Vorticity dynamics for transient high-pressure liquid injection

Abstract

The liquid jet from a round orifice during the transient start-up and steady mass flux periods of a high pressure injector is studied via Navier-Stokes and level-set computations. Via post-processing, the role of vorticity dynamics is examined and shown to reveal crucial new insights. A brief review of relevant literature is made. An unsteady, axisymmetric full-jet case is solved. Then, a less computationally intensive case is studied with a segment of the jet core undergoing temporal instability; agreement with the full-jet calculation is satisfactory justifying the segment analysis for three-dimensional computation. The results for surface-shape development are in agreement with experimental observations and other three-dimensional computations; the initial, axisymmetric waves at the jet surface created by Kelvin-Helmholtz (KH) instability distort to cone shapes; next, three-dimensional character develops through an azimuthal instability that leads to the creation of streamwise vorticity, lobe shapes on the cones, and formation of liquid ligaments which extend from lobes on the cones. The cause of this azimuthal instability has been widely described as a Rayleigh-Taylor instability. However, additional and sometimes more important causes are identified here. Counter-rotating, streamwise vortices within and around the ligaments show a relationship in the instability behavior for jets flowing into like-density fluid; thus, density difference cannot explain fully the three-dimensional instability as previously suggested. Furthermore, the formation of ligaments that eventually break into droplets and the formation of streamwise vorticity are caused by the same vortical dynamics. Waviness is identified on the ligaments which should result in droplet formation. The nonlinear development of the shorter azimuthal waves and ligament waves explains the experimental results that droplet sizes are usually smaller than KH wavelengths. The higher the relative velocity and/or the lower the surface tension the shorter are the values of the most unstable wavelengths.

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

“…Recent ballistic images, near the nozzle of diesel-like sprays at high pressure, high Re and We by Duran, Porter & Parker (2015) show that the cone angle increases with ambient pressure; see figure 2. They found resemblance between the sizes of their observed structures and the previous computational results of Jarrahbashi & Sirignano (2014), hereinafter cited as JS. However, more studies are required to delineate the liquid structures before final break up into droplets.…”

Transient behavior near liquid-gas interface at supercritical pressure

“…An explicit first-order timeintegration scheme is used instead of high-order explicit approaches or implicit methods [14] to discretize Eqs. (4) and (5). Since we are interested in the early stages of flow evolution, the small time step restriction does not become a critical point of the numerical solution.…”

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

“…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.…”

“…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].…”

“…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.…”