Particle subgrid stress models for large Stokes numbers in particle-laden turbulence

Abstract

For the Stokes number based on the Kolmogorov time scale ${St}_K$ up to $O(10^{2})$ , the particle subgrid stress (particle stress) in the volume-average framework is studied by comparing the fluid residual stress, the particle Smagorinsky model and the particle scale-similarity model. To obtain the numerical database of the particle-laden turbulence, two-way coupling direct numerical simulation is carried out with isotropic and anisotropic forcing conditions. As the particle stress is related to the local flow structure, which is not reflected by ${St}_K$ , a new Stokes number ${St}_R$ is introduced to extract the effect of the intensity of the fluid velocity fluctuation in the averaging volume. The degrees of agreement of the principal axes (eigenvectors) of the particle stress models to those of the fully resolved particle stress are regarded as functions of ${St}_R$ regardless of the averaging volume size. The fluid residual stress model shows the highest degree of agreement over a small ${St}_R$ range for both of the forcing cases, and similar predominance is also observed for the correlation coefficient reflecting the magnitude of the particle stress. The effects of ${St}_R$ , ${St}_K$ , the averaging volume size and the Reynolds number on the model coefficients are investigated based on the intensities of the deviatoric and isotropic parts of the fully resolved particle stress and its models. The Stokes number ${St}_R$ is found to be an essential factor to determine the model coefficients, as each effect is extracted reasonably by fixing ${St}_R$ .