Description of clustering of inertial particles in turbulent flows via finite-time Lyapunov exponents

TL;DR

This paper derives an asymptotic solution for inertial particle clustering in turbulent flows, linking finite-time Lyapunov exponents to flow properties, and validates predictions with numerical simulations.

Contribution

It introduces a novel analytical approach to quantify inertial particle clustering using finite-time Lyapunov exponents in unsteady flows.

Findings

Maximum clustering occurs at intermediate Stokes numbers.

Clustering diminishes at very small and large Stokes numbers.

Numerical simulations agree reasonably with the analytical predictions.

Abstract

An asymptotic solution is derived for the motion of inertial particles exposed to Stokes drag in an unsteady random flow. This solution provides the finite-time Lyapunov exponents as a function of Stokes number and Lagrangian strain- and rotation-rates autocovariances. The sum of these exponents, which corresponds to a concentration-weighted divergence of particle velocity field, is considered as a measure of clustering. For inertial particles dispersed in an isotropic turbulent flow our analysis predicts maximum clustering at an intermediate Stokes number and minimal clustering at small and large Stokes numbers. Direct numerical simulations are performed for quantitative validation of our analysis, showing a reasonable agreement between the two.