In reactor core nodal analysis, the dependence of few-group, homogenized cross sections on the local physical conditions (i.e., the thermal-hydraulic state and material composition) is commonly represented via multivariate interpolation in parameterized libraries. In this paper, we propose a novel approach to model the spectral effects of changes in the moderator density and in the concentrations of diluted boron and xenon. This method is based on the spectral rehomogenization technique developed at Framatome and TU Delft to account for neighbor effects on the nodal cross sections. We compute on the fly the variation in the infinite-medium energy-collapsing spectrum from a nominal state to a perturbed condition (i.e., with different values of the aforementioned state parameters). The dependence of the microscopic and macroscopic cross sections on these three variables is thus resolved without the standard multidimensional interpolation. This strategy reduces substantially the computational burden of the lattice calculation, the cross-section library memory requirements, and the run time of the on-line cross-section reconstruction. The proposed approach is applied to a pressurized-water-reactor UO₂ fuel assembly at zero burn-up, covering a wide range of the values of the water density and of the concentrations of boron and xenon. Both normal and abnormal operating conditions are considered. We show that, in most cases, cross-section changes are predicted with an accuracy comparable to that of traditional interpolation. Higher errors (but reasonably small compared to the range of accuracy of nodal computational tools) are only found at very low moderator densities, typical of accidental conditions. As further validation of the methodology, we simulate a heterogeneous multiassembly configuration. With this benchmark problem, we prove that the method can reconstruct the spectrum variation between the real environment in a perturbed state and the infinite lattice in the nominal one, thus modeling simultaneously the non-separable spectral effects of local physical conditions and internodal neutron leakage.

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We propose a two-dimensional (2-D) modal approach for spatial rehomogenization of nodal cross sections in light water reactor analysis. This algorithm aims to synthesize the variation in the 2-D intranodal distributions of the few-group flux and directional net currents between the core environment and the infinite-lattice approximation. Assembly discontinuity factors are also corrected. The method is validated on a broad set of pressurized-water-reactor benchmark problems. Its accuracy is assessed on both nodal quantities and the reconstructed pin-by-pin flux and power distributions. We show that the errors in the effective multiplication factor and assembly-averaged fission power significantly decrease compared to the calculation with infinite-medium homogenization parameters. In most cases, an improvement is also found at the pin level. A thorough discussion follows, which addresses the use of the 2-D neutron current information to compute the transverse-leakage distribution for the transverse-integrated nodal equations, the potential dual application of the method for rehomogenization and dehomogenization, and the quantification of the contributions of various environmental effects (spatial, spectral, and cross energy-space) to homogenization errors.

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Modeling spectral effects due to core heterogeneity is one of the major challenges for current nodal analysis tools, whose accuracy is often deteriorated by cross-section homogenization errors. AREVA NP recently developed a spectral rehomogenization method that estimates the variation of the assembly-averaged neutron flux spectrum between environmental and infinite-lattice conditions using a modal synthesis. The effectiveness of this approach is tied to the evaluation of the spectrum of the neutron leakage from or into the assembly in the environment. In this paper, we propose a method for the leakage spectral distribution building upon Fick's diffusion law. The neutron-exchange spectrum at a nodal interface is computed as a function of the gradient of the environmental flux spectrum, which is determined by the rehomogenization algorithm. This diffusive approach is applied to PWR benchmark problems exhibiting strong interassembly heterogeneity. We show that the method accurately reproduces the energy dependence of streaming effects, and that significant improvements in the input nodal cross sections, fission power and multiplication factor estimates are achieved at a low computational cost. The proposed model is compared with an alternative approach, that uses the fundamental-mode leakage spectrum obtained from the solution of the B₁ equations. This second strategy is generally less accurate, and can only provide an adequate approximation of the environmental leakage in weakly heterogeneous systems.

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Nodal diffusion is currently the preferred neutronics model for industrial reactor core calculations, which use few-group cross-section libraries generated via standard assembly homogenization. The infinite-medium flux-weighted cross sections fail to capture the spectral effects triggered in the core environment by nonreflective boundary conditions at the fuel-assembly edges. This poses a serious limitation to the numerical simulation of current- and next-generation reactor cores, characterized by strong interassembly heterogeneity. Recently, a spectral rehomogenization method has been developed at AREVA NP. This approach consists of an on-the-fly modal synthesis of the spectrum variation between the environmental and infinite-medium conditions. It uses information coming from both the nodal simulation and the lattice transport calculation performed to compute the standard cross sections. The accuracy of the spectral corrections depends on the choice of the basis and weighting functions for the expansion and on the definition of a realistic energy distribution of the neutron leakage. In this paper, we focus on the first aspect. Two tracks are researched: a combination of analytical functions (with a physically justified mode) and a mathematical approach building upon the Proper Orthogonal Decomposition. The method is applied to relevant pressurized-water-reactor benchmark problems. We show that the accuracy of the cross sections is significantly improved at reasonably low computational cost and memory requirement. Several aspects of the methodology are discussed, such as the interplay with space-dependent corrections. We demonstrate that this approach can model not only the spectral interactions between dissimilar neighbor assemblies but also the spectral effects due to different physical conditions (namely, multiplicative properties) in the environment and in the infinite medium.@en

This thesis develops novel first-principle methods to correct homogenization errors in nodal cross sections and discontinuity factors. Its aim is to improve the accuracy of nodal diffusion simulations of heterogeneous core configurations. This research builds upon previous work conducted at Framatome (Paris, France). It is based on a modal reconstruction of variations in the neutron flux distribution (in space and energy) between the core environment and the infinite-medium approximation, which is typically used in lattice transport calculations for few-group constant generation. Focus is given to the correction of the nodal cross sections. @en

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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