Radiative view factor correlations in particulate media from ray tracing simulations and data-driven modeling

Abstract

Thermal radiation has been extensively modeled in static particulate media with effective radiative properties or with statistical ray tracing techniques. However, these techniques are not directly compatible to evaluate radiative fluxes on discrete particles, which is more suitable for particle flow systems. This study focuses on such a discrete approach to compute radiative fluxes by developing view factors correlations for particle-particle and particle-wall. Training data is generated from physics-based Monte Carlo ray tracing simulations on a monodisperse, packed bed with solid volume fractions ranging from 0.016 to 0.45. This data was used to develop reduced-order correlations to determine particle-particle and particle-wall radiative view factors as a function of particle-particle and particle-wall separation distance, viewing angle, and the number of shading particles. Uniquely, we determine best-fit functions that are physically interpretable to account for shading effects by particles. A sigmoid function with a non-linear dependence on viewing angle governs the extent of shading by an intermediate particle. A correction factor with the particle-wall normal separation distance as the feature variable is introduced to account for shading effects between a particle and a planar wall surface. View factor correlations result in reliable and reasonably accurate predictions. For a solid volume fraction of 0.45, the root mean squared errors of particle-particle and particle-wall view factors are 2.7e-4 and 0.021 with corresponding training data in the ranges of 0–0.08 and 0–0.5 respectively. To scale these correlations for large number of particles, restricting shading detection up to 5 nearest neighbors is demonstrated to be an effective strategy to balance prediction accuracy with computational efficiency. With thousands of particles, the computational cost of proposed view factor correlations with thresholding of 5 shading particles is about 100 times faster than serial Monte Carlo ray tracing simulations for a solid volume fraction of 0.45.