Linear stability of confined swirling annular liquid layers in the presence of gas velocity oscillations with heat and mass transfer

The linear stability of confined swirling annular liquid layers is studied in the presence of gas velocity oscillations with heat and mass transfer. The dispersion relation is obtained and is solved using Floquet theory. Results show that parametric instability regions appear when oscillations are considered and the oscillations play a destabilizing role. The forcing frequency controls the location of parametric instability regions and plays a slight destabilizing role. Heat and mass transfer has a stabilizing effect at small Weber numbers but a destabilizing effect at large Weber numbers. In addition, heat and mass transfer promotes the dispersion effect, vanishing the gap between the parametric and Kelvin-Helmholtz (K-H) instability regions. The effect of mode order is complex. The order n=0 is the most unstable. Rotating restrains the instability. The effect of confinement is complex. Confinement plays a stabilizing role at all the range of Weber numbers when ignoring heat and mass transfer. However, confinement promotes the instability at small Weber numbers but suppresses it at large Weber numbers when considering heat and mass transfer.