Instability and breakup of liquid sheets and liquid jets

Linear stability analyses are performed for the instability of liquid sheets and liquid jets under 3-D disturbances. The first part of the dissertation presents a theoretical model to predict mean droplet sizes from simplex atomizers. It is observed that the relative velocity between liquid and gas phase, density ratio and surface curvature enhance the interfacial aerodynamic instability. Combination of axial and swirling velocity components is more effective than only axial component for disintegration of liquid sheet. For both large and small-scale fuel nozzles, mean droplet sizes are predicted based on the linear stability analysis and the proposed breakup model. The predictions agree well with experimental data at both large and small scale. In the second and third part of the dissertation, a theoretical model to predict the instability of an annular liquid sheet subjected to coaxial swirling air streams is developed. It is found that swirl not only increases the growth rate and the range of unstable wave numbers, but also shifts the dominant mode from the axisymmetric to a helical mode. With the presence of air swirl, the most unstable wave number and maximum growth rate are higher than its no-swirl counterpart. Liquid viscosity was found to have a damping effect on the growth of unstable waves. As Reynolds number increases, both the maximum growth rate and the most unstable wave number increase dramatically at first and then gradually approaching the values corresponding to the inviscid case. In the fourth part of this dissertation, the instability of a viscous liquid jet surrounded by a swirling air stream is studied. The range of wave numbers in which asymmetric modes have higher growth rates than the axisymmetric mode and dominate the instability is predicted and agrees very well with experimental data. The density ratio significantly enhances the instability as the axial Weber number does. Liquid viscosity inhibits the disintegration process and damps higher helical modes more significantly than the axisymmetric mode. It is observed that air swirl has a stabilizing effect on the liquid jet. The local and global effect of air swirl profile are also investigated.