(An) equivalence relation and grey dancoff factor calculated by monte carlo method for irregular fuel assemblies

Abstract

The equivalence theorem providing a relation between a homogeneous and a heterogeneous medium has been used in the resonance calculation for the heterogeneous system. The accuracy of the resonance calculation based on the equivalence theorem depends on how accurately the fuel collision probability is expressed by the rational terms. The fuel collision probability is related to the Dancoff factor in closely packed lattices. The calculation of the Dancoff factor is one of the most difficult problems in the core analysis because the actual configuration of fuel elements in the lattice is very complex. Most reactor physics codes currently used are based on the roughly calculated black Dancoff factor, where total cross section of the fuel is assumed to be infinite. Even the black Dancoff factors have not been calculated accurately though many methods have been proposed. The equivalence theorem based on the black Dancoff factor causes some errors inevitably due to the approximations involved in the Dancoff factor calculation and the derivation of the fuel collision probability, but they have not been evaluated seriously before. In this study, a Monte Carlo program - G-DANCOFF - was developed to calculate not only the traditional black Dancoff factor but also grey Dancoff factor where the medium is described realistically. G-DANCOFF calculates the Dancoff factor based on its collision probability definition in an arbitrary arrangement of cylindrical fuel pins in full three-dimensional fashion. G-DANCOFF was verified by comparing the black Dancoff factors calculated for the geometries where accurate solutions are available. With 100,000 neutron histories, the calculated results by G-DANCOFF were matched within maximum 1% and in most cases less than 0.2% with previous results. G-DANCOFF also provides graphical information on particle tracks which makes it possible to calculate the Dancoff factor independently. The effects of the Dancoff factor on the criticality cal...