Effect of heat and mass transfer on the instability of an annular liquid sheet

Abstract

A temporal linear instability analysis has been conducted to investigate the effect of heat and mass transfer on the instability of an annular liquid sheet axially moving in the gas medium. The dispersion relation is obtained and solved numerically. Energy budget is calculated to provide physical insights of various instability driving mechanisms. The results show that heat and mass transfer promotes the wave growth rate mainly at small wave numbers. In contrast to the case without heat and mass transfer, the wave growth rate with strong heat and mass transfer peaks at zero wave number. Liquid viscosity is found to have a minimal stabilizing effect on the sheet instability. Regardless of the heat and mass transfer, increasing liquid Weber number suppresses the sheet instability below a crossover point of wave number at 1.15, and promotes the sheet instability above the crossover point. In the presence of strong heat and mass transfer, increasing gas-to-liquid density ratio reduces the wave growth rate at small wave numbers below 0.28, and beyond which increases the wave growth rate. Reducing sheet thickness promotes the sheet instability for all wave numbers. The energy budgets show that the inner gas disturbance is most responsible for promoting the wave growth rate at large liquid Weber numbers; and the inner interface dominates the outer one in destabilizing the annular liquid sheet.