Stability of confined gas-liquid shear flows in recessed shear coaxial injectors

The linear-temporal and spatiotemporal instability behavior of a confined gas-liquid shear flow was investigated theoretically. The practical situation which motivated this investigation is the recessed gas-liquid shear coaxial injector, usually used in liquid propellant rocket engines. The corresponding dispersion relation between the complex wave growth rate and the complex wave number was derived. The temporal stability analysis shows that a more strongly confined gas-liquid shear flow exhibits a larger temporal growth rate than a weakly confined gas- liquid shear flow. A larger nondimensional outer injector radius, a larger liquid-to-gas density ratio and velocity ratio, and a smaller liquid Weber number would stabilize the confined gas-liquid shear flow. In spatiotemporal mode, when the confinement is strong, flow is absolutely unstable. When the confinement becomes weak, the flow can transit to become convectively unstable. Under strong confinement, the confined jet is always absolutely unstable.