The effect of streamwise braid vortices on the particle dispersion in a plane mixing layer. I. Equilibrium points and their stability

Abstract

The dynamics of small, heavy, spherical particles are investigated in an analytical model of the stretched counterrotating streamwise braid vortices commonly found in three-dimensionally evolving mixing layers. The flow field consists of two superimposed rows of Stuart vortices of opposite sign, with an additional two-dimensional strain field. The particle dynamics are determined by a balance of inertial, gravitational, and viscous drag forces, i.e., the dimensionless Stokes and Froude numbers, St and Fr, as well as by the dimensionless strain rate, and the Stuart vortex family parameter. Equilibrium points for the particles, as well as their stability criteria, are determined analytically, both in the absence and in the presence of gravity, and for different orientations of the gravity vector. In the absence of gravity, accumulation of low St particles can occur at the center of the braid vortices. An analytical expression for the critical particle diameter, below which accumulation is possible, is derived. The presence of gravity can lead to the emergence of multiple equilibrium points, whose stability properties depend on their locations. For a horizontal mixing layer flow and strong gravity effects, unconditional accumulation can occur midway between the streamwise braid vortices in the upwelling regions. Conditionally stable accumulation regions exist a short horizontal distance away from the centers of the braid vortices. If the gravity vector lies within the plane of the mixing layer, accumulation points exist only for moderate strengths of gravity. Under these circumstances, conditional accumulation is possible near the streamwise vortex centers.

Parallel Algorithms for Particles–Turbulence Two-Way Interaction Direct Numerical Simulation

“…Recent reviews on the particle-demixing effects in turbulent two-phase flows can be found in [3][4][5]. Pioneering numerical simulations of tree-dimensional flows based on one-way coupling effects have been done by [1,[6][7][8][9]. However, the research on two-way momentum coupling effects in two-phase flow is still at a fundamental stage of study.…”

LES modelling of flow in a simple airway model

“…It is theoretically possible to directly resolve the whole spectrum of turbulent scales using direct numerical simulation (DNS). Indeed, DNS has been successfully used on particle dispersion in temporal mixing layers [21,24] as well as in spatial mixing layer [13]. However, DNS is extremely expensive and requires huge computer power, as the grid density required is proportional to Re 3 .…”

The effect of streamwise braid vortices on the particle dispersion in a plane mixing layer. II. Nonlinear particle dynamics

“…In Part I of the present investigation, 1 we introduced an analytical model of the counterrotating strained streamwise braid vortices commonly found in three-dimensionally developing plane mixing layers. [2][3][4][5][6] These flow structures are expected to result in a significant modification of the dominant two-dimensional particle dispersion mechanisms, [7][8][9][10][11][12] which are known to lead to the formation of bands of particles in the braid region.…”