Inviscid Stability of Bubbly Jets

This paper investigates the effects of bubble dynamics on the stability of bubbly and cavitating jets 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 of a two-dimensional jet. 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 problem for the modified Rayleigh equation of a Bickley jet are obtained by a multiple shooting method. Depending on the jet velocity, the void fraction, and the ambient pressure, the presence of air bubbles can induce significant departures from the classical results for a single phase fluid.