Multigroup, spatial kinetics for MOX -fueled LWRs based on harmonic analytical nodal method

There has been substantial evidence during the last several years that the core neutronics methods that have been developed for uranium fueled LWRs do not perform satisfactorily when applied to the same cores fueled with mixed oxide, or more generally to heterogeneous cores with very different neutron spectra. A two-dimensional, 97 group MOX benchmark problem was developed and applied to analyze deficiencies of the current generation of LWR analysis methods. The errors in the current two group, coarse mesh nodal diffusion methods were described in terms of four primary effects: (1) a homogenization effect, (2) a spatial discretization effect, (3) a group collapsing effect, and (4) a transport effect. The specific objective of the research here was to address the first three of these effects with the development of a four energy group advanced nodal method. Several methods have been proposed over the last several years for extending the current class of nodal methods to four energy groups. A Taylor series analysis was performed of the order of error in the various analytic nodal methods proposed. The analysis showed that the harmonic part of the error dominated in the Taylor expansion and it was therefore prudent to retain the harmonic solution in all four energy groups. A new nodal kernel referred to as the Harmonic Analytic Nodal Method (HANM) was developed and implemented within the framework of the nonlinear nodal method. HANM was applied to a MOX benchmark problem and results were compared to a 97 group reference solution. The errors in the two group solution were reduced by about 50% through the application of a four group HANM with minimal increase in the computational burden