High-order cross-section homogenization method

A high-order cross-section homogenization method based on boundary condition perturbation theory is developed to improve the accuracy of nodal methods for coarse-mesh eigenvalue calculations. The method expands the homogenized parameters such as the cross-sections and the neutron flux discontinuity factor in terms of the node surface current-to-flux ratio. The expansion coefficients are evaluated during the nodal calculations using additional precomputed homogenization parameters. As a result, it is possible to correct (update) the homogenized parameters to arbitrary order of accuracy for the effect of reactor core environment (fuel assembly neutron leakage) with very little computational effort in the core calculation. The reconstructed fine-mesh flux (fuel-pin power) is a natural byproduct of the new method. A benchmark problem typical of a BWR core is analyzed in one dimension, monoenergetic diffusion theory by modifying a nodal method based on a bilinear, flat as well as a fine-mesh intranodal flux shape. The homogenized parameters are first computed using exact (fine-mesh) albedos and compared to those determined from a fine-mesh core calculation. Two nodal (coarse-mesh) examples are given to show how well this approach works as a higher-order perturbation method is utilized. The paper concludes by showing that this method succeeds in giving excellent results for cores that may be difficult to model using standard nodal methods.