Fluctuations of particle concentration in a turbulent two-phase shear layer

Abstract

Measurements and calculations of mean and rms of fluctuations of particle velocities and concentration and cross-correlation coefficients of two particle velocity components and concentration fluctuations in a horizontal plane shear layer laden with glass beads with mean diameters 55 and 90 μm are presented. The particles were injected at the low speed side of the flow, which is different from previous studies, and enhances the influence of gravity on particle dispersion. The ranges of Stokes numbers, based on the time scale of the large eddies, were 0.2–0.6 and 0.6–1.4 for 55 and 90 μm respectively. The particle gravitational settling parameter, due to gravity acting normal to the main flow direction at the low speed side of the shear layer, was for the mean flow 0.2 and 0.5 and for the turbulent flow 0.5 and 1 for 55 and 90 μm respectively. Velocity measurements were obtained by particle image velocimetry (PIV) and instantaneous particle concentration by counting the number of particles in each interrogation cell of the PIV images. The effect of interrogation cell size on instantaneous particle concentration was assessed and an appropriate interrogation cell size was chosen to quantify the non-random contribution of particle concentration fluctuations. The intensity of spatially-resolved non-random concentration fluctuations varied between 0.6 and 0.9 of the local mean concentration at the edge of the shear layer, where particles dispersed only due to centrifuging by fluid flow large scale structures and between 0.15 and 0.35 in the central region of the shear layer, where particles are convected by the flow or arrive due to centrifuging from the fluid eddies and gravitational effects and, as a consequence, random contributions on particle concentration become more important. The contribution of various fluid flow structures and gravity on concentration fluctuations was quantified and explained by quadrant analysis of the cross-correlation between measured particle streamwise velocity and concentration. The calculations of the fluid flow in the shear layer were based on the discrete vortex method and the discrete phase motion was calculated by Lagrangian particle tracking. The calculations showed fluid velocity fluctuations frequency spectra with −5/3 decay, as measured in the experiments, and the simulated particle mean and rms velocities and cross-correlation coefficients of particle concentration and velocity fluctuations agreed qualitatively with the measurements. Remaining discrepancies in the absolute values were due to the omission of gravity in the calculations and the resulting narrower range of fluid flow eddy sizes predicted by the calculations relative to experiments. The consequences of current findings on the operation of light detection and ranging (LIDAR) systems for measurements of atmospheric turbulence due to vortices of the wake of airplanes are discussed and improvements in the data processing are suggested.