Three-Dimensional Temporal Instability of Compressible Gas Jets Injected in Liquids

Abstract

A temporal linear stability analysis was conducted to study the growth rates of three-dimensional disturbances on a compressible inviscid gas jet injected into an incompressible viscous liquid coflow in the absence of gravitational effects. The primary parameters that governed the growth rates of the disturbances were the gas Weber number, Mach number, Ohnsorge number, density ratio, and velocity ratio. As the Mach number was increased, the range of unstable wave numbers and the growth 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 wave numbers were reduced as the liquid coflow was increased. With an increase in liquid viscosity, the growth rates were reduced and the maximum growth 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 growth rates of the unstable disturbances and the disturbance velocities