Numerical study of the subgrid fluid turbulence effects on the statistics of heavy colliding particles

Abstract

The main purpose of this article is to investigate the effects of the subgrid fluid turbulence on the motion of nonsettling colliding particles suspended in steady homogeneous isotropic turbulent flow. An additional goal is to characterize the statistical properties of the subgrid fluid turbulence “viewed” by inertial particles to support the development of large eddy simulation (LES) approach for particle-laden turbulent flows. Two types of numerical experiments have been carried out: first, the discrete particle trajectories were computed using the fluid velocity field given by direct numerical simulation (DNS) in order to characterize the small-scale fluid velocity fluctuations “seen” by the particles. In a second stage, the particle trajectory simulations were performed using several filtered velocity fields computed from the DNS data to evaluate the effect of the subgrid fluid turbulence on the particle statistics (turbulent dispersion, kinetic energy, accumulation efficiency, particle-particle relative velocity and collision frequency). The first part of this study shows that particle inertia has a limited effect on the subgrid fluid turbulent statistics: subgrid kinetic energy and Lagrangian integral time scale measured along the particle trajectories. In addition, the subgrid fluid Lagrangian integral time scale is found to be nearly equal to the subgrid Eulerian integral time scale and proportional to the ratio of the filter width to the whole fluid turbulent velocity. The second part shows that the particle turbulent dispersion and kinetic energy are affected by the filtering only when a significant percentage of the turbulent kinetic energy was removed from the velocity field seen by the particles. In contrast, accumulation and collision phenomena are found to be significantly influenced by the subgrid fluid velocity fluctuations when the particle response time is of the same order or smaller than the subgrid Lagrangian integral time scale measured along particle paths. Finally, these results are used to characterize, in terms of particle response time to subgrid time scale ratio, the validity range of LES for the computation of gas-solid turbulent flow.