Experimental Study of Inertial Particles in Turbulence: Preferential Concentration, Relative Velocity and Droplet Collisions

Abstract

Wind tunnel experiments are used to investigate the dynamics of small inertial particles (water droplets ≈ 5-150 μm in diameter) in homogeneous, isotropic, slowly decaying grid turbulence (Re_λ ≈ 350, ε ≈ 0.1 m^2/s^3). Phase Doppler Particle Analyzer (PDPA), high-speed imaging measurements and a new 4-frame N+2 Best Estimated Position Particle Tracking Velocimetry (PTV) algorithm are used to determine droplet locations in space and time. Experimental evidence is found of droplet preferential concentration and enhanced relative velocity resulting from the droplets' inertial interactions with the underlying turbulence. The Radial Distribution Functions (RDF) have strong peaks at small separation distances that indicate the preferential accumulation of droplets in the flow. This result is confirmed by Voronoi analysis results that show droplets with small Voronoi areas (high local concentration) are present with a probability higher than that predicted by a Random Poisson Process (RPP). The 2D RDFs show a consistent trend where the results from the horizontal imaging configurations are always lower than those from the vertical planes. The Voronoi PDFs indicate the same anisotropic particle clustering. This observation that the 2D RDFs and Voronoi PDFs are sensitive to orientation is likely the first experimental evidence that clustering is anisotropic and stronger in the direction of gravity. Droplet settling velocities are conditioned on Voronoi areas to assess the relationship between settling and local droplet concentration. The settling velocity data, for all but the largest droplets, presents a clear dependency on Voronoi area: as the Voronoi areas decrease (local concentration increases), collective settling effects result in enhanced settling velocities. The non-dimensional Closing Time ratio is proposed as a new way to interpret droplet relative velocity data that incorporates the fact that the particle collision probabilities depend on both a large relative closing velocity and a small separation distance. The Closing Time shows that once the relative velocity joint PDF is re-framed in the correct non-dimensional ratio, it provides a more meaningful representation of the inertial droplet dynamics. Beyond the ability to provide qualitative understanding, the main benefit of the Closing Time statistics is that they can be used to compute collision probabilities from experimentally measurable quantities of separation distance and relative velocity. This is a novel contribution that provides significant new understanding and quantifying capability for inertial particle dynamics leading to collisions.