On the Inviscid Stability of Parallel Bubbly Flows

This paper investigates the effects of bubble dynamics on the stability of parallel bubbly flows of low void fraction. The equations of motion for the bubbly mixture are linearized for small perturbations and the parallel flow assumption is used to obtain a modified Rayleigh equation governing the inviscid stability problem. This is then used for the stability analysis of two-dimensional shear layers, jets and wakes. Inertial effects associated with the bubble response and energy dissipation due to the viscosity of the liquid, the heat transfer between the two phases, and the liquid compressibility are included. Numerical solutions of the eigenvalue problems for the modified Rayleigh equation are obtained by means of a multiple shooting method. Depending on the characteristic velocities of the various flows, the void fraction, and the ambient pressure, the presence of air bubbles can induce significant departures from the classical stability results for a single-phase fluid.