Anisotropic diffusion of neutral particles in stochastic media

This work introduces a new homogenization theory for the transport of particles in stochastic media. This theory utilizes a nonclassical form of the Boltzmann equation in which the locations of the scattering centers in the system are correlated and the distance-to-collision is not exponentially distributed. We take the diffusion limit of this equation and derive an anisotropic diffusion equation. (The diffusion is anisotropic because the mean and mean square distances between collisions in the horizontal and vertical directions are slightly different.) We then generate different possible realizations of modeled 2-D and 3-D Pebble-Bed Reactor cores, divided into crystal (honeycomb in 2-D, face-centered in 3-D) and random structures. (To generate the random structures, we developed 2-D and 3-D ballistic deposition algorithms.) We apply Monte Carlo codes (which we also developed) in these structures to simulate neutron transport in both 2-D and 3-D systems; results from these simulations are presented. We show that the results predicted using the new theory more closely agree with the numerical experiments than the atomic mix results and its corrections, and that the new theory can accurately predict small anisotropic effects detected in the simulations. We conclude by discussing the general anisotropic behavior of particles that are born close to the wall of the core, and by showing that the new theory can be used to accurately estimate this effect.