A two-dimensional, semi-analytic expansion method for nodal calculations

Abstract

Most modern nodal methods used today are based upon the transverse integration procedure in which the multi-dimensional flux shape is integrated over the transverse directions in order to produce a set of coupled one-dimensional flux shapes. The one-dimensional flux shapes are then solved either analytically or by representing the flux shape by a finite polynomial expansion. While these methods have been verified for most light-water reactor applications, they have been found to have difficulty predicting the large thermal flux gradients near the interfaces of highly-enriched MOX fuel assemblies. A new method is presented here in which the neutron flux is represented by a non-seperable, two-dimensional, semi-analytic flux expansion. The main features of this method are (1) the leakage terms from the node are modeled explicitly and therefore, the transverse integration procedure is not used, (2) the corner point flux values for each node are directly edited from the solution method, and a corner-point interpolation is not needed in the flux reconstruction, (3) the thermal flux expansion contains hyperbolic terms representing analytic solutions to the thermal flux diffusion equation, and (4) the thermal flux expansion contains a thermal to fast flux ratio term which reduces the number of polynomial expansion functions needed to represent the thermal flux. This new nodal method has been incorporated into the computer code COLOR2G and has been used to solve a two-dimensional, two-group colorset problem containing uranium and highly-enriched MOX fuel assemblies. The results from this calculation are compared to the results found using a code based on the traditional transverse integration procedure.