Lagrangian filtered density function for LES-based stochastic modelling of turbulent dispersed flows

TL;DR

This paper introduces a Lagrangian stochastic SGS model for LES-based simulations of turbulent dispersed flows, improving accuracy in particle dynamics by accounting for sub-grid scale effects.

Contribution

It extends the velocity-filtered density function method to particle-laden flows using a Lagrangian Monte Carlo approach, enhancing LES modeling of dispersed turbulence.

Findings

Improved accuracy in particle concentration predictions.

Reduced errors compared to no SGS modeling.

Effective capture of particle segregation phenomena.

Abstract

The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study turbulent dispersed flows when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGS) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves for a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is provided by LES and then used to advance the SDEs in time. The model consistency is assessed in the limit of particles with zero inertia, when "duplicate fields" are available from both the Eulerian LES and the Lagrangian tracking. Tests with inertial particles were performed to examine the capability of the model to capture particle preferential concentration and near-wall segregation. Upon comparison with DNS-based statistics, our results show improved accuracy and considerably reduced errors with respect to the case in which no SGS model is used in the equations of particle motion.