The pdf approach to turbulent polydispersed two-phase flows

The purpose of this paper is to develop a probabilistic approach to turbule nt polydispersed two-phase flows. The two-phase flows considered are compos ed of a continuous phase, which is a turbulent fluid, and a dispersed phase , which represents an ensemble of discrete particles (solid particles, drop lets or bubbles). Gathering the difficulties of turbulent flows and of part icle motion, the challenge is to work out a general modelling approach that meets three requirements: to treat accurately the physically relevant phen omena, to provide enough information to address issues of complex physics ( combustion, polydispersed particle flows,...) and to remain tractable for g eneral non-homogeneous flows. The present probabilistic approach models the statistical dynamics of the system and consists in simulating the joint pr obability density function (pdf) of a number of fluid and discrete particle properties. A new point is that both the fluid and the particles are inclu ded in the pdf description. The derivation of the joint pdf model for the f luid and for the discrete particles is worked out in several steps. The mat hematical properties of stochastic processes are first recalled. The variou s hierarchies of pdf descriptions are detailed and the physical principles that are used in the construction of the models are explained. The Lagrangi an one-particle probabilistic description is developed first for the fluid alone, then for the discrete particles and finally for the joint fluid and particle turbulent systems. In the case of the probabilistic description fo r the fluid alone or for the discrete particles alone, numerical computatio ns are presented and discussed to illustrate how the method works in practi ce and the kind of information that can be extracted from it. Comments on t he current modelling state and propositions for future investigations which try to link the present work with other ideas in physics are made at the e nd of the paper. (C) 2001 Elsevier Science B.V. All rights reserved.