Probability density function modeling of dispersed two-phase turbulent flows

摘要

This paper discusses stochastic approaches to dispersed two-phase flow modeling; A general probability density function (PDF) formalism is used since it provides a common and convenient framework to analyze the relations between different formulations. For two-phase how PDF modeling, a key issue is the choice of the state variables. In a first formulation, they include only the position and velocity of the dispersed particles. The kinetic equation satisfied by the corresponding PDF is derived in a different way using tools from the theory of stochastic differential equations. The final expression is identical to an earlier proposal by Reeks [Phys. Fluids A 4, 1290 (1992)] obtained with a different method. As the kinetic equation involves the instantaneous fluid velocity sampled along the particle trajectories, it is unclosed. Another, more general, formulation is then presented, where the fluid velocity "seen" by the solid particles along their paths is added to the state variables. A diffusion model, where trajectories of the process follow a Langevin type of equation, is proposed for the time evolution equation of the fluid velocity "seen" and is discussed; A general PDF formulation that includes both fluid and particle variables, and from which both fluid and particle mean equations can be obtained, is then put forward. [S1063-651X(99)09901-8]. [References: 20]