A PDF model for dispersed particles with inelastic particle-wall collisions

A simple model is proposed for the phase-space distribution of dispersed, h igh-inertia particles in a turbulent boundary layer. This model includes a boundary condition describing inelastic particle-wall collisions. Two model s for the normal coefficient of restitution are considered. The simpler mod el treats this coefficient as a constant, and this is shown to lead to a si ngular distribution of particle velocities at the boundary. A numerical sch eme for treating this model is presented, and results from this are compare d with those obtained from particle random-walk simulations. An asymptotic analysis is given for this singular model; the asymptotic behavior of the p hase-space distribution shows that the one-dimensional steady state distrib ution exists only for relatively high values of the coefficient of restitut ion, epsilon>0.5. The more detailed model for the coefficient of restitutio n treats this coefficient as a function of the normal impact velocity. Nume rical results from this model are also given and compared with those obtain ed by simulation. For both models the particle number density and particle fluctuation energy at the wall, required to formulate boundary conditions f or the "macroscopic" two-fluid models, are calculated as functions of model parameters. The results also illustrate the phenomenon of particle segrega tion towards the wall in turbulent gas-particulate suspensions, i.e., the f ormation of the near-wall dense layer of particles; the thickness of this l ayer is also determined as a function of model parameters. (C) 1999 America n Institute of Physics. [S1070-6631(99)00507-3].