A stochastic model for solid particle dispersion in a nonhomogeneous turbulent field

Abstract

Dispersion of solid particles in three dimensions in a fully developed nonhomogeneous turbulent flow in a channel was studied. A particle point source at a distance of 40 wall units from the bottom wall was considered. Data were obtained by carrying out experiments in a direct numerical simulation. The relative roles of gravity and of turbulence in dispersing the particles are examined. The results are used to test the accuracy of a stochastic Lagrangian model which utilizes a modified Langevin equation to represent the fluid fluctuations seen by a solid particle. All of the parameters, with the exception of the time scales, are obtained from Eulerian statistics. Good agreement is obtained by assuming the spatial variation of the time scales is the same as would be obtained by examining the dispersion of fluid particles. The Langevin equation is further tested by considering the settling of particles that are uniformly distributed in the flow field at time zero. There is some evidence to support the suggestion that the gravitational settling velocity at the wall is greater than the free-fall velocity.