A multiscale model for dilute turbulent gas-particle flows based on the equilibration of energy concept

Abstract

The objective of this study is to improve Eulerian-Eulerian models of particle-laden turbulent flow. We begin by understanding the behavior of two existing models—one proposed by Simonin [von Kármán Institute of Fluid Dynamics Lecture Series, 1996], and the other by Ahmadi [Int. J. Multiphase Flow 16, 323 (1990)]—in the limiting case of statistically homogeneous particle-laden turbulent flow. The decay of particle-phase and fluid-phase turbulent kinetic energy (TKE) is compared with direct numerical simulation results. Even this simple flow poses a significant challenge to current models, which have difficulty reproducing important physical phenomena such as the variation of turbulent kinetic energy decay with increasing particle Stokes number. The model for the interphase TKE transfer time scale is identified as one source of this difficulty. A new model for the interphase transfer time scale is proposed that accounts for the interaction of particles with a range of fluid turbulence scales. A new multiphase turbulence model—the equilibration of energy model (EEM)—is proposed, which incorporates this multiscale interphase transfer time scale. The model for Reynolds stress in both fluid and particle phases is derived in this work. The new EEM model is validated in decaying homogeneous particle-laden turbulence, and in particle-laden homogeneous shear flow. The particle and fluid TKE evolution predicted by the EEM model correctly reproduce the trends with important nondimensional parameters, such as particle Stokes number.