Analytic function expansion nodal (AFEN) method for solving multigroup neutron simplified P3 (SP3) equations in hexagonal-z geometry

Abstract

In this paper, analytic function expansion nodal (AFEN) method was developed to solve multi-group and multi-dimensional neutron simplified P3 (SP3) equation in reactor cores with hexagonal fuel assembly. In this method, the intranodal fluxes are expanded into a set of analytic basis functions for each group and Legendre moment. Fourteen boundary conditions has been considered that constrain the intranodal flux distributions in the hexagonal-z node, which include twelve radial surface-averaged partial currents and two axial surface-averaged partial currents. The code takes few-groups cross sections produced by a lattice code and calculates the effective multiplication factor (keff), flux in multi-group energy, reactivity, and the relative power density at each fuel assembly. Finally, the solution accuracy is tested for the two and three dimensional IAEA benchmark problem. The 3D IAEA problem has been calculated for three different cases. The numerical results demonstrate that the SP3 AFEN method exhibits better accuracy compared to diffusion method especially when the control materials are inserted in the core.