Abstract

The motion of liquid jets ejected from elliptical orifices is studied theoretically and experimentally. In the theoretical part of the study, the linear evolution of initially small disturbances on the inviscid jets is investigated using a three-dimensional analysis. In addition, to study the viscous free-surface flows, an approach based on the Cosserat theory (also called directed theory) is used. Temporal and spatial analyses are performed and the dispersion equations of waves on the jet column are derived to show the growth rate of disturbances for different modes under various conditions. An equation for the jet profile is suggested which describes the axis-switching phenomenon and breakup for various conditions. The equations are approximated for small and large ellipticities, and well-known dispersion relations of circular and planar jets are retrieved. It is shown that in the capillary dominant regimes, the effect of ellipticity is increasing the growth rate and range of unstable wavenumbers. In this case only modes symmetric to both major and minor axes are unstable. At higher Weber numbers, as the aerodynamic forces become dominant, by increasing the ellipticity, growth rate is decreased. In these Weber numbers, as the ellipticity increases, the growth rates of the modes that are symmetric with respect to the major axis are larger than those of antisymmetric with respect to the major axis. Increasing the gas to liquid density ratio increases the disturbances growth rate, while increasing the liquid viscosity dampens the growth rate and shifts the maximum growth rate toward longer waves. Experiments are performed to validate the linear results and to investigate the jet velocity profile. Several nozzles with different ellipticities and length to diameter ratios are designed and their behaviors are examined under free (natural) and excited (forced) perturbations. The spatial evolution of the jet shape is captured using a high speed camera. In the forced breakup case, the stimulations are performed by modulating the jet velocity with a piezoelectric actuator through given sinusoidal perturbations. The measured data are in good agreement with theoretical predictions except at high ellipticities where nonlinear effects are strong.