Analysis of 2-D LWR benchmarks with an interface current method for solving the integral transport equation

Abstract

Sanchez (1977) developed an interface current method in combination with the small scale collision probability (CP) method for solving the integral transport equation for LWR fuel assemblies. The fuel rod, cladding and associated coolant in a pin cell was considered explicitly. In this method, the angular flux at region interfaces is expanded separately in the incoming and outgoing directions in terms of linearly independent functions called representation functions. He considered only upto three terms in this expansion (corresponding to P 1 half-space expansion). Later on, Mohanakrishnan (1982) considered six terms (half-space P 2 expansion) in the angular flux expansion at region interfaces of rectangular homogeneous cells (i.e. with pincell smearing). It showed that when strong heterogeneities like control rod or burnable poison are present, more than three terms are required in the expansion of angular flux. In this paper, we have extended the method of Sanchez for LWR fuel assemblies by considering six terms (half-space P 2 expansion) in the expansion of angular flux at region interfaces. We have, further, identified the most important terms in the expansion and shown that generally two terms are sufficient and to improve these results one may have to consider four terms in the expansion. Further, in the presence of a control rod one will have to consider at least three terms in the expansion of angular flux.