A Kinetic Equation for Particle Transport in Turbulent Flows

TL;DR

This paper derives a new kinetic equation for particle transport in turbulent flows, providing a closed-form diffusion term that accounts for non-Gaussian forcing and long correlation times, advancing the PDF approach in disperse two-phase turbulence.

Contribution

It introduces a novel kinetic equation derived via cumulant expansion and path density operators, enabling better modeling of particle dispersion in complex turbulent flows.

Findings

The kinetic equation has coefficients based on particle path cumulants.

It applies to non-Gaussian, long-correlation turbulent forcing.

It reveals new mechanisms for particle diffusion.

Abstract

One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent flows by ensemble averaging over all possible realisations of state transition paths in the phase space. The probability density function is expanded as a series in terms of the cumulants of particle paths in the phase space, by introducing a local path density operator to identify the distribution of particle paths. The expansion enables us to directly obtain a kinetic equation with the diffusion term in closed form. The kinetic equation derived in this study has following features that: (1) it has its coefficients expressed as functions of the cumulants of particle paths in the phase space; (2) it applies to particle dispersion by non-Gaussian random forcing with long correlation time scales; (3) it presents new mechanisms responsible for particle diffusion. An application of the kinetic equation is also presented in this paper.