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 Flow16, 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. 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, 1996͔, and the other by Ahmadi ͓Int. J. Multiphase Flow 16, 323 ͑1990͔͒-in the limiting case of statistically homogeneous particle-laden turbulent flow. The decay of particle-phase and fluid-phase turbulent kinetic energy ͑TKE͒ 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 ͑EEM͒-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 parameter...

Two-way coupled stochastic model for dispersion of inertial particles in turbulence

“…The model constants C ε1 and C ε2 are to be 1.44 and 1.92, respectively. These model constants are identical to those employed in EE models that are described in Simonin (1996a,b) and Xu & Subramaniam (2006). The constant C 3 is equal to 3, as this value provided the best agreement with DNS datasets in our tests.…”

“…The first term on the right-hand side of the above equations represents the modelled interphase TKE transfer term (Xu & Subramaniam 2006;Pai & Subramaniam 2007), while the second term represents the production due to the constant mean velocity gradient. The effects of viscous dissipation on the fluid phase TKE manifest themselves in the ε f term of (4.11).…”

“…It was shown in that study that the new time scale accurately captures the dependence of the interphase TKE transfer on St η . This time scale has been successfully employed in the context of EE two-phase turbulence modelling by Xu & Subramaniam (2006). The constant C π is chosen to be 1.0 in this study.…”

“…However, the system of equations (cf. (5.1)-(5.2)) needs to be augmented by an equation for the dissipation rate evolution (details can be found in Xu & Subramaniam (2006), where the extension of the EoE concept to inhomogeneous flows in the context of EE statistical representation of two-phase flows is also presented):…”

“…To explain the EoE concept, which was proposed by Xu & Subramaniam (2006), the following model system of equations for the evolution of TKE in a dilute homogeneous two-phase flow system are assumed to hold:…”