Anisotropic Diffusion Coefficient in a Cylindrical Cell by Integral Transport Theory

Abstract

The anisotropic diffusion coefficient has been calculated in a cylindrical cell with use made of the integral transport theory. The previous method(1) of calculating the diffusion coefficient requires much computer time to evaluate the generalized first-flight collision probabilities between two mesh points for a square cell. To circumvent this drawback, we introduce new calculation methods for determining the anisotropic diffusion coefficient in a cylindrical cell. Two methods are proposed-one uses the diffusion theory in the outermost moderator region of a cell; the other adopts the integral transport theory in that region as well. For the latter method, a new boundary condition is introduced for the cell surface, which, in the present problem, supersedes the usual isotropic return boundary condition. Using these two methods, the anisotropic diffusion coefficient can be evaluated with very short computer time. Moreover, an analytic expression is obtained for the special case where a cell is composed of a fuel and a moderator.