A filtering strategy for the numerical convergence of radiation transport through purely absorbing particle clouds. (May 2020) - Paul, Immanuvel; Bassenne, Maxime; Mani, Ali
Highlights: We confirm the non-verifiability of the radiation transport equation (RTE) on a Eulerian domain for particle clouds. We develop a novel filtering strategy for the computation of number density to circumvent the issue of homogenization error. We test the dependency of filter width on the transmission profiles for radiation transport through particle clouds. We demonstrate that the solution of RTE converges to the gold-standard for the cases that satisfy the BB-law assumptions. We apply our methodology to turbulent particle clouds to study the influence of Stokes number on the transmission profiles. Abstract: Radiation transport through particle clouds plays a major role in many engineering applications. In this paper, we study this problem by means of solving the radiative transport equation (RTE) on a Eulerian continuous domain. The particle clouds are generated through direct numerical simulation of Navier-Stokes equations coupled with Lagrangian particle transport at different Stokes numbers. We confirm the earlier observation noted in the literature that the solution to the RTE on Eulerian mesh diverges when the Eulerian mesh size is of the order of the particle diameter. This observation is often called the homogenization error stemming from relegation of number density onto the Eulerian domain. In order to circumvent this divergence problem, we propose a filtering strategy that spreads the information of the particles to the neighboring cells in a way that the representation of the particles remains the same even when the mesh size is smaller than that of the particle size. We show through our simulations that our filtering strategy solves the issue of homogenization error for the cases where the Beer-Bouger law is valid.