Temporal Instability of Confined Viscoelastic Swirling Liquid Film with High-speed Compressible Gas

The linear instability of a confined viscoelastic liquid film with central compressible gas is theoretically investigated in this study. And the heat and mass transfer is also considered. The dispersion relation including both heat and mass transfer and gas compressibility is obtained. The heat and mass transfer is characterized by the ratio between the conduction heat flux and evaporation heat flux, and the gas compressibility is characterized by the gas Mach number. The results suggest that both the maximum growth rate and unstable wavenumber range increase as the ratio of the conduction heat flux to evaporation heat flux increases. The gas Mach number has a destabilizing effect on the gas-liquid interface. However, its effect is neglectable when the gas Mach number is small. Increasing the gas-liquid density can promote the breakup process. Furthermore, the effect of viscoelasticity of liquid phase is also examined. The stress relaxation time has an unstable effect on the gas-liquid interface, and the increasing deformation retardation time plays a stabilizing role. And the effects of Weber number, Reynolds number and other dimensionless parameters are also studied.