  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. 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 is decreased. Analysing the
fluid-particle relative motion, we find that the mean settling speed is
progressively reduced while reducing the density ratio 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).
