Analytical Discrete-Ordinates Solution for 3D Particle Transport in Ducts as Described by a 1D Model with Three Basis Functions

摘要

An analytical discrete-ordinates (ADO) solution is developed for an approximate model of particle transport in ducts. The model is based on the use of three basis functions to represent the transverse and azimuthal-angle dependencies of the angular flux in the duct and a weighted residual procedure that reduces the original 3D transport problem to a three-group-like 1D problem. Numerical results of benchmark quality for the reflection and transmission probabilities are tabulated for the cases of isotropic incidence and incidence described by the Dirac delta distribution.