Probabilistic formalism and hierarchy of models for polydispersed turbulent two-phase flows

This paper deals with a probabilistic approach to polydispersed turbulent two-phase flows following the suggestions of Pozorski and Minier [Phys. Rev. E 59, 855 (1999)]. A general probabilistic formalism is presented in the form of a two-point Lagrangian PDF (probability density function). A new feature of the present approach is that both phases, the fluid as well as the particles, are included in the PDF description. It is demonstrated how the formalism can be used to show that there exists a hierarchy between the classical approaches such as the Eulerian and Lagrangian methods. It is also shown that the Eulerian and Lagrangian models can be obtained in a systematic way from the PDF formalism. Connections with previous papers are discussed.