Probability density function modeling of dispersed two-phase turbulent flows

This paper discusses stochastic approaches to dispersed two-phase flow mode ling; A general probability density function (PDF) formalism is used since it provides a common and convenient framework to analyze the relations betw een different formulations. For two-phase how PDF modeling, a key issue is the choice of the state variables. In a first formulation, they include onl y the position and velocity of the dispersed particles. The kinetic equatio n satisfied by the corresponding PDF is derived in a different way using to ols from the theory of stochastic differential equations. The final express ion is identical to an earlier proposal by Reeks [Phys. Fluids A 4, 1290 (1 992)] obtained with a different method. As the kinetic equation involves th e instantaneous fluid velocity sampled along the particle trajectories, it is unclosed. Another, more general, formulation is then presented, where th e fluid velocity "seen" by the solid particles along their paths is added t o the state variables. A diffusion model, where trajectories of the process follow a Langevin type of equation, is proposed for the time evolution equ ation of the fluid velocity "seen" and is discussed; A general PDF formulat ion that includes both fluid and particle variables, and from which both fl uid and particle mean equations can be obtained, is then put forward. [S106 3-651X(99)09901-8].