A stochastic description of wall sources in a turbulent field: part 2. Calculation for a simplified model of horizontal annular flows

A stochastic approach that uses a modified Langevin equation to calculate fluid velocities seen by particles dispersing in a turbulent flow was verified at Reτ=150, VT+=0.11, τp+=20 in Part 1 of this paper. It is now used to examine the effects of particle inertia and gravitational settling on the deposition rate at Reτ=590. The system considered is an idealized annular flow in a horizontal channel. Drops are admitted from the top and the bottom walls at relative rates such that a fully-developed field is realized. The walls are considered to be arrays of point sources. The theoretical problem is to model the behavior of an instantaneous wall source. Particles are ejected from the source with a velocity Vi0 at time zero. They are mixed by the fluid turbulence and eventually deposit at the top and bottom walls. Of particular interest are the strong effect of very small gravitational settling on the rate of deposition and the definition of a critical condition for particles (ejected from the bottom wall) to reach the top wall to create an annular flow.