Stochastic modeling of fluid velocity seen by heavy particles for two-phase LES of non-homogeneous and anisotropic turbulent flows

摘要

The neglect of the effects of sub-filter scale velocities often remains a source of error in LES predictions of particle dispersion and deposition. Indeed, sub-filter fluctuations should be expected to be more significant for particles with smaller relaxation times compared to the LES-resolved turbulence time scales. In this work, a stochastic diffusion process is used to include the sub-filter scale transport when tracking a dilute suspension of heavy particles (glass beads in air with different Stokes' numbers, namely 0.022 and 2.8) in a high Reynolds number, equilibrium turbulent shear flow (Re_τ = 2,200 based on the friction velocity and the pipe diameter). A Langevin-type equation is proposed to model the Lagrangian fluid velocity seen by solid particles, taking into account inertia and cross-trajectory effects. LES predictions are compared to RANS results and experimental observations. It is shown that the RANS approach is unable to predict particle dispersion statistics as accurately as LES does, especially for inertial particles characterized by a Stokes number smaller than one. For particles with Stokes number higher than one, both LES and RANS predictions compare reasonably well with the experimental results. More importantly, the use of a stochastic approach to model the sub-filter scale fluctuations has proven crucial for results concerning the small-Stokes-number particles. The model requires additional validation for non-equilibrium turbulent flows.