Particle dispersion in organized vortex structures within turbulent free shear flows

Abstract

A discrete vortex model is used to approximate adequately large eddy features in turbulent free shear flows and the effects of such eddy structures on Lagrangian particle trajectories and particle dispersion are investigated. Two independent scaling parameters (i) the ratio of the particle's aerodynamic response time to the characteristic flow time, the Stokes number S t = ρ p d 2 p Δ U(1+ C m / γ)/18 μδ; and (ii) the ratio of inertia to gravitational forces, the Froude number Fr= ΔU/ gδ , together with the mass ratio parameter γ, have been introduced to determine the particle dynamics. The Stokes number has been modified to account for the effect of the density ratio of particles to the carrier fluid on particle dispersion. It is demonstrated that St, Fr and γ, which constitute a dominant single scaling group, can be used to characterise particle transport dynamics in turbulent free shear flows. In seeking quantification of the particle dispersion, the Eulerian approach based on the particle number fluxes at different downstream cross-sections of the mixing layer in terms of ensemble trajectory statistics and Lagrangian approach based on the particle mean square displacement are adopted. The simulations show the existence of different parameter regimes, in which the particle motion is dominated by both the large-scale vortices and gravity. At intermediate Stokes numbers, the particles acquire larger dispersion than the particles do at other ranges of the Stokes number. The particle dispersion patterns obtained are consistent with earlier experimental observations and numerical simulations ( Wen, Kamalu, Chung, Crowe & Troutt, 1992; Crowe, Chung & Troutt, 1993) that heavy particles accumulate at the periphery of the large-scale vortices and particularly near the braid stagnation points between the consecutive vortices.