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

Abstract

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 flow 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_ω corresponding to the maximum of the dissipation (vorticity) spectrum. However, the increase of the average settling rate, 〈Δv_S〉, also depends strongly on the large energetic eddies. The small eddies with wavenumber greater than 2.5k_ω 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_ω). Detailed calculations show that 〈Δv_S〉 is maximized and is of order u′/10 when τ_p/τ_k≈1 and v_d/u′≈0.5 for R_λ=22.6–153, where τ_p is the particle's relaxation time, τ_k is the Kolmogorov timescale, v_d is the settling rate in still fluid, u′ is the root mean square of the velocity fluctuation, and R_λ is the Reynolds number based on the Taylor microscale.