Stability of an annular viscous liquid jet in compressible gases with different properties inside and outside of the jet

A spatial linear instability analysis is conducted on an annular viscous liquid jet injected into compressible gases and a three-dimensional model of the jet is developed. The model takes into account differences between the velocities, densities of the gases inside and outside of the liquid jet. Theoretical analysis reveals that there exist 9 dimensionless parameters controlling the instability of the liquid jet. Numerical computations reveal some basic characteristics in the breakup and atomization process of the liquid jet as well as influences of these relevant parameters. Major observations and findings of this study are as follows. The Mach number plays a destabilizing role and the inner Mach number has a greater effect on the jet instability than the outer Mach number. The Reynolds number always tends to promote the instabilities of the liquid jet, but its influence is very limited. The Weber number and the gas-to-liquid density ratio also have unstable effects and can improve the atomization of liquid jets. Furthermore, the effects of the Weber number and gas-to-liquid density ratio on the maximum growth rates of axisymmetric and non-axisymmetric disturbances and corresponding dominant wave numbers are manifested in a linear way, while that of the Mach number is non-linear. The effect of Reynolds on the maximum growth rates is non-linear, but the dominant wavenumber is almost not affected by the Reynolds number.