Early spray development at high gas density: hole, ligament and bridge formations

Abstract

Three-dimensional temporal instabilities, leading to spray formation of a round liquid jet segment with an outer, coaxial high-density gas flow, are studied with Navier-Stokes and level-set computations. These computations predict the liquid surface shape showing the smaller structures on the conical wave crests, i.e. lobes, holes, bridges and ligaments, which are the precursors to droplet and spray formations. These structures and their time scales affect droplet size and velocity distributions as well as spray cone angles. The gas-to-liquid density ratio, liquid Reynolds number (Re) and liquid Weber number (We) range between 0.02-0.9, 320-16 000 and 2000-230 000, respectively, which cover three distinct physical domains. (1) At higher Re and We, ligaments and then drops develop following hole and liquid bridge formations. (2) At higher gas densities throughout the Re range, several holes merge forming two bridges per lobe before breaking to form ligaments; this hole merging is explained by slower development of hairpin vortices and lobe shape. (3) In cases where both gas density and Re or We are lower, the well-ordered lobes are replaced by more irregular, smaller-scale corrugations along the conical wave crest edge; ligaments form differently by stretching from the lobes before holes form. Thicker ligaments and larger droplets form in the low Re, low gas density range. The surface wave dynamics, vortex dynamics and their interactions are explained. Understandings of liquid stream break up and concurrent smaller structure formation are built upon an examination of both translation and rotation of the fluid. In all cases, hole formation is correlated with hairpin and helical vortices; fluid motion through a perforation in the thin sheet near the wave crest corresponds to these vortices. The hole formation process is dominated by inertial forces rather than capillary action, which differs from mechanisms suggested previously for other configurations. Circulation due to streamwise vorticity increases while the lobes thin and holes form. For larger surface tension, cavities in the jet core rather than perforations in a sheet occur. The more rapid radial extension of the two-phase mixture with increasing gas density is explained by greater circulation in the ring (i.e. wave crest) region. Experimental descriptions of the smaller structures are available only at lower Re and lower density, † Email address for correspondence: sirignan@uci.edu Hole, ligament and bridge formations 187 agreeing with the computations. Computed scales of bridges, ligaments, early droplets and emerging spray radii agree qualitatively with experimental evidence through the high Re and We domains.

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

“…on the streamwise wave trough. As shown in Figure 7 and also described by Jarrahbashi et al [5], the liquid sheet between a pair of these overlapping hairpins becomes thinner. Figure 7(a) schematically depicts two neighboring hairpin vortices in the liquid-gas interface region -one originating from the lobe crest and stretching downstream (shown by the slender black tube) and the other originating from the braid and stretching upstream (shown by the red tube).…”

“…The velocity decays exponentially to zero at the center of the liquid sheet. For more detailed description of the initial conditions, see Zandian et al [22] Grid independency and domain-size independency tests have also been performed [4,5,22]. The liquid-gas interface is initially perturbed symmetrically on both sides with a sinusoidal profile and predefined wavelength and amplitude obtained from 2D full-jet simulations [22].…”

“…The main focus of these studies has been on understanding and relating vortex stretching [7], vortex tilting [8], and baroclinic effects [9] to the appearance of three-dimensionality in liquid jet instabilities. Earlier experimental studies in this field [6,[8][9][10][11][12][13][14] have been followed and reproduced in more detail by numerical computations [1,4,5,[15][16][17][18][19][20][21]. In the first studies of the role of streamwise vorticity for round liquid jets flowing into a gas, Jarrahbashi and Sirignano [4] and Jarrahbashi et al [5] showed how the mechanisms of the formation of lobes and ligaments are related to the growth of streamwise vorticity.…”

“…In the first studies of the role of streamwise vorticity for round liquid jets flowing into a gas, Jarrahbashi and Sirignano [4] and Jarrahbashi et al [5] showed how the mechanisms of the formation of lobes and ligaments are related to the growth of streamwise vorticity. For control of spray character, it is very valuable to understand the details in the cascade processes following liquid injection for each of the various atomization domains that have been identified [5]. While we do not address control and optimization in this study, it gives justification for the detailed exploration and the behavioral characterizations reported here.…”

“…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.…”