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Model for the initiation of atomization in a high-speed laminar liquid jet

Published online by Cambridge University Press:  29 September 2014

Akira Umemura
Akira Umemura*
Affiliation:
Department of Aerospace Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan
*
†Email address for correspondence: akira@nuae.nagoya-u.ac.jp
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Abstract

A laminar water jet issuing at high speed from a short circular nozzle into air exhibits various instability features at different distances from the nozzle exit. Near the exit, the effects of gaseous friction and pressure are relatively weak. Deformation of the jet surface in this region is mainly due to the instability of a thin liquid shear layer flow, which relaxes from the velocity profile produced by the nozzle wall. In this paper, a model for this type of instability based on linear stability analysis is investigated to describe the process initiating the formation of liquid ligaments disintegrating into fine droplets near the nozzle exit. The modelling comprises identifying unstable waves excitable in the liquid shear layer and exploring a self-destabilizing mechanism by which unstable waves responsible for the formation of liquid ligaments are naturally reproduced from the upstream-propagating capillary waves produced by the growth of the unstable waves themselves. An expression for the location of ligament formation onset is derived that can be compared with experiments. The model also explains changes in jet instability features away from the nozzle exit and for very short nozzles.

JFM classification

Drops and Bubbles: Aerosols/atomization Waves/Free-surface Flows: Capillary waves Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 757 , 25 October 2014 , pp. 665 - 700
Copyright
© 2014 Cambridge University Press 

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References

Arai, M., Shimizu, M. & Hiroyasu, H. 1985 Break-up length and spray angle of a high speed liquid jet. In Proceedings of the 3rd International Conference on Liquid Atomization and Spray Systems, vol. 1, pp. IB/4/1–IB/4/10.Google Scholar
Batchelor, G. K. & Gill, A. E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14, 529–551.CrossRefGoogle Scholar
Benjamin, T. B. & Ursell, F. 1954 The stability of the plane free surface of a liquid in vertical periodic motion. Proc. R. Soc. Lond. A 225, 505–515.Google Scholar
Briggs, R. J. 1964 Electron–Stream Interaction with Plasmas. MIT Press.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.Google Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.CrossRefGoogle Scholar
Davies, J. T. & Young-Hoon, A. A. 1974 Restrained turbulent jets of a non-Newtonian solution. Chem. Engng Sci. 29, 1115–1121.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.CrossRefGoogle Scholar
Esch, R. E. 1957 The instability of a shear layer between two parallel streams. J. Fluid Mech. 3, 289–303.CrossRefGoogle Scholar
Faraday, M. 1831 On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 52, 299–318.Google Scholar
Fenn, R. W. & Middleman, S. 1969 Newtonian jet stability: the role of air resistance. AIChE J. 12, 379–383.CrossRefGoogle Scholar
Gallaire, F. & Chomaz, J.-M. 2004 The role of boundary conditions in a simple model of incipient vortex breakdown. Phys. Fluids 16, 274–286.CrossRefGoogle Scholar
Goodridge, C. L., Hentschel, H. & Lathrop, D. P. 1999 Breaking Faraday waves: critical slowing of droplet ejection rates. Phys. Rev. Lett. 82, 3062–3065.CrossRefGoogle Scholar
Goodridge, C. L., Shi, W. T. & Lathrop, D. P. 1996 Threshold dynamics of singular gravity–capillary waves. Phys. Rev. Lett. 76, 1824–1827.CrossRefGoogle ScholarPubMed
Gordillo, J. M. & Pérez-Saborid, M. 2005 Aerodynamic effects in the break-up of liquid jets: on the first wind-induced break-up regime. J. Fluid Mech. 541, 1–20.CrossRefGoogle Scholar
Gorokhovski, M. & Herrmann, M. 2008 Modeling primary atomization. Annu. Rev. Fluid Mech. 40, 343–366.CrossRefGoogle Scholar
Hoyt, J. W. & Taylor, J. J. 1977 Waves on water jets. J. Fluid Mech. 88, 119–123.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.CrossRefGoogle Scholar
Huh, K. Y., Lee, E. J. & Koo, J. Y. 1998 Diesel spray atomization model considering nozzle exit turbulence conditions. Atomiz. Sprays 8, 453–469.CrossRefGoogle Scholar
Inoue, O. 1985 A new approach to flow problems past a porous plate. AIAA J. 23, 1916–1921.CrossRefGoogle Scholar
Karasawa, T., Tanaka, M., Abe, K., Shiga, S. & Kurabayashi, T. 1992 Effect of nozzle configuration on the atomization of a steady spray. Atomiz. Sprays 2, 411–426.CrossRefGoogle Scholar
Kelvin, Lord 1871 Hydrokinetic solutions and observations. Phil. Mag. 42, 362–377.Google Scholar
Lang, R. J. 1962 Ultrasonic atomization of liquids. J. Acoust. Soc. Am. 34, 6–8.CrossRefGoogle Scholar
Lasheras, J. C. & Hopfinger, E. J. 2000 Liquid jet instability and atomization in a coaxial gas stream. Annu. Rev. Fluid Mech. 32, 275–308.CrossRefGoogle Scholar
Levich, V. G. 1992 Physicochemical Hydrodynamics. Prentice-Hall.Google Scholar
Li, Y. & Umemura, A. 2014 Two-dimensional numerical investigation on the dynamics of ligament formation by Faraday instability. Intl J. Multiphase Flow 60, 64–75.CrossRefGoogle Scholar
Lin, S. P. 2003 Breakup of Liquid Sheets and Jets. Cambridge University Press.CrossRefGoogle Scholar
Lin, S. P. & Reitz, R. 1998 Drop and spray formation from a liquid jet. Annu. Rev. Fluid Mech. 30, 85–105.CrossRefGoogle Scholar
Love, A. E. H. 1911 Some Problems of Geodynamics. Cambridge University Press.Google Scholar
Lyngshansen, P. & Alstrøm, P. 1997 Perturbation theory of parametrically driven capillary waves at low viscosity. J. Fluid Mech. 351, 301–344.CrossRefGoogle Scholar
Marmottan, P. & Villermaux, E. 2004 On spray formation. J. Fluid Mech. 498, 73–111.CrossRefGoogle Scholar
Mattingly, G. E. & Chang, C. C. 1974 Unstable waves on an axi-symmetric jet column. J. Fluid Mech. 65, 541–560.CrossRefGoogle Scholar
Mayer, E. 1961 Theory of liquid atomization in high velocity gas stream. Am. Rocket Soc. J. 31, 1783–1785.Google Scholar
McCarthy, M. J. & Malloy, N. A. 1974 Review of stability of liquid jets and the influence of nozzle design. Chem. Engng J. 7, 1–20.CrossRefGoogle Scholar
Papageorgiou, D. T. & Smith, F. T. 1989 Linear stability of the wake behind a flat plate placed parallel to a uniform stream. J. Fluid Mech. 208, 67–89.CrossRefGoogle Scholar
Phinney, R. E. 1975 Breakup of a turbulent liquid in a low-pressure atmosphere. AIChE J. 21, 996–999.CrossRefGoogle Scholar
Plateau, J. 1873 Soumis aux Seules Forces Moleculaires, vol. 2. Gauthier-Villars.Google Scholar
Ranz, W. E. 1958 Some experiments on orifice sprays. Can. J. Chem. Engng 36, 175–181.CrossRefGoogle Scholar
Rayleigh, Lord 1878 On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13.CrossRefGoogle Scholar
Rayleigh, Lord 1880 On the stability, or instability, of certain fluid motions. Proc. Lond. Math. Soc. 12, 57–70.Google Scholar
Rayleigh, Lord 1883 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. R. Soc. 14, 170–177.Google Scholar
Rees, S. J. & Juniper, M. P. 2009 The effect of surface tension on the stability of unconfined and confined planar jets and wakes. J. Fluid Mech. 633, 71–97.CrossRefGoogle Scholar
Reitz, R. D. & Bracco, F. V. 1982 Mechanism of atomization of liquid jets. Phys. Fluids 25, 1730–1742.CrossRefGoogle Scholar
Schlichting, H. 1968 Boundary-Layer Theory. McGraw-Hill.Google Scholar
Shinjo, J. & Umemura, A. 2010 Simulation of liquid jet primary breakup: dynamics of ligament and droplet formation. Intl J. Multiphase Flow 36, 513–532.CrossRefGoogle Scholar
Shinjo, J. & Umemura, A. 2011 Surface instability and primary atomization characteristics of straight liquid jet sprays. Intl J. Multiphase Flow 37, 1294–1304.CrossRefGoogle Scholar
Sterling, A. M.. & Sleicher, C. A. 1975 The instability of capillary jets. J. Fluid Mech. 68, 477–495.CrossRefGoogle Scholar
Takemoto, Y. & Mizushima, J. 2010 Mechanism of sustained oscillations in a fluid flowing past a circular cylinder obstacle. Phys. Rev. E 82, 056316.CrossRefGoogle Scholar
Taylor, G. I. 1950 Hydrodynamic instabilities. Proc. R. Soc. Lond. A 201, 192–196.Google Scholar
Taylor, G. I. 1963 Generation of ripples by wind blowing over a viscous liquid. In The Scientific Papers of Sir Geoffrey Ingram Taylor (ed. Bachelor, G. K.), vol. III, pp. 244–254. Cambridge University Press.Google Scholar
Taylor, J. J. & Hoyt, J. W. 1983 Water jet photography – techniques and methods. Exp. Fluids 1, 113–120.CrossRefGoogle Scholar
Taylor, M. J. & Peake, N. 1999 A note on the absolute instability of wakes. Eur. J. Mech. (B/Fluids) 18, 573–579.CrossRefGoogle Scholar
Trinh, H. P.2007 Modeling of turbulence effect on liquid jet atomization. NASA/TM-2007-215189.Google Scholar
Umemura, A. 2011 Self-destabilizing mechanism of a laminar inviscid liquid jet issuing from a circular nozzle. Phys. Rev. E 83, 046307.CrossRefGoogle ScholarPubMed
Umemura, A., Kawanabe, S., Suzuki, S. & Osaka, J. 2011 Two-valued breakup length of a water jet issuing from a finite-length nozzle under normal gravity. Phys. Rev. E 84, 036309.CrossRefGoogle ScholarPubMed
Villermaux, E. & Clanet, C. 2002 Life of a flapping liquid sheet. J. Fluid Mech. 462, 341–363.CrossRefGoogle Scholar
Wood, W. R. & Loomis, A. L. 1927 Physical and biologic effects of high frequency sound waves of great intensity. Phil. Mag. 4, 417–437.CrossRefGoogle Scholar
Woodley, B. M. & Peake, N. 1997 Global linear stability analysis of thin aerofoil wakes. J. Fluid Mech. 339, 239–260.CrossRefGoogle Scholar
Wu, P.-K., Miranda, R. F. & Faeth, G. M. 1995 Effect of initial flow conditions on primary breakup of nonturbulent and turbulent round liquid jets. Atomiz. Sprays 5, 175–196.CrossRefGoogle Scholar
Wu, P.-K., Tseng, L.-K. & Faeth, G. M. 1992 Primary breakup in gas/liquid mixing layers for turbulent liquids. Atomiz. Sprays 2, 295–317.CrossRefGoogle Scholar
Yecko, S. & Zaleski, S. 2005 Transient growth in two-phase mixing layers. J. Fluid Mech. 528, 43–52.CrossRefGoogle Scholar
Yecko, P., Zaleski, S. & Fullana, J. M. 2002 Viscous modes in two-phase mixing layers. Phys. Fluids 14, 4115–4122.CrossRefGoogle Scholar
Yu, M.-H. & Monkewitz, P. A. 1990 The effect of non-uniform density on the absolute instability of planar inertial jets and wakes. Phys. Fluids A 2 (7), 1175–1181.CrossRefGoogle Scholar