A subgrid model for clustering of high-inertia particles in large-eddy simulations of turbulence

Abstract

Clustering (or preferential concentration) of inertial particles suspended in a homogeneous, isotropic turbulent flow is strongly influenced by the smallest scales of the turbulence. In particle-laden large-eddy simulations (LES) of turbulence, these small scales are not captured by the grid and hence their effect on particle motion needs to be modelled. In this paper, we use a subgrid model based on kinematic simulations of turbulence (Kinematic Simulation based SubGrid Model or KSSGM), for the first time in the context of predicting the clustering and the relative velocity statistics of inertial particles. This initial study focuses on the special case of inertial particles in the absence of gravitational settling. We show that the KSSGM gives excellent predictions for clustering in a priori tests for inertial particles with St ≥ 2.0, where St is the Stokes number, defined as the ratio of the particle response time to the Kolmogorov time-scale. To the best of our knowledge, the KSSGM represents the first model that has been shown to capture the effect of the subgrid scales on inertial particle clustering for St ≥ 2.0. We also show that the mean inward radial relative velocity between inertial particles (⟨w_r⟩⁽⁻⁾, which enters into the formula for the collision kernel) is accurately predicted by the KSSGM for all St. We explain why the model captures clustering at higher St but not for lower St , and provide new insights into the key statistical parameters of turbulence that a subgrid model would have to describe, in order to accurately predict clustering of low-St particles in an LES.

Keywords:

• inertial particle
• large-eddy simulation
• subgrid model
• kinematic simulation
• turbulence

Acknowledgements

The authors gratefully acknowledge Andrew D. Bragg for insightful inputs throughout the course of this work. The authors also gratefully acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources on Ranger and Stampede that have contributed to the research results reported in this paper..

Additional information

Funding

This study was supported by the National Science Foundation [grant number CBET 0756510], [grant number CBET 0967349]. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by the National Science Foundation [grant number OCI-1053575].