Three-dimensional temporal instability of compressible gas jets injected in liquids

A temporal linear stability analysis was conducted to study the grow th rat es of three-dimensional disturbances on a compressible inviscid gas jet inj ected into an incompressible viscous liquid coflow in the absence of gravit ational effects. The primary parameters that governed the growth rates of t he disturbances were the gas Weber number Mach number, Ohnsorge number, den sity ratio, and velocity ratio. As the Mach number was increased, the range of unstable wave numbers and the grow th rates of the unstable modes were increased. Also, the maximum growth rate was shifted to larger wave numbers (smaller wavelengths). The disturbance velocities were small, on the order of the coflowing liquid velocity. The growth rates and range of unstable w ave numbers were reduced as the liquid coflow was increased. With an increa se in liquid viscosity, the growth rates were reduced and the maximum growt h rates were shifted to longer wavelengths. A reduction in the ratio of the liquid density to the mean gas density resulted in an increase in the grow th rates of the unstable disturbances and the disturbance velocities.