Turbulent pair dispersion of inertial particles

TL;DR

This paper investigates how inertial particles disperse in turbulence, revealing distinct regimes for heavy and light particles, with detailed analysis supported by direct numerical simulations at different Reynolds numbers.

Contribution

It introduces a new statistical closure model for heavy particle separation and provides detailed numerical analysis of inertial particle dispersion in turbulence.

Findings

Heavy particles exhibit two dispersion regimes influenced by caustics and flow velocities.

Light particles with high density ratios tend to cluster and sometimes do not separate.

Dispersal behavior varies significantly with particle inertia and density ratios.

Abstract

The relative dispersion of pairs of inertial particles in incompressible, homogeneous, and isotropic turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number $Re_{\lambda} \sim 200$ and 400. The evolution of both heavy and light particle pairs is analysed at varying the particle Stokes number and the fluid-to-particle density ratio. For heavy particles, it is found that turbulent dispersion is schematically governed by two temporal regimes. The first is dominated by the presence, at large Stokes numbers, of small-scale caustics in the particle velocity statistics, and it lasts until heavy particle velocities have relaxed towards the underlying flow velocities. At such large scales, a second regime starts where heavy particles separate as tracers particles would do. As a consequence, at increasing inertia, a larger transient stage is observed, and the Richardson diffusion of simple tracers is recovered only at large times and large scales. These features also arise from a statistical closure of the equation of motion for heavy particle separation that is proposed, and which is supported by the numerical results. In the case of light particles with high density ratios, strong small-scale clustering leads to a considerable fraction of pairs that do not separate at all, although the mean separation increases with time. This effect strongly alters the shape of the probability density function of light particle separations.