Implementation of Chord Length Sampling for Transport Through a Binary Stochastic Mixture

Abstract

Neutron transport through a special case stochastic mixture is examined, in which spheres of constant radius are uniformly mixed in a matrix material. A Monte Carlo algorithm previously proposed and examined in 2-D has been implemented in a test version of MCNP. The Limited Chord Length Sampling (LCLS) technique provides a means for modeling a binary stochastic mixture as a cell in MCNP. When inside a matrix cell, LCLS uses chord-length sampling to sample the distance to the next stochastic sphere. After a surface crossing into a stochastic sphere, transport is treated explicitly until the particle exits or is killed. Results were computed for a simple model with two different fixed neutron source distributions and three sets of material number densities. Stochastic spheres were modeled as black absorbers and varying degrees of scattering were introduced in the matrix material. Tallies were computed using the LCLS capability and by averaging results obtained from multiple realizations of the random geometry. Results were compared for accuracy and figures of merit were compared to indicate the efficiency gain of the LCLS method over the benchmark method. Results show that LCLS provides very good accuracy if the scattering optical thickness of the matrix is small (≤1). Comparisons of figures of merit show an advantage to LCLS varying between factors of 141 and 5. LCLS efficiency and accuracy relative to the benchmark both decrease as scattering is increased in the matrix.

A benchmark comparison of Monte Carlo particle transport algorithms for binary stochastic mixtures

“…Donovan and Danon did not examine for their specific problem the approach of using Algorithm B for both materials in the problem. Donovan and Danon extended the LCLS algorithm to the simulation of particle transport through a binary stochastic mixture of spheres of constant radius mixed in a three-dimensional matrix material [9] as well as to the simulation of a single spherical pebble fuel cell [10]. A recent paper by Ji and Martin [11] examined Monte Carlo chord length sampling algorithms for the neutronics analysis of Very High Temperature Gas-Cooled Reactors.…”

Multi-scale modeling and rendering of granular materials

“…As Torquato and Lu [1993] showed, this formula is only an approximation, albeit one that works remarkably well. Several authors [Levitz 1993;Donovan et al 2003;Olson et al 2006] have shown that this formula is incorrect for very small distances (< 1 grain radius), but this is usually ignored in favor of the simple analytical model. We also found the same effect in our experiments (see Figure 6, top), but did not find that accounting for this difference by using tabulations or non-exponential analytical models provided a substantial benefit.…”