Reduced particle settling speed in turbulence

We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, $Ga$ . The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio [STIX]x1D70Cₚ/[STIX]x1D70Cf . The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular, it reduces by 6 %–60 % with respect to the terminal velocity of an isolated sphere in quiescent fluid as the ratio between the latter and the turbulent velocity fluctuations u is decreased. Analysing the fluid–particle relative motion, we find that the mean settling speed is progressively reduced while reducing [STIX]x1D70Cₚ/[STIX]x1D70Cf due to the increase of the vertical drag induced by the particle cross-flow velocity. Unsteady effects contribute to the mean overall drag by about 6 %–10 %. The probability density functions of particle velocities and accelerations reveal that these are closely related to the features of the turbulent flow. The particle mean-square displacement in the settling direction is found to be similar for all $Ga$ if time is scaled by (2a)/u (where $2a$ is the particle diameter and u is the turbulence velocity root mean square).