A stochastic description of wall sources in a turbulent field. Part 1: Verification

A stochastic model for the dispersion and deposition of particles in a turbulent field is explored. The trajectories of particles originating from a wall source in a horizontal channel are considered. The fluid turbulence seen by the particles is modeled by a Langevin equation that is modified to account for spatial nonhomogeneities. The results of these studies are used to describe a simplified version of an annular flow in which particles, admitted to the field at the two walls, mix and deposit downstream. In these calculations the walls are represented as arrays of point sources. The relative strengths of the sources at the two walls are adjusted so as to realize a stationary state. The results are compared with calculations done in a direct numerical simulation of the turbulence. Considering the simplicity of the model, the agreement is quite good. The work described in this paper opens the possibility of carrying out studies of the diffusion and deposition processes over a wide range of conditions. The development of a physical understanding of the concentration distribution and of the rate of deposition is of particular interest.