Extension of cross section homogenization method for particle-dispersed media to layered particles

A cross section homogenization method for media containing randomly dispersed particles, which was originally developed by Shmakov et al., and then was improved by Yamamoto et al., is extended to layered particles, such as coated fuel particles of gas-cooled reactors. A new extended formulation is derived for concentric double-layered spherical particles. This formulation is successfully implemented into a continuous energy Monte Carlo code MCNP and is applied to some examples including a simplified gas-cooled reactor core. The extended method for double-layered spherical particles provides as accurate results as the previously developed method for mono-layered particles does. For the simple gas-cooled reactor core, the new method reproduces keff within several hundreds of pcm as compared to the direct heterogeneous calculation in which double-layered spherical particles are explicitly distributed in the fuel compact. Whereas the previously developed method for mono-layered particles can be performed analytically, this new technique requires numerical integration, worsening the computation efficiency of the new method. However, this method allows one to perform Monte Carlo criticality calculations for double-layered particle-dispersed media with much less computing time than direct heterogeneous calculations.