THE EFFECT OF STREAMWISE BRAID VORTICES ON THE PARTICLE DISPERSION INA PLANE MIXING LAYER .1. EQUILIBRIUM POINTS AND THEIR STABILITY

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 o f opposite sign, with an additional two-dimensional strain field. The particle dynamics are determined by a balance of inertial, gravitation al, and viscous drag forces, i.e., the dimensionless Stokes and Froude numbers, St and Pr, as well as by the dimensionless strain rate, and the Stuart vortex family parameter. Equilibrium points for the particl es, 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, accumul ation of low St particles can occur at the center of the braid vortice s. An analytical expression for the critical particle diameter, below which accumulation is possible, is derived. The presence of gravity ca n lead to the emergence of multiple equilibrium points, whose stabilit y 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 di stance away from the centers of the braid vortices. If the gravity vec tor lies within the plane of the mixing layer, accumulation points exi st only for moderate strengths of gravity. Under these circumstances, conditional accumulation is possible near the streamwise vortex center s. (C) 1996 American Institute of Physics.