Turbulent dispersion of particles in self-generated homogeneous turbulence

Turbulent dispersion of particles in their self-generated homogeneous turbulent field was studied both experimentally and theoretically. Measurements involved nearly monodisperse spherical glass particles (nominal diameters of 0.5, 1.0 and 2.0 mm) falling with uniform particle number fluxes in a nearly stagnant water bath. Particle Reynolds numbers based on terminal velocities were 38, 156, and 545 for the three particle sizes. The flows were dilute with particle volume fractions less than 0.01%. Measurements included particle motion calibrations, using motion-picture shadowgraphs; and streamwise and cross-stream mean and fluctuating particle velocities, using a phase-discriminating laser velocimeter. Liquid-phase properties were known from earlier work. Particle properties were predicted based on random-walk calculations using statistical time-series methods to simulate liquid velocities along the particle path. Calibrations showed that particle drag properties were within 14% of estimates based on the standard drag correlation for spheres, however, the particles (particularly the 1.0 and 2.0 mm diameter particles) exhibited self-induced lateral motion even in motionless liquid due to eddy-shedding and irregularities of shape. Particle velocity fluctuations were primarily a function of the rate of dissipation of kinetic energy in the liquid since this variable controls liquid velocity fluctuations. Streamwise particle velocity fluctuations were much larger than cross-stream particle velocity fluctuations (2–5:1) largely due to varying terminal velocities caused by particle size variations. Cross-stream particle and liquid velocity fluctuations were comparable owing to the combined effects of turbulent dispersion and self-induced motion. Predicted mean and fluctuating particle velocities were in reasonably good agreement with the measurements after accounting for effects of particle size variations and self-induced motion. However, the theory must be extended to treat self-induced motion and to account for observations that this motion was affected by the turbulent environment.