Stochastic modelling of inertial particle dispersion by subgrid motion for LES of high Reynolds number pipe flow

Abstract

Aiming at the better prediction of inertial particle dispersion in LES of turbulent shear flow, a stochastic diffusion process of the Langevin type is adopted to model the time increments of the fluid velocity seen by inertial particles. This modelling is particularly crucial for dispersion and deposition of inertial particles with small relaxation times compared to the smallest LES-resolved turbulence time scales. Simple closures for drift and diffusion terms are described. The effects of inertia and external forces on particle trajectories are modelled. To numerically validate the proposed model, LES calculations are performed to track solid particles (glass beads in air with different Stokes' numbers) in a high Reynolds number, equilibrium turbulent pipe flow (Re = 50 000 based on the maximum velocity and the pipe diameter). LES predictions are compared to RANS results and experimental observations. Simulation findings demonstrate the superiority of LES compared to RANS in predicting particle dispersion statistics. More importantly, the use of a stochastic approach to model the subgrid scale fluctuations has proven crucial for results concerning the small-Stokes-number particles. The influence of the model on particle deposition needs to be assessed and additional validation for non-equilibrium turbulent flows is required.