The role of the turbulent scales in the settling velocity of heavy particles in homogeneous isotropic turbulence

The average settling velocity of heavy particles under a body force field is studied numerically in stationary homogeneous isotropic turbulent flows generated by the direct numerical simulation and the large eddy simulation of the continuity and Navier-Stokes equations. The how fields corresponding to different selected ranges of turbulent scales are obtained by filtering the results of the direct numerical simulation, and employed for calculating the particle motion. Wang & Maxey (1993) showed that as a consequence of the particle accumulation in the low vorticity region and the preferential sweeping phenomenon, the average settling rate in turbulence is greater than that in still fluid. In the present study, the phenomenon of particle accumulation in the low vorticity region is found to be controlled mainly by the small scales with wavenumber k(omega) corresponding to the maximum of the dissipation (vorticity) spectrum. However, the increase of the average settling rate, <Delta upsilon(s), also depends strongly on the large energetic eddies. The small eddies with wavenumber greater than 2.5k(omega) have essentially no effect on the particle accumulation and the average settling velocity. The large eddy simulation is thus adequate for the present study provided the smallest resolved scale is greater than 1/(2.5k(omega)). Detailed calculations show that <Delta upsilon(s) is maximized and is of order u'/10 when tau(p)/tau(k) approximate to 1 and upsilon d/u' approximate to 0.5 for R-lambda = 22.6-153, where tau(p) is the particle's relaxation time, tau(k) is the Kolmogorov timescale, upsilon(d) is the settling rate in still fluid, u' is the root mean square of the velocity fluctuation, and R-lambda is the Reynolds number based on the Taylor microscale.