Stochastic modeling of direct radiation transmission in particle-laden turbulent flow

Direct radiation transmission in turbulent flows laden with heavy particles plays a fundamental role in systems such as clouds and particle solar receivers. Owing to their inertia, particles are preferentially concentrated by the turbulence, and the resulting voids and clusters lead to deviations in mean transmission from the classical Beer-Lambert law for exponential extinction. Additionally, the transmission fluctuations can exceed those of Poissonian media by an order of magnitude, which implies a gross misprediction in transmission statistics if the correlations in particle positions are neglected. On the other hand, tracking millions of particles in a turbulence simulation can be prohibitively expensive. We propose stochastic processes as computationally inexpensive reduced order models for the instantaneous particle number density field and radiation transmission therein. Results from the stochastic processes are compared to Monte Carlo Ray Tracing (MCRT) simulations using the particle positions obtained from the point-particle direct numerical simulation (DNS) of isotropic turbulence at a Taylor Reynolds number of 150. Accurate transmission statistics are predicted with respect to MCRT by matching the mean, variance, and correlation length of the DNS number density fields. Formulation of the stochastic processes in terms of stochastic differential equations allows an exact solution for arbitrary moments of radiation transmission to be derived from the Kolmogorov backwards equations. Higher order statistics such as the transmission variance, and correlations between particle number density, transmission, and absorption are compared to MCRT and discussed.