Influence of gravity on collisions of monodispersed droplets in homogeneous isotropic turbulence

This paper studies the gravity influence on collisions of monodispersed droplets in homogeneous isotropic turbulence by means of direct numerical simulations (DNSs). The DNS results show that, in certain Stokes and Reynolds regimes, collision frequencies are significantly reduced in the presence of gravity. Those decreases are mainly attributable to the decrease in the droplet relative velocity, since the change in radial distribution function-often referred to preferential concentration-is small. Further analysis of the results reveals that droplet sedimentation due to gravity shortens the droplet-fluid interaction time, consequently weakening the relative motions between droplets. These observations lead to an analytical model that can be used to estimate the velocity fluctuations of sedimenting particles under gravity. Utilizing this model, we constructed a further analytical model for estimating the gravitational influence on collisions. Given flow and particle parameters, the model calculates the ratio of collision frequencies with and without the effect of gravity. Past studies simply noted that the gravitational influence is negligible when the droplet sedimenting velocity is much smaller than the flow velocity fluctuations. Our analytical model further suggests that the gravitational influence on collisions of monodispersed cloud droplets with non-negligible sedimentation rates stays negligibly small even in high Reynolds number flows, such as those typically found in convective clouds.