TRANSFER PROBABILITY CALCULATION FOR SQUARE PIN CELLS BY 2-DIMENSIONAL GAUSSIAN QUADRATURE

Efficient methods for the evaluation of collision, escape, and transmi ssion probabilities in the flat-flux, isotropic approximation have bee n developed for various heterogeneous pin cells. The cells may be eith er cylindricalized or square with the moderator treated as either a si ngle region or subdivided into the four segments between the diagonals . The conventional ''Flurig'' scheme by Carlvik is applied to the circ ular regions and to the four partial surfaces in the cylindricalized c ases. For the noncircular regions and surfaces of the square-cell type s, the numerical integration in both the radial and the angular direct ion is based on Gaussian quadrature. The mesh layout is designed with due regard to the directions to corners and vertices to avoid overlap between neighboring regions or surfaces. For rays outside the circular regions, the integration in the radial direction is performed analyti cally. Furthermore, the symmetry properties as well as the reciprocity and conservation relations are utilized to the maximum possible exten t. Thus, high efficiency is achieved, requiring only a few mesh points in both directions as demonstrated by application to various test cas es from the literature.