Constitutive Relations for Dispersed Particles in Nonuniform Flows

摘要

An application of a kinetic approach to two-fluid modelling of particle laden flows is examined. This is based on a probability density function (pdf) approach analogous to that used in the kinetic theory of gases. The continuum equations, representing the transport of mass, momentum and the particle Reynolds stresses of the dispersed phase, are obtained by an appropriate integration of the pdf equation over all particle velocities at a fixed location in space. However, these equations are not closed in that they contain certain terms for which there are no transport equations. Using purely formal techniques, closed expressions can be found for these unknowns. We also compare the numerical solution of the resultant closed system of equations to results obtained from random walk simulations of particle dispersion in a channel flow with perfectly reflecting walls.