Spatial instability in annular swirling viscous liquid sheet

The spatial linear instability of an annular swirling viscous liquid sheet moving in an inviscid gas medium was investigated. With both para-sinuous and para-varicose modes analyzed, results show that under certain conditions the mode difference for the maximum disturbance growth rate is small. However, the para-sinuous mode is always the dominant mode for an annular swirling viscous liquid sheet in the parameter range studied here. Liquid swirls have a stabilizing effect at low swirling strengths. Two regions were identified: the initial region, where the maximum disturbance growth rate decreases with increasing dimensionless liquid swirling strength, and a region of monotonic increase of maximum disturbance growth rate with increasing liquid swirling strength. The non-axisymmetric mode is the dominant mode when swirling strength is large in an annular liquid sheet. The drop in axial size of non-axisymmetric mode is larger than that for the axisymmetric mode. Liquid viscosity suppresses increases in the maximum disturbance growth rates and the dominant wavenumber. Surface tension has a destabilizing effect when liquid swirling strength is absent or small, subject to a certain criterion, and a stabilizing effect irrespective of the presence of liquid swirling strength otherwise. Curvature in the annular sheet stabilizes the breakup of the liquid sheet. This effect is more obvious if the liquid swirling strength is large. For different liquid swirling strengths, the dominant disturbance modes of annular liquid sheets become axisymmetric modes as the annular liquid curvature decreases. The dominant wavenumber increases as annular liquid curvature decreases; this trend is more obvious with larger liquid swirling strengths. (C) 2015 AIP Publishing LLC.