Two-way coupled particle-laden mixing layer. Part 1: Linear instability

Abstract

The two-way coupled particle-laden mixing layer is studied numerically and theoretically in order to understand how the addition of solid particles affects the stability of the gas flow. Numerical simulations are undertaken to obtain results equivalent to solving the Orr–Sommerfeld equation of a dusty gas mixing layer first derived by Saffman. The growth rate of a viscous particle-laden mixing layer depends on the wavenumber, flow Reynolds number, Stokes number, and bulk particulate mass loading. Two asymptotic relations proposed by Saffman have been confirmed for the first time by numerical simulations. In addition to the stabilizing effect of particles on the gas flow at large Stokes number, a destabilizing influence at small Stokes number is also observed at finite flow Reynolds number. The fact that the addition of particles can destabilize the gas flow in the absence of gravity has been shown to follow the original speculation of Saffman. Physically, the increase of effective inertia of the fluid–particle mixture causes a destabilization effect, while the enhanced viscous dissipation around particles gives a stabilization effect. These qualitatively different effects have been shown to be directly related to the direction of interphase energy transfer. Results at arbitrary mass loading, Stokes number, and wavenumber show that for a given mass loading and wavenumber, there is an intermediate Stokes number which corresponds to a maximum flow stability. We have shown that this Stokes number is on the order of one, and depends on the wavenumber. An analytical model for predicting the growth rate in a viscous, particle-laden gas mixing layer is proposed and compared with the simulation results.