Mechanisms of Liquid Stream Breakup: Vorticity and Time and Length Scales

Abstract

The 3D, temporal instabilities on a planar liquid jet are studied using DNS with level-set and VoF interface-capturing methods. The λ2 method has been used to relate the vortex dynamics to the surface dynamics at different stages of the jet breakup. The breakup character depends on the Ohnesorge number (Oh) and gas-to-liquid density ratio. At high Reynolds number (Re) and high Oh, hairpin vortices form on the braid and overlap with the lobe hairpins, thinning the lobes, which then puncture creating holes and bridges. The bridges break, creating ligaments that stretch and break into droplets by capillary action. At low Oh and high Re, lobe stretching and thinning is hindered by high surface tension and splitting of the original Kelvin-Helmholtz vortex, preventing early hole formation. Corrugations form on the lobe edges, influenced by the split vortices, and stretch to form ligaments. Both mechanisms are present in a transitional region in the W e-Re map. At lower Re and not-too-large Weber number (W e), lobe stretching occurs but with longer and larger ligaments in this third domain which has a hyperbolic transition to the hole formation domain as W e increases. The three domains with differing breakup behaviors each occupy distinct portions of a plot of W e based on gas density versus Re based on liquid properties. Characteristic times for the hole formation, as well as the lobe and ligament stretching are different -the former depending on the surface tension and the latter on liquid viscosity. In the transitional region, both times are of the same order. KeywordsGas/liquid flow, primary atomization, breakup mechanism, hydrodynamic instability, vortex dynamics. IntroductionEarlier computational works on the breakup of liquid streams at higher Weber number (W e) and Reynolds number (Re) focused on the surface dynamics using either volume-of-fluid or level-set methods [1][2][3]. More recently, Jarrahbashi and Sirignano [4] and Jarrahbashi et al. [5] numerically simulated the temporal behavior of round jets with additional data analysis that related the vorticity dynamics to the surface dynamics. Jarrahbahsi et al. [5] showed that important spray characteristics, e.g. droplet size and spray angle, differed in different ranges of W e, Re, and density ratio. Therefore, further studies of the breakup mechanisms are needed to fully understand the causes of these differences. Consequently, there are remaining questions to be addressed in this paper: What are the details of the liquid dynamics in each breakup domain? What causes the difference in the breakup cascade? What are the roles of surface tension, liquid viscosity, and gas density? The answers to these questions would be crucial in understanding and controlling the droplet size distribution in primary atomization of liquid jets. Vortex dynamics concepts can clearly explain surface deformation of a liquid jet in the primary atomization process. The Kelvin-Helmholtz (KH) instability promotes the formation of spanwise vorticity waves growing into coherent ...