Turbulence in Multiphase Flows

Abstract

An overview of the fundamental modeling aspects related to disperse multiphase flow is provided. For clarity and accessibility, the discussion is limited to two-phase flows where one phase is disperse (e.g., solid particles) and the other phase is continuous (i.e., a fluid). Because the ultimate goal is to understand the fundamental modeling aspects related to multiphase turbulent flows, a disperse phase with constant-in-time and uniform-in-space particle properties (e.g., size, density, chemical composition, temperature) is assumed. Likewise, the continuous-phase properties (i.e., density, viscosity) are assumed to be constant and uniform. With these assumptions, a disperse multiphase flow can be described mathematically by (i) the positions and velocities of the particles in the disperse phase and (ii) the continuity and momentum equations for the continuous phase. A further distinction is made between the microscale description where the interface coupling between the phases is treated explicitly, and the mesoscale description where the interphase coupling is modeled. These different levels of description capture different turbulent length scales, and, hence, the multiscale nature of multiphase turbulence is discussed (i.e., particle-scale or “pseudo-turbulence” and macroscale turbulence). In cases where an adequate separation of scales exists between the particle scale and the macroscale turbulent integral length scale, it is possible to derive fundamental turbulence models from the mesoscale description of a disperse multiphase flow. For clarity, the two simplest types of turbulence models are described: Reynolds-averaged transport equations and probability density function methods, focusing on the novel unclosed terms that arise due to interphase coupling. Finally, examples of gravity-driven, particle-laden flows in bounded and unbounded domains are used to illustrate the various turbulence regimes observed in practice.