Development of 3D finite element methodology for neutron diffusion equations to estimate the reactivity change due to core deformation in sodium-cooled fast reactors

Abstract

Thermomechanical effects, irradiation, and structural restrictions result in tangled behavior of assemblies in sodium-cooled fast reactors (SFRs). Reactivity feedback caused by the assembly behavior (deformation or distortion) is one of the key parameters in the inherent safety analysis of fast reactor systems. Indirect analyses such as perturbation theory and limited reactivity coefficient application have been used because the conventional neutronics codes are mainly applicable only to regular mesh. Therefore, this study evaluates the feasibility of applying the multi-group neutron diffusion analysis based on Galerkin finite element method (GFEM) to the estimation of the reactivity changes due to core deformation, in a fast reactor that has hexagonal assemblies, using direct core modeling. GMSH has been used for whole core modeling and a 3-D GFEM solver has been developed for this study. To replicate assembly deformations in SFRs, 1-layer and 2-layer assembly modeling has been introduced. The reference reactivity changes were calculated by using the Monte Carlo code (Serpent2) based on continuous energy, and the reactivity changes from GFEM analysis were compared to the reference. The key idea of this study is that the neutron diffusion analysis based on low-order approximation can accurately evaluate the reactivity change sufficiently close to the result of the high-fidelity Monte Carlo simulation by appropriately using the error cancellation effect for the estimation of reactivity change due to core deformation. The numerical results show that diffusion analysis based on the GFEM using direct core modeling has a good feasibility to accurately estimate the reactivity changes caused by geometrical deformations in sodium-cooled fast reactor.