A coarse mesh radiation transport method for 2-D hexagonal geometry

Abstract

In this paper, a whole-core stochastic–deterministic hybrid coarse mesh transport method is extended to 2-D hexagonal geometry. This method may be used to calculate the eigenvalue and explicit pin fission density profile of hexagonal reactor cores. It models the exact detail within complex heterogeneous cores without homogenizing regions or materials, and neither block-level nor core-level asymmetry poses any limitations to the method. It solves eigenvalue problems by first splitting the core into a set of coarse meshes, and then using Monte Carlo methods to create a library of response expansion coefficients, found by expanding the angular current in phase-space distribution using a set of polynomials orthogonal on the angular half-space defined by mesh boundaries. The coarse meshes are coupled by the angular current at their interfaces. A deterministic sweeping procedure is then used to iteratively construct the solution.The method is evaluated using benchmark problems based on a gas-cooled, graphite-moderated high temperature reactor. The method quickly solves problems to any level of detail desired by the user. In this paper, it is used to explicitly calculate the fission density of individual fuel pins and determine the reactivity worth of individual control rods. In every case, results for the core multiplication factor and pin fission density distribution are found within several minutes. Results are highly accurate when compared to direct Monte Carlo reference solutions; errors in the eigenvalue calculations are on the order of 0.02%, and errors in the pin fission density average less than 0.1%.