Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-19T13:00:02.569Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  01 March 2016

D. Jarrahbashi ,
W. A. Sirignano ,
P. P. Popov  and
F. Hussain
D. Jarrahbashi
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
W. A. Sirignano*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
P. P. Popov
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
F. Hussain
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
*
†Email address for correspondence: sirignan@uci.edu
Get access Rights & Permissions [Opens in a new window]

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, 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.

JFM classification

Drops and Bubbles: Aerosols/atomization Multiphase and Particle-laden Flows: Gas/liquid flow Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 792 , 10 April 2016 , pp. 186 - 231
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramovich, G. N. 1963 Theory of Turbulent Jets. MIT Press.Google Scholar
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499–525.CrossRefGoogle Scholar
Bremond, N. & Villermaux, E. 2005 Bursting thin liquid films. J. Fluid Mech. 524, 121–130.CrossRefGoogle Scholar
Collis, S. S., Lele, S. K., Moser, R. D. & Rogers, M. M. 1994 The evolution of a plane mixing layer with spanwise nonuniform forcing. Phys. Fluids 6, 381–396.CrossRefGoogle Scholar
Comte, P., Lesieur, M. & Lamballais, E. 1992 Large- and small-scale stirring of vorticity and a passive scalar in a 3-d temporal mixing layer. Phys. Fluids 4 (12), 2761–2778.CrossRefGoogle Scholar
Dabiri, S.2009 Effects of cavitation on high pressure atomization. PhD thesis, University of California, Irvine.Google Scholar
Dabiri, S., Sirignano, W. A. & Joseph, D. D. 2007 Cavitation in an orifice flow. Phys. Fluids 19, 072112.CrossRefGoogle Scholar
Dabiri, S., Sirignano, W. A. & Joseph, D. D. 2008 Two-dimensional and axisymmetric viscous flow in apertures. J. Fluid Mech. 605, 1–18.CrossRefGoogle Scholar
Desjardins, O. & Pitsch, H. 2010 Detailed numerical investigation of turbulent atomization of liquid jets. J. Atomiz. Sprays 20, 311–336.Google Scholar
Dombrowski, N. & Fraser, R. P. 1954 A photographic investigation into the disintegration of liquid sheets. Phil. Trans. A 247, 101–130.Google Scholar
Duran, S. P., Porter, J. M. & Parker, T. E. 2015 Picosecond ballistic imaging of diesel injection in high-temperature and high-pressure air. Exp. Fluids 56 (4), 1–12.CrossRefGoogle Scholar
Hayase, T., Humphrey, J. A. C. & Greif, R. 1992 A consistently formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedure. J. Comput. Phys. 98, 108–118.CrossRefGoogle Scholar
Herrmann, M. 2011 On simulating primary atomization using the refined level set grid method. J. Atomiz. Sprays 21, 283–301.CrossRefGoogle Scholar
Hiroyasu, H., Arai, M. & Tabata, M.1989 Empirical equations for the sauter mean diameter of a diesel spray. SAE Tech. Paper 890464.CrossRefGoogle Scholar
Hiroyasu, H. & Kadota, T.1974 Fuel droplet size distribution in diesel combustion chamber. SAE Tech. Paper 740715.CrossRefGoogle Scholar
Hussain, A. K. M. F. & Clark, A. R. 1981 On the coherent structure of the axisymmetric mixing layer: a flow-visualization study. J. Fluid Mech. 104, 263–294.CrossRefGoogle Scholar
Jarrahbashi, D. & Sirignano, W. A. 2014 Vorticity dynamics for transient high-pressure liquid injection. Phys. Fluids 26, 101304.CrossRefGoogle Scholar
Lhuissier, H. & Villermaux, E. 2013 Effervescent atomization in two dimensions. J. Fluid Mech. 714, 361–392.CrossRefGoogle Scholar
Liepmann, D. & Gharib, M. 1992 The role of streamwise vorticity in the near-field entrainment of round jets. J. Fluid Mech. 245, 643–668.CrossRefGoogle Scholar
Linne, M., Paciaroni, M., Hall, T. & Parker, T. 2006 Ballistic imaging of the near field in a diesel spray. Exp. Fluids 40, 836–846.CrossRefGoogle Scholar
Mansour, A. & Chigier, N. 1990 Disintegration of liquid sheets. Phys. Fluids A 2, 706–749.CrossRefGoogle Scholar
Marmottant, P. & Villermaux, E. 2004 On spray formation. J. Fluid Mech. 498, 73–111.CrossRefGoogle Scholar
Nygaard, K. J. & Glezer, A. 1990 Core instability of the spanwise vortices in a plane mixing layer. Phys. Fluids A 2 (3), 461–464.CrossRefGoogle Scholar
Ohrn, T. R., Senser, D. W. & Lefebvre, A. H. 1991 Geometric effects on spray cone angle for plain-orifice atomizers. J. Atomiz. Sprays 1 (3), 253–268.CrossRefGoogle Scholar
Osher, S. & Fedkiw, R. P. 2001 Level set methods: an overview and some recent results. J. Comput. Phys. 169, 463–502.CrossRefGoogle Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Taylor & Francis.Google Scholar
Rangel, R. H. & Sirignano, W. A. 1991 The linear and nonlinear shear instability of a fluid sheet. Phys. Fluids A 3, 2392–2400.CrossRefGoogle Scholar
Reitz, R. D. & Bracco, F. V.1979 On the dependence of spray angle and other spray parameters on nozzle design and operating conditions. SAE Tech. Paper 790494.CrossRefGoogle Scholar
Schoppa, W., Hussain, F. & Metcalfe, R. W. 1995 A new mechanism of small-scale transition in a plane mixing layer: core dynamics of spanwise vortices. J. Fluid Mech. 298, 23–80.CrossRefGoogle Scholar
Shinjo, J. & Umemura, A. 2010 Simulation of liquid jet primary break-up: dynamics of ligament and drolpet formation. Intl J. Multiphase Flow 36, 513–532.CrossRefGoogle Scholar
Sirignano, W. A. & Mehring, C. 2000 Review of theory of distortion and disintegration of liquid streams. Prog. Energy Combust. Sci. 26, 609–655.CrossRefGoogle Scholar
Sirignano, W. A. & Mehring, C. 2005 Distortion and disintegration of liquid streams. In Liquid Rocket Combustion Devices: Aspects of Modeling, Analysis, and Design (ed. Hulba, J., Yang, V., Habiballah, M. & Popp, M.), AIAA Progress in Astronautics and Aeronautics, vol. 200, pp. 167–249. Springer.Google Scholar
Sussman, M., Fatemi, E., Smereka, P. & Osher, S. 1998 An improved level set method for incompressible two-phase flows. Comput. Fluids 27, 663–680.CrossRefGoogle Scholar
Yokota, K. C. & Matsuoka, S. 1977 An experimental study of fuel spray in diesel engine. Trans. JSME 43, 3455–3464.CrossRefGoogle Scholar
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1980 Vortex pairing in a circular jet under controlled excitation. Part 1. General jet response. J. Fluid Mech. 101, 449–491.CrossRefGoogle Scholar