A Pebble Bed Reactor cross section methodology

A method is presented for the evaluation of microscopic cross sections for the Pebble Bed Reactor (PBR) neutron diffusion computational models during convergence to an equilibrium (asymptotic) fuel cycle. This method considers the isotopics within a core spectral zone and the leakages from such a zone as they arise during reactor operation. The randomness of the spatial distribution of fuel grains within the fuel pebbles and that of the fuel and moderator pebbles within the core, the double heterogeneity of the fuel, and the indeterminate burnup of the spectral zones all pose a unique challenge for the computation of the local microscopic cross sections. As prior knowledge of the equilibrium composition and leakage is not available, it is necessary to repeatedly re-compute the group constants with updated zone information. A method is presented to account for local spectral zone composition and leakage effects without resorting to frequent spectrum code calls. Fine group data are pre-computed for a range of isotopic states. Microscopic cross sections and zone nuclide number densities are used to construct fine group macroscopic cross sections, which, together with fission spectra, flux modulation factors, and zone buckling, are used in the solution of the slowing down balance to generate a new or updated spectrum. The microscopic cross-sections are then re-collapsed with the new spectrum for the local spectral zone. This technique is named the Spectral History Correction (SHC) method. It is found that this method accurately recalculates local broad group microscopic cross sections. Significant improvement in the core eigenvalue, flux, and power peaking factor is observed when the local cross sections are corrected for the effects of the spectral zone composition and leakage in two-dimensional PBR test problems.