A Hybrid S_n-Diffusion Theory Computational Scheme for Efficient Neutronic Calculations of Externally Moderated Gas Core Reactors

Examination of externally moderated gas core reactor (GCR) neutronic calculations indicates that, in general, neutron diffusion theory is invalid and a higher order approximation to the transport equation needs to be employed. The S_n approximation yields accurate results but can require relatively long CPU computation times. A one-dimensional hybrid S_n-diffusion theory model is developed that employs the S_n approximation in the gas core region and for the first several mean free paths into the reflector region until the angular flux converges to its characteristic distribution in the reflector; diffusion theory is then used in the remaining portion of the reflector. A critical aspect of the hybrid scheme is to ensure proper interfacing between the S_n transport theory and diffusion theory approximations at the mathematical interface where the S_n-to-diffusion theory transition occurs. It is found that the point of transition from S_n theory to diffusion theory can be located closer to the core-reflector interface as the gas density in the core is reduced. Calculations performed on spherical GCR configurations for fuel gas densities ranging from 10¹⁸ to 10²⁰ atom/cm³ and with both uniform and nonuniform fuel gas density distributions in the core show that the hybrid model gives accurate k_eff values and flux distributions as compared with results from the standard S_n approximation. For four energy groups and reflector thicknesses of 0.5 to 1.0 m, the hybrid model is roughly five times faster than a standard S_n calculation. For multigroup calculations on GCRs with thick (1 to 2 m) external moderator reflectors, the hybrid model is found to be about an order of magnitude faster than a standard S_n calculation.