Velocity modulation on the linear instability of liquid jets in ambient gas

Abstract

The linear instability analysis of liquid jets with periodic velocity modulation in the ambient gas is carried out. Utilizing the viscous potential theory and the Floquet theory, an analytical dispersion relation for the perturbation growth can be obtained. Due to the parametric resonance caused by velocity modulation, the oscillatory Kelvin–Helmholtz instability (OKHI) can be triggered in the short-wavelength region, leading to the competition between the OKHI and the intrinsic Rayleigh–Plateau and Kelvin–Helmholtz instability (RP-KHI). The parametric study shows that the increase in the velocity oscillation amplitude can enhance the jet instability and lead to the transition of the instability mechanism from the RP-KHI to the OKHI. The velocity oscillation frequency mainly affects the growth of the OKHI. Specifically, the maximum growth rates of perturbation vary with the oscillation frequency at moderate frequencies due to the competition between the RP-KHI and the OKHI, whereas they converge to constant values as the frequency either increases or decreases continuously. The increase in the Weber number promotes the RP-KHI and the OKHI simultaneously, and the jet breakup is dominated by the axisymmetric perturbation of the RP-KHI consistently. The increase in the Reynolds number enhances the jet instability, but hardly affects unstable wavenumber regions. By comparing the maximum growth rates of axisymmetric and non-axisymmetric perturbations, the predominant mode of the jet instability can be identified. Considering variations in the velocity oscillation amplitude and frequency, the transition between the RP-KHI and the OKHI can be predicted by a phase diagram.