The role of relative motion between solid particles and the carrier flow on the turbulent kinetic energy transfer

In this talk, we will examine the general question how the presence of solid particles affects the production and transfer of turbulent kinetic energy. It is argued that if there is a relative motion in the mean velocity between the particulate phase and the carrier flow, then the relative motion will provide a mechanism for production of the turbulent kinetic energy. Furthermore, at a specific grid scale, the turbulent fluctuating motion of each phase can be divided into a resolved component and a subgrid component: the relative motion in the resolved component provides a mechanism to transfer energy across the grid scale, while the subgrid relative motion contributes to the added viscous dissipation near the fluid-particle interfaces. This conceptual picture provides a basis for establishing a generalized balance equation of the turbulent kinetic energy for a particle-laden turbulent flow, which could be used to quantify the turbulence modulation by solid particles. This balance equation could be applied to address the effects of flow Reynolds number, particle volume fraction, particle-to-fluid density ratio, particle size, and particle sedimentation on turbulence modulation.