The growth of instabilities in annular liquid sheets

An annular liquid sheet surrounded by parallel co-flowing gas is an effective atomiser. However, the initial instabilities which determine the primary break-up of the liquid sheet are not well understood. Lack of agreement on the influence of the boundary conditions and the non-dimension scaling of the initial instability persists between theoretical stability analyses and experiments, since there is little experimental data available on the near-field behaviour of the instability. To address this matter, we have undertaken an experimental parametric study of an aerodynamically-driven, non-swirling annular water sheet. The effects of sheet thickness, inner and outer gas–liquid momentum ratio were investigated over an order of magnitude variation in Reynolds and Weber number. From high-speed image correlation measurements in the near-nozzle region, we propose new empirical correlations for the frequency of the instability as a function of the total gas–liquid momentum ratio, with good non-dimensional collapse. From analysis of the instability velocity probability densities, we find two persistent and distinct superimposed instabilities with different growth rates. The first is a short-lived, rapidly saturating sawtooth-like instability. The second is a slower-growing stochastic instability which persists through the break-up of the sheet. The presence of multiple instabilities whose growth rates do not strongly correlate with the shear velocities may explain some of the discrepancies between experiments and stability analyses.