Optical measurements and flow modeling to characterize solid volume fractions in gravity-driven particle curtains

Abstract

Solid volume fraction is a defining characteristic of multiphase gas–solid flows. In the case of gravity-driven particle curtains, it changes significantly along the flow direction. This has implications for the performance of falling-particle solar receivers, which use particle curtains to capture and store heat from concentrated sunlight. This study reports on the characterization of solid volume fraction as a function of height in gravity-driven particle curtains using optical techniques and simulations performed with a discrete element method (DEM) model. The experimental domain is a hopper-fed vertical channel, and the modeling domain is designed to match the experimental setup. Solid volume fraction was obtained from experimentally measured transmittance using two techniques: (1) a thermopile detector paired with a visible light source and (2) a high-speed camera. The DEM simulations were calibrated by identifying the coefficient of static friction between particles that resulted in equivalent mass flow rates to the experiments. All techniques, including an analytical model derived from first principles and empirical relationships, showed very similar trends of solid volume fraction decreasing along the flow direction, where it drops off rapidly initially before leveling off in a power law relationship. Both experimental and computational tests were performed with 1 mm and 2 mm particles, and solid volume fraction is found to decrease with increasing particle size at any location in the channel. Furthermore, the solid volume fractions calculated from transmittance measurements were found to be sensitive to the optical properties of the particles through Monte Carlo ray tracing simulations. To account for this effect, a new scale factor dependent on particle reflectivity is derived, which leads to significantly improved agreement between experimental and simulated results. A simple, closed-form equation is proposed to transform measured transmittance to a solid volume fraction while accounting for particle reflectivities. Even though solid volume fractions above 0.1 were not measured in this study, the technique developed is suitable to measure even larger solid volume fractions, especially for more reflective particles.