Approximate One-Dimensional Models for Monoenergetic Neutral Particle Transport in Ducts with Wall Migration

摘要

The problem of monoenergetic neutral particle transport in a duct, whereparticles travel inside the duct walls, is treated using an approximateone-dimensional model. The one-dimensional model uses three-basis functions, aspart of a previously derived weighted-residual procedure, to account for thegeometry of particle transport in a duct system (where particle migration intothe walls is not considered). Our model introduces two stochastic parameters toaccount for particle-wall interactions: an albedo approximation yielding thefraction of particles that return to the duct after striking the walls, and amean-distance travelled in the walls transverse to the duct by particles thatre-enter the duct. Our model produces a set of three transport equations with anon-local scattering kernel. We solve these equations using discrete ordinateswith source iteration. Numerical results for the reflection and transmissionprobabilities of neutron transport in ducts of circular cross section arecompared to Monte Carlo results computed using the MCNP code.