A further study of history force effect on particle clustering in turbulence

Abstract

We examine the effects of the history force on the preferential concentration of small particles in homogeneous isotropic turbulence under a wide range of the particle-to-fluid mass density ratio γ (from 0 to 10000) by direct simulations of the Navier–Stokes equations. As to the history integral kernel, we introduce two expressions: i.e., the classical Basset kernel valid only in the limit of creeping flow conditions and for short times, and the Mei–Adrian kernel (Mei and Adrian, 1992) applicable for finite Reynolds numbers and large times. It is revealed that the presence of the history force weakens the level of preferential concentration to some extent, specifically under the conditions of the mass density ratio of around 1.5–10 for heavy particles (e.g., solid particles in liquid) and smaller than 0.7 for light particles (e.g., bubbles in liquid) and that the overprediction of particle accumulation by neglecting the history force is much more remarkable for light particles. A comparison between the Basset kernel and the Mei–Adrian kernel has shown that the Basset kernel overestimates the history effect but only slightly.