Spectral Rehomogenization of Nodal Cross-Sections via Proper Orthogonal Decomposition

Abstract

Industrial reactor-core calculations mostly resort to the nodal-diffusion methodology, relying on the homogenization paradigm for the generation of few-group assembly cross-sections. The incapability of cross-sections condensed with the infinite-medium spectrum to model core-environment spectral effects is one of the major limitations in the numerical simulation of current- and next-generation reactor cores, characterized by strongly heterogeneous geometrical layouts. AREVA NP has recently proposed a spectral-correction method to reproduce the variation of the neutron spectrum between environmental and infinite-lattice conditions by means of a modal expansion approach, which is solved for by Galerkin or Petrov-Galerkin projection of the local fine-group neutron balance equation over a set of weighting operators. The accuracy of this method significantly depends on the choice of the basis and test functions. Purely analytical modes turn out to be often inadequate to reproduce the strongly varying shape of the spectrum deformation in the reactor core. The present paper investigates an alternative strategy building upon the Proper Orthogonal Decomposition (POD). This approach relies on the calculation of the optimal (in a least-square sense) orthonormal basis functions for the space spanned by a set of snapshots of the reference spectrum variation. In our work, we test the capability of the POD modes to contain characteristics of the spectral interactions between fuel-assemblies in the reactor core. It is shown that the POD-Galerkin-based spectral rehomogenization can reconstruct very accurately the spectrum in the real environment.