Linear Stability Analysis of a Conical Liquid Sheet

A linear instability analysis method has been used to investigate the breakup of a conical liquid sheet under the combined influence of sinuous and varicose modes of disturbances at the liquid―gas interfaces. The maximum disturbance wave growth rate of two disturbance modes has been worked out by solving the dispersion equation of a conical liquid sheet, and the corresponding angular frequencies and dominant wave numbers have been obtained. A modified model to predict the breakup length of the conical liquid sheet was adopted. Furthermore, the surface deformation curves, which can estimate how long time the breakup process will take, have been plotted by solving the surface deformation equation. For both modes, the maximum disturbances growth rate and the dominant wave number increase as the pressure drop increase, while the breakup length and breakup time decrease with the increase of the pressure drop. Although the whole conical liquid sheet presents the varicose shape when the breakup takes place, the sinuous mode dominates the breakup process. With the increase of the geometrical characteristic parameter, the breakup length and breakup time decrease. The phase angle between the two modes affects the breakup slightly. To validate the conical sheet breakup model, the experiments were performed with the injectors of different geometry characteristics parameters and a high-speed dynamic measurement system was used to grab the detailed information of the liquid sheet breakup process. Comparison with experimental results shows that the calculation results coincide with the experiments, and the present analysis provides a good starting point for predicting unstable, wave-type behavior of the conical liquid sheet.