## Abstract

A surface current methodology is developed to respond to the need for treating the various levels of material heterogeneity in a double-heterogeneous multilayer multicell in processing neutron multigroup cross sections in the resonance as well as in the thermal energy range. First, the basic surface cosine current transport equations to calculate the energy-dependent neutron flux spatial distribution in the multilayered multicell are formulated. Slab, spherical, and cylindrical geometries, as well as square and hexagonal lattices and pebble-bed configurations with white or reflective cell boundary conditions, are considered. Second, starting from the surface cosine current formulation, a two-zone three-layer multicell formalism for reduction of the heterogeneous flux expressions to equivalent homogeneous flux expressions for the 'table' method is developed. The 'outer (right side)' as well as 'inner (left side)' Dancoff probabilities can be calculated for any particular layer. This formalism allows an infinite as well as a limited number of second-heterogeneity cells within a partial first-heterogeneity cell layer to be considered. Also, the number of the first- as well as second-heterogeneity cell types is quite general. An accurate, efficient, and compact interpolation procedure is used to calculate the basic collision probabilities. These are transmission and escape probabilities for shells in slab, cylindrical, and spherical geometries, as well as Dancoff probabilities for cylinders in square and hexagonal lattices. The use of the interpolation procedure is exemplified in a multilayer multicell approximation for the Dancoff probability, enabling a routine evaluation of the equivalence-based shielded resonance integral in highly complex lattices of slab, cylindrical, or spherical cells.

Original language | English |
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Pages (from-to) | 215-229 |

Number of pages | 15 |

Journal | Nuclear Science and Engineering |

Volume | 108 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jan 1991 |

Externally published | Yes |

## ASJC Scopus subject areas

- Nuclear Energy and Engineering