Direct numerical simulations of sedimenting spherical particles at non-zero Reynolds number

Abstract

We performed direct numerical simulations, using a smoothed profile method to investigate the inertial effects on the static and dynamic properties of a sedimenting suspension over a wide range of volume fractions from 0.01 to 0.4. We found that at Reynolds number Re ≤ 0.5, static and dynamic properties show the typical non-Brownian, Stokes regime characteristics, due to insignificant inertial effects. The microstructure analysis at the high Re revealed that at Re = 1 inertial forces have significant effects and these create a deficiency of particles around a given particle, which is more pronounced in the direction of gravity than in the perpendicular direction. This deficiency decreased the velocity fluctuations and particle diffusion in the vertical direction, whereas both of these properties remain unchanged in the perpendicular direction. Moreover, at Re = 10, strong inertial forces generated a significant deficit of particles in both directions, which decreased velocity fluctuations and particle diffusion in both directions. We also observed that the range of volume fraction affected by inertial forces is increased with the increase of Re. At high volume fraction ϕ ≳ 0.15, intrinsic many-body interactions dominate the phenomena and govern the transport properties thereafter.