Temporal instability of confined three-dimensional liquid jet with heat and mass transfer under longitudinal acoustic oscillations

The temporal instability of a confined viscous liquid jet surrounded by high-speed co-flowing viscous gas phase is studied in this work. The effect of the longitudinal acoustic oscillations, which is regarded as gas axial velocity oscillations, is also considered. The heat and mass transfer is characterized by the ratio between conduction heat flux and the evaporation heat flux; then, an explicit dispersion relation equation is obtained. The results suggest that more than one unstable region appears because of the gas velocity oscillations, including Kelvin-Helmholtz (K-H) instability and parametric instability regions. Increasing the forcing frequency enhances the K-H instability, while it has a stabilizing effect on the parametric instability. In addition, the liquid jet tends to be more unstable in non-axisymmetric modes when the gas rotating strength is strong. Although the gas viscosity has a destabilizing effect on the gas-liquid interface, the destabilizing effect is weak due to the low viscosity of the gas phase. According to the linear instability theory, the dominant wavenumber will locate in the most unstable region. Moreover, the parametric instability in non-axisymmetric modes may be observable when the Weber number is large.