Analytical Discrete-Ordinates Solutions for Improved 1D Models of Particle Transport in Ducts with Wall Migration

Analytical discrete-ordinates (ADO) solutions are developed for two improved one-dimensional (1D) models of particle transport in ducts that include wall migration. One of the studied models is based on an approximation of the transverse and azimuthal dependencies of the angular flux in terms of two basis functions, while the other uses three. Particle migration in the wall is modeled by an exponential displacement kernel. Numerical results for duct reflection and transmission probabilities are reported for various test cases, including some cases of thermal-neutron transport through iron, concrete, and graphite ducts that have been defined and studied by other authors. A comparison is performed with a set of published results comprising realistic results obtained with the Monte Carlo code MCNP and results from a numerical implementation of the discrete-ordinates method for the model based on three basis functions. To resolve some issues raised during the comparison process, a numerical discrete-ordinates solution of the problem has also been implemented in the course of this work.