Assembly Discontinuity Factors for the Neutron Diffusion Equation discretized with the Finite Volume Method. Application to BWR

Abstract

The neutron flux spatial distribution in Boiling Water Reactors (BWRs) can be calculated by means of the Neutron Diffusion Equation (NDE), which is a space-and time-dependent differential equation. In steady state conditions, the time derivative terms are zero and this equation is rewritten as an eigenvalue problem. In addition, the spatial partial derivatives terms are transformed into algebraic terms by discretizing the geometry and using numerical methods. As regards the geometrical discretization, BWRs are complex systems containing different components of different geometries and materials, but they are usually modelled as parallelepiped nodes each one containing only one homogenized material to simplify the solution of the NDE. There are several techniques to correct the homogenization in the node, but the most commonly used in BWRs is that based on Assembly Discontinuity Factors (ADFs). As regards numerical methods, the Finite Volume Method (FVM) is feasible and suitable to be applied to the NDE. In this paper, a FVM based on a polynomial expansion method has been used to obtain the matrices of the eigenvalue problem, assuring the accomplishment of the ADFs for a BWR. This eigenvalue problem has been solved by means of the SLEPc library.

Multigroup neutron diffusion equation with the finite volume method in reactors using MOX fuels

“…Second, the heterogeneous neutron flux continuity and the current continuity should be accomplished at the inner faces of the discretized geometry. The heterogeneous flux continuity can be calculated by using the Assembly Discontinuity Factors (ADFs) as explained in [7]. These continuity conditions are expressed in Equations 5-6, for the cells i and l, which are adjacent to face j.…”

“…Among these works, those developed in [4,5] can calculate multiple eigenvalues, but the results are accurate in fine meshes. For improving the solution in coarser meshes, the authors developed a polynomial expansion method in [6,7]. This method works accurately in LWR, but it was applied to the 2 energy group approach, without upscattering and with fission production in the first group.…”

“…Thus, one obtains better computational times with this method in comparison with the solution of the generalized eigenvalue problem. For these reasons, this algorithm is not only an extension of the method developed in [6,7], but also an improvement. It should be pointed out that this algorithm can be applied to any number of energy groups with upscattering, but there is one restriction: no upscattering to the first energy group.…”

Response Surface Methodology Control Rod Position Optimization of a Pressurized Water Reactor Core Considering Both High Safety and Low Energy Dissipation

“…For simplification, the Neutron Diffusion Equation (NDE) is also used. These equations can be solved by the Finite Different Method (FDM) [5][6][7], the Finite Volume Method (FVM) [8][9][10][11], the Finite Element Method (FEM) [10,[12][13][14], etc. Normally, the neutron flux density distribution matches the fission heat source distribution.…”

Development of a 3D Modal Neutron Code with the Finite Volume Method for the Diffusion and Discrete Ordinates Transport Equations. Application to Nuclear Safety Analyses

“…The matrix M 1,2 contains the terms corresponding to V i νΣ i f,2 of Equation 3.76. This method was applied in the Neutron Diffusion Equation and published in Bernal et al 2016a. In addition, one can subdivide matrices L g,g and M g,g as in Equations 3.80-3.82. The important issue of this subdivision is that matrix LA g is a diagonal matrix and its dimension is N c .…”