Abstract
A temporal linear stability analysis has been carried out to predict the instability of an annular swirling liquid sheet emanating from an atomizer that is subjected to cocurrent inner and outer gas streams. The analysis considers three-dimensional disturbances. The effect of the liquid swirl-velocity profile on the instability is investigated by considering free-vortex-type and solid-vortex-type swirl-velocity variations in the liquid sheet. A large range of liquid axial Weber numbers and liquid swirl Weber numbers are considered that encompasses most practical operating conditions. Results for disturbance growth rate as a function of wave number are obtained by solving the dispersion equations obtained with the two types of liquid swirl-velocity profiles. Effects of density ratio, radius-of-curvature ratio, surface tension, and outer air axial Weber number on the liquid sheet stability are examined. It is seen that the presence of liquid swirl and the type of swirl-velocity profile have a significant impact on the instability of the liquid sheet. Liquid swirl imposed on an annular liquid sheet has a dual effect on its stability, where swirl has a stabilizing effect at low values of liquid swirl Weber number, whereas it has a destabilizing effect at higher values of swirl Weber number. With increasing liquid swirl Weber number, the growth rate of parasinuous disturbances increases. However, the growth rate for paravaricose disturbances decreases with increasing liquid swirl, and eventually, at higher liquid swirl, the sheet is no longer unstable to paravaricose disturbances. The disturbance growth rates with a free-vortex-type profile are lower compared to those with a solid-vortex-type profile at very low swirl Weber numbers. The behavior is opposite at moderate-to-high swirl Weber numbers.