NEMHEX solution of benchmark problems on thermal and fast breeder reactor cores with hexagonal lattice

Abstract

This paper gives the solution of some benchmark problems for reactor core calculations in hexagonal geometry using a computer code NEMHEX (Nodal Expansion Method for HEXagonal geometry). The problems cover a wide range of thermal reactor cores including large heavy water, fast breeder and VVER reactors in both two and three dimensional. The code is based on higher order nodal expansion method (NEM) for the solution of the neutron diffusion equation in 3-D hexagonal geometry. In this method, flux in each mesh/node and energy group is expanded in terms of polynomial up to third order in X–Y plane and fourth order in axial direction (Z). Weighted residual method is used to calculate the higher order expansion coefficients of the polynomials. Both the partially integrated radial and axial leakages are approximated by the quadratic polynomial. Higher order polynomial expansion [with respect to the work by Lawrence (DIF3D nodal neutronics option for two-and three-dimensional diffusion theory calculations in hexagonal geometry, 1983)] of flux as well as leakage in each node improves the accuracy in power distribution of VVER-1000 type reactor (which is having large size lattice) in terms of maximum reduction in error from 8 to 2%. The final inhomogeneous response matrix equation involves spatial moments of nodal flux and surface averaged partial currents across the surfaces of node. These equations are solved using conventional fission source iteration. This code is used for calculation of effective multiplication factor, neutron flux and fission power distribution. The results of the analysis establish the adequacy of NEMHEX for thermal as well as fast reactor core calculations in hexagonal geometry.