Nonlinear spatial instability of an annular swirling viscous liquid sheet

Instability and breakup of a viscous annular liquid sheet that is exposed to co-flowing inner and outer gas streams have been investigated using a nonlinear spatial stability analysis. A perturbation expansion method is used with the initial amplitude of the disturbance as the perturbation parameter. The evolution of the two gas–liquid interfaces is tracked until the sheet breaks up and the breakup length is determined. The model is validated by comparison with available experimental data. The effects of liquid swirl strength, gas-to-liquid density ratio, radius of curvature ratio, and liquid viscosity on the sheet instability and breakup have been studied. The results show that at very low values of liquid swirl, it has a stabilizing effect on sheet breakup, but as the swirl strength increases, it strongly destabilizes the sheet. Also, with increasing swirl strength, the occurrence of the large surface deformations moves from the inner interface to the outer interface. The sheet breakup length increases slightly and then decreases rapidly with an increase in liquid swirl strength. Without liquid swirl, the axisymmetric mode is the dominant instability mode. However, with increasing liquid swirl strength, the higher helical modes become dominant and the breakup becomes increasingly asymmetric. When the undisturbed liquid sheet has a purely axial motion, the inner gas stream is more effective in sheet breakup than the outer gas stream. In the presence of liquid swirl, the outer gas stream is more disruptive than the inner gas stream. The breakup length becomes shorter as gas-to-liquid density ratio and the radius of curvature ratio increases. Increase in liquid viscosity tends to slow the disturbance growth and increases the sheet breakup length.