Nonclassical Particle Transport in One-Dimensional Random Periodic Media. (2nd January 2017)

• Record Type: Journal Article
• Authors: Vasques, Richard; Krycki, Kai; Slaybaugh, Rachel N.
• Is Part Of: Nuclear science and engineering. Volume 185:Number 1(2017)
• Page Start: 78
• Page End: 106
• Publication Date: 2017-01-02
• Subjects: Nonclassical transport -- random media -- atomic mix; Nuclear energy -- Periodicals; Nuclear engineering -- Periodicals; Nuclear energy; Nuclear engineering; Periodicals; 539.705
• DOI: 10.13182/NSE16-35
• Languages: English
• ISSNs: 0029-5639

Abstract

Abstract : We investigate the accuracy of the recently proposed nonclassical transport equation. This equation contains an extra independent variable compared to the classical transport equation (the path length s ), and models particle transport in homogenized random media in which the distance to collision of a particle is not exponentially distributed. To solve the nonclassical equation, one needs to know the s -dependent ensemble-averaged total cross section Σ t (μ, s) or its corresponding path-length distribution function p (μ, s). We consider a one-dimensional (1-D) spatially periodic system consisting of alternating solid and void layers, randomly placed along the x -axis. We obtain an analytical expression for p (μ, s ) and use this result to compute the corresponding Σ t (μ, s). Then, we proceed to solve numerically the nonclassical equation for different test problems in rod geometry; that is, particles can move only in the directions μ = ±1. To assess the accuracy of these solutions, we produce benchmark results obtained by (i) generating a large number of physical realizations of the system, (ii) numerically solving the transport equation in each realization, and (iii) ensemble-averaging the solutions over all physical realizations. We show that the numerical results validate the nonclassical model; the solutions obtained with the nonclassical equation accurately estimate the ensemble-averaged scalar flux in this 1-D random periodic system, greatly outperforming the widely used atomic mix model in most problems.