Linear instability of two-way coupled particle-laden jet

Abstract

The two-way coupled particle-laden jet is studied numerically in order to understand how the addition of solid particles affects the stability of the jet. In contrast with the particle-laden mixing layer studied, the jet flow stability is complicated by a variable wave (or phase) velocity and an additional curvature parameter, i.e., the ratio of jet radius to shear layer thickness. Nevertheless, we have demonstrated that the following similar scenario holds for a particle-laden jet: the addition of particles can destabilize the flow at small particle Stokes number, while the stabilizing effect prevails for intermediate to large Stokes numbers. Both these competing effects scale approximately linearly with the particle mass loading. We also found that the addition of particles increases the wave velocity at high wave numbers but decreases the wave velocity at low wave numbers. The fact that the addition of particles can destabilize the gas flow in the absence of gravity has been shown to follow the previous speculation. Two general asymptotic relations proposed by Saffman have been confirmed numerically for the case of the particle-laden jet. Physically, the increase of effective inertia of the fluid–particle mixture causes a destabilization effect while the enhanced viscous dissipation around the particles gives a stabilization effect. Results for various mass loadings, Stokes numbers, and wave numbers show that for a given mass loading and wave number, there is an intermediate Stokes number that corresponds to a maximum flow stability. We have shown that this Stokes number is on the order of 1 and depends weakly on the wave number.