Clustering and relative velocities of heavy particles under gravitational settling in isotropic turbulent flows

TL;DR

This paper investigates how gravity influences the clustering and relative velocities of heavy particles in turbulent flows, proposing a model to explain gravity-enhanced clustering and its effects on collision rates.

Contribution

It introduces a new model for the timescale of fluid velocity gradients experienced by particle pairs and an effective Kubo number to explain gravity's role in clustering.

Findings

Gravity can both enhance and reduce particle clustering depending on conditions.

The model links gravity effects to the fluid velocity gradient timescale and Kubo number.

Implications for collision kernel parameterization in turbulent particle suspensions.

Abstract

Spatial clustering and intermittency in the relative velocity of heavy particles of the same size settling in turbulent flows can be strongly affected by gravity. We present a model for the timescale of the fluid velocity gradient seen by particle pairs and propose an effective Kubo number based on this timescale to explain the mechanism of gravity-enhanced clustering. We explore the mechanisms of the gravity-induced reduction or enhancement of the intermittency in the particle radial relative velocity (RRV) at different Stokes numbers based on backward-in-time relative dispersion and preferential sampling of the fluid field. These effects of gravity on clustering and the RRV must be parameterized in the geometric collision kernel.