Length-scale cascade and spread rate of atomizing planar liquid jets

The primary breakup of a planar liquid jet is explored via direct numerical simulation (DNS) of the incompressible Navier-Stokes equation with level-set and volume-of-fluid interface capturing methods. PDFs of the local radius of curvature and the local cross-flow displacement of the liquid-gas interface are evaluated over wide ranges of the Reynolds number ($Re$), Weber number ($We$), density ratio and viscosity ratio. The temporal cascade of liquid-structure length scales and the spread rate of the liquid jet during primary atomization are analyzed. The formation rate of different surface structures, e.g. lobes, ligaments and droplets, are compared for different flow conditions and are explained in terms of the vortex dynamics in each atomization domain that we identified recently. With increasing $We$, the average radius of curvature of the surface decreases, the number of small droplets increases, and the cascade and the surface area growth occur at faster rates. The spray angle is mainly affected by $Re$ and density ratio, and is larger at higher $We$, at higher density ratios, and also at lower $Re$. The change in the spray spread rate versus $Re$ is attributed to the angle of ligaments stretching from the jet core, which increases as $Re$ decreases. Gas viscosity has negligible effect on both the droplet-size distribution and the spray angle. Increasing the wavelength-to-sheet-thickness ratio, however, increases the spray angle and the structure cascade rate, while decreasing the droplet size. The smallest length scale is determined more by surface tension and liquid inertia than by the liquid viscosity, while gas inertia and liquid surface tension are the key parameters in determining the spray angle.