Refinement of analytic function expansion nodal method with transverse gradient basis functions and interface flux moments

Abstract

The Analytic Function Expansion Nodal (AFEN) method has been successfully used in reactor analysis for its accuracy and flexibility in various geometries. Proposed is a refinement of AFEN method to enhance the accuracy and flexibility even more by increasing the number of flux expansion terms in a way that the original basis functions are combined with the transverse-direction linear functions. The refined AFEN method can describe the flux shape in the nodes more accurately, since the added flux expansion terms still satisfy the diffusion equation. The additional nodal unknowns, the interface flux moments, are introduced, and the additional constraints required are provided by the continuity conditions of the interface flux moments and interface current moments. By increasing the number of interface flux moments and interface current moments with different weighting functions, the refined AFEN method can be generalized consistently to describe the flux shape more accurately with increased flux expansion terms. Also presented is an algebraically exact method for removing the numerical singularity that can occur in any analytic nodal methods when the core contains nearly no-net-leakage nodes. The refined AFEN method is tested on the Organization for Economic Cooperation and Development (OECD)-L336 MOX benchmark problem in rectangular geometry, and VVER-440 benchmark problem in hexagonal geometry. For a three-dimensional rectangular problem, the Langenbuch, Maurer and Werner problem is tested. To test the singularity removal method in rectangular geometry and hexagonal geometry respectively, the Electric Power Research Institute (EPRI)-9R problem and the VVER-440 problem are modified so that they contain no-net-leakage nodes. The results show that the method improves not only the accuracy in predicting the flux distribution but also the computing time, and that it can replace the corner-point fluxes with the interface flux moments without accuracy degradation, unl...