Temporal analysis of planar liquid-jet atomization
The temporal evolution of three-dimensional instabilities on an incompressible planar liquid sheet segment is studied using direct numerical simulation (DNS), and the level-set and volume-of-fluid methods for the liquid-gas interface tracking. The purpose of this study is to reveal new crucial insights into the development of three-dimensional instabilities on liquid sheets, which result in formation of lobes, bridges and ligaments, and eventually break into droplets. Three atomization cascades are distinguished at early breakup, which are well categorized on a gas Weber number (Weg) versus liquid Reynolds number (Rel) map. Each atomization domain has a distinct breakup mechanism with its own characteristic time and length scales in the cascade process. λ2 method is used to identify the vortices near the liquid-gas interface and relate the vortex interactions to the surface dynamics at different stages of the jet breakup - namely, lobe formation, lobe perforation, ligament formation, stretching and tearing. Vortex dynamics explains the hairpin formation, and the interaction between the hairpins and the Kelvin-Helmholtz (KH) roller explains the perforation of the lobes at high Weg, the formation of corrugations on the lobe front edge at high Rel, and the stretching of lobes into ligaments at low Rel and low Weg. Streamwise vorticity generation - resulting in three-dimensional instabilities - is mainly caused by vortex stretching and baroclinic torque at high and low density ratios, respectively. Generation of streamwise vortices and their interaction with spanwise vortices produce the liquid structures seen at various flow conditions, understanding of which is crucial for controlling the droplet-size distribution and jet spread rate in primary atomization. Probability density functions (PDFs) of the local radius of curvature and the local cross-flow displacement of the liquid-gas interface are evaluated over wide ranges of Rel, Weg, gas-to-liquid density ratio and viscosity ratio, and wavelength-to-sheet-thickness ratio. A novel analysis enables us to show the temporal cascade of liquid-structure length scales as well as quantify the spread rate of the liquid jet during primary atomization. The spray angle and the mean surface length scale are evaluated from the PDFs and are compared for wide ranges of dimensionless parameters. The validity and usefulness of the temporal analysis is established by a comparison with dynamics of a spatially developing liquid jet with slower coaxial gas flow. It is shown that the deformations in the upstream region of the jet cap follow a periodic behavior that can be well portrayed in a frame moving with the convective velocity of the liquid jet, as is implemented in our temporal model.