Abstract
The paper provides an overview of the challenges and progress associated with the task of numerically predicting particle-laden turbulent flows. The review covers the mathematical methods based on turbulence closure models as well as direct numerical simulation (DNS). In addition, the statistical (pdf) approach in deriving the dispersed-phase transport equations is discussed. The review is restricted to incompressible, isothermal flows without phase change or particle-particle collision. Suggestions are made for improving closure modelling of some important correlations.