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. @en

Few-group cross sections used in nodal calculations derive from standard energy collapsing and spatial homogenization performed during preliminary lattice transport calculations, that implicitly assume an infinite array of identical fuel-assemblies. The infinite-medium neutron flux used for cross section weighting does not account for environmental effects arising in case of heterogeneous configurations, which can lead to considerable leakages out of or into the assembly and thus invalidate the reflective boundary conditions used for the lattice simulation. Core-environment effects can also cause variations, with respect to the infinite-lattice calculation, in the reference cross section distribution used for few-group constant collapsing. These sources of inaccuracy prevent from reproducing with high fidelity the best estimate of the reaction rates and multiplication factor coming from the reference transport global solution. Rehomogenization techniques are therefore needed. The purpose of the present paper, which builds upon previous work done at AREVA in the area of rehomogenization, is to formalize a mathematical model that encompasses the different kinds of homogenization errors. In order to investigate the accuracy of the corresponding cross section corrections, numerical tests of an assembly-configuration sample are presented.

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