A mesoscopic description of polydispersed particle laden turbulent flows

Turbulent polydispersed multiphase flows are encountered in many engineering and environmental applications and particularly in combustion applications, spray polydispersity is the norm rather than the exception. In this review we summarize the current state of Eulerian transport models for turbulent polydispersed particulate flows without size class discretization. The stochastic nature of both carrier and dispersed phase justifies a stochastic approach to describe the behavior of such systems. In this regard Brownian motion of a single microscopic particle is discussed to intuitively introduce the subject and point out the need for a stochastic representation of the phenomena based on stochastic differential equations (SDEs). Understanding the stochastic tools and mathematical framework based on Langevin equation is compulsory for the rest of this review but here we restrict our coverage to definitions and general remarks and give references for further readings. A stochastic foundation based on Langevin equation is defined for fluid and particle and derivation of the transport equation up to third order statistics without binning the particle diameter is discussed based on corresponding Fokker–Planck equation. Terms that appear in the process of contracting a probability density function (PDF) causing closure problems are identified. The Maximum entropy method is discussed as a tool for closure of particle acceleration terms in Eulerian transport equations followed by current closure issues such as realizability and generality.