The effect of a mean fluid velocity gradient on the streamwise velocity variance of a particle suspended in a turbulent flow

Abstract

The effect of a mean fluid velocity gradient on the motion of a small solid particle suspended in a turbulent gas is analyzed using Fourier transform techniques. The presence of a mean fluid velocity gradient is shown to elevate the streamwise particle velocity variance above the level predicted without such gradients; the particle velocity variance in the direction normal to the flow is shown to be only indirectly affected by the existence of fluid velocity gradients. When the particle Stokes number is small, the streamwise particle velocity variance is elevated above the level predicted in flows without mean velocity gradients at a rate which is linearly proportional to both the particle Stokes number, α, and the ratio of the streamwise velocity gradient to the characteristic frequency of the energy-containing eddies in the turbulent field, G/ω e , For particles with large Stokes numbers, the dominant mechanism by which particle streamwise velocity fluctuations are generated is through random interaction between the particle path and the mean fluid velocity gradient.