A Lagrangian probability-density-function model for collisional turbulent fluid-particle flows. II. Application to homogeneous flows

Abstract

The Lagrangian probability-density-function model, proposed in Part I for dense particle-laden turbulent flows, is validated here against Eulerian-Lagrangian direct numerical simulation (EL) data for different homogeneous flows, namely statistically steady and decaying homogeneous isotropic turbulence, homogeneous-shear flow and cluster-induced turbulence (CIT). We consider the general model developed in Part I adapted to the homogeneous case together with a simplified version in which the decomposition of the phase-averaged (PA) particle-phase fluctuating energy into the spatially correlated and uncorrelated components is not used, and only total exchange of kinetic energy between phases is allowed. The simplified model employs the standard two-way coupling approach. The comparison between EL simulations and the two stochastic models in homogeneous and isotropic turbulence and in homogeneous-shear flow shows that in all cases both models are capable to reproduce rather well the flow behaviour, notably for dilute flows. The analysis of the CIT gives more insights on the physical nature of such systems and about the quality of the models. Results elucidate the fact that simple two-way coupling is sufficient to induce turbulence, even though the granular energy is not considered. Furthermore, first-order moments including velocity of the fluid seen by particles can be fairly well represented with such a simplified stochastic model. However, the decomposition into spatially correlated and uncorrelated components is found to be necessary to account for anisotropic energy exchanges. When these factors are properly accounted for as in the complete model, the agreement with the EL statistics is satisfactory up to second order.