cross sections. The calculation of the F matrix is straightforward, noniterative, and extendable to any number of groups.This approach was validated for a 2D small-core representation of a pressurized water reactor with different fuel loadings and a steel reflector. The calculations show that standard NEM and ANM codes are capable of handling such matrices as input, while giving results comparable to reflectors modeled by DFs. These results show that the approach presented in this paper may be a suitable option for calculating reflector parameters for nodal diffusion calculations.