Simulation of a particle-laden turbulent channel flow using an improved stochastic Lagrangian model

TL;DR

This paper introduces an improved stochastic Lagrangian model for simulating particle-laden turbulent flows, accurately capturing velocity statistics and outperforming previous models in predicting particle concentration and drift velocity.

Contribution

A new Langevin-type stochastic model compatible with transport equations across particle inertia limits is developed and validated against DNS data, showing improved predictions.

Findings

The model accurately predicts velocity moments and correlations.

It outperforms previous models in predicting particle concentration and drift velocity.

Parameters are highly space-dependent and anisotropic, as shown by DNS data.

Abstract

The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift velocity in the limits of low and high particle inertia, is derived. It is also shown that some previously proposed stochastic models are not compatible with this transport equation in the limit of high particle inertia. The drift and diffusion parameters of these stochastic differential equations are then estimated using direct numerical simulation (DNS) data. It is observed that, contrary to the conventional modeling, they are highly space dependent and anisotropic. To investigate the performance of the present stochastic model, a comparison is made with DNS data as well as with two different stochastic models. A good prediction of the first and second order statistical moments of the particle and fluid seen velocities is obtained with the three models considered. Even for some components of the triple particle velocity correlations, an acceptable accordance is noticed. The performance of the three different models mainly diverges for the particle concentration and the drift velocity. The proposed model is seen to be the only one which succeeds in predicting the good evolution of these latter statistical quantities for the range of particle inertia studied.