On the motion of small particles in a homogeneous turbulent shear flow

Abstract

The motion of small spherical solid particles is simulated numerically in a homogeneous turbulent gas shear flow generated by the large eddy simulation for two different mean shear rates (Γ), 12.9 sec−1 and 44 sec−1, which correspond to two different flow regimes. The results include a detailed study of the effect of the particle’s inertia and the particle’s free-fall velocity in still fluid (vd) on the particle dispersion and settling velocities. Let 〈YiYj〉 be the displacement tensor of the particles, where subscripts 1, 2, and 3 refer to the streamwise, the upward, and the spanwise directions, respectively. For the case with Γ=12.9 sec−1, the turbulence intensity of the flow decreases as time (t) increases and approaches an essentially constant value. It was found that 〈Y21〉∝t3, 〈Y22〉∝t, and 〈Y23〉∝t essentially when Γt=3–5, which agrees with the asymptotic behavior of the previous theoretical result for the fluid point dispersion in a stationary sheared turbulence. For the case with Γ=44 sec−1, the turbulence intensity of the flow increases with time monotonically. It was found that 〈Y21〉∝t4, 〈Y1Y2〉∝t3, 〈Y22〉∝t2, and 〈Y23〉∝t2 for large values of Γt. For both cases with different Γ’s, a particle falling in the direction perpendicular to the mean flow is found to approach an asymptotic state and the relative velocity between the particle and the fluid reaches a constant value. A particle leads the fluid in the streamwise direction but falls less rapidly in sheared turbulence than that in still fluid. It is also found that the magnitudes of the relative velocity components between the particle and the fluid in a turbulent shear flow are less than those in a corresponding laminar Couette flow.