Skip to main content

Numerical simulation of the aerobreakup of a water droplet

  • Jomela C. Meng (a1) and Tim Colonius (a1)

We present a three-dimensional numerical simulation of the aerobreakup of a spherical water droplet in the flow behind a normal shock wave. The droplet and surrounding gas flow are simulated using the compressible multicomponent Euler equations in a finite-volume scheme with shock and interface capturing. The aerobreakup process is compared with available experimental visualizations. Features of the droplet deformation and breakup in the stripping breakup regime, as well as descriptions of the surrounding gas flow, are discussed. Analyses of observed surface instabilities and a Fourier decomposition of the flow field reveal asymmetrical azimuthal modulations and broadband instability growth that result in chaotic flow within the wake region.

Corresponding author
Email address for correspondence:
Hide All
Aalburg, C., Leer, B. V. & Faeth, G. M. 2003 Deformation and drag properties of round drops subjected to shock-wave disturbances. AIAA J. 41 (12), 23712378.
Allaire, G., Clerc, S. & Kokh, S. 2002 A five-equation model for the simulation of interfaces between compressible fluids. J. Comput. Phys. 181, 577616.
Batchelor, G. K. 1987 The stability of a large gas bubble rising through liquid. J. Fluid Mech. 184, 399422.
Castrillon Escobar, S., Rimbert, N., Meignen, R., Hadj-Achour, M. & Gradeck, M. 2015 Direct numerical simulations of hydrodynamic fragmentation of liquid metal droplets by a water flow. In 13th Triennial International Conference on Liquid Atomization and Spray Systems. ILASS.
Chang, C. H., Deng, X. & Theofanous, T. G. 2013 Direct numerical simulation of interfacial instabilities: a consistent, conservative, all-speed, sharp-interface method. J. Comput. Phys. 242, 946990.
Chen, H. 2008 Two-dimensional simulation of stripping breakup of a water droplet. AIAA J. 46 (5), 11351143.
Coralic, V.2015 Simulation of shock-induced bubble collapse with application to vascular injury in shockwave lithotripsy. PhD thesis, California Institute of Technology, Pasadena, CA.
Coralic, V. & Colonius, T. 2013 Shock-induced collapse of a bubble inside a deformable vessel. Eur. J. Mech. (B/Fluids) 40, 6474.
Coralic, V. & Colonius, T. 2014 Finite-volume WENO scheme for viscous compressible multicomponent flows. J. Comput. Phys. 274, 95121.
Engel, O. G. 1958 Fragmentation of waterdrops in the zone behind an air shock. J. Res. Natl Bur. Stand. 60 (3), 245280.
Gojani, A. B., Ohtani, K., Takayama, K. & Hosseini, S. H. R. 2016 Shock Hugoniot and equations of states of water, castor oil, and aqueous solutions of sodium chloride, sucrose, and gelatin. Shock Waves 26 (1), 6368.
Guildenbecher, D. R., López-Rivera, C. & Sojka, P. E. 2009 Secondary atomization. Exp. Fluids 46, 371402.
Han, J. & Tryggvason, G. 2001 Secondary breakup of axisymmetric liquid drops. Part II. Impulsive acceleration. Phys. Fluids 13 (6), 15541565.
Hanson, A. R., Domich, E. G. & Adams, H. S. 1963 Shock tube investigation of the breakup of drops by air blasts. Phys. Fluids 6 (8), 10701080.
Harlow, F. H. & Amsden, A. A.1971 Fluid dynamics. Tech. Rep. LA-4700. LASL.
Hinze, J. O. 1949 Critical speeds and sizes of liquid globules. Appl. Sci. Res. A1, 273288.
Hsiang, L. P. & Faeth, G. M. 1992 Near-limit drop deformation and secondary breakup. Intl J. Multiphase Flow 18 (5), 635652.
Hsiang, L. P. & Faeth, G. M. 1995 Drop deformation and breakup due to shock wave and steady disturbances. Intl J. Multiphase Flow 21 (4), 545560.
Igra, D. & Takayama, K. 2001a Experimental and numerical study of the initial stages in the interaction process between a planar shock wave and a water column. In 23rd International Symposium on Shock Waves. The University of Texas at Arlington.
Igra, D. & Takayama, K. 2001b Numerical simulation of shock wave interaction with a water column. Shock Waves 11, 219228.
Igra, D. & Takayama, K.2001c A study of shock wave loading on a cylindrical water column. Tech. Rep. vol. 13, pp. 19–36. Institute of Fluid Science, Tohoku University.
Jain, M., Prakash, R. S., Tomar, G. & Ravikrishna, R. V. 2015 Secondary breakup of a drop at moderate Weber numbers. Proc. R. Soc. Lond. A 471, 20140930.
Jalaal, M. & Mehravaran, K. 2014 Transient growth of droplet instabilities in a stream. Phys. Fluids 26, 012101.
Johnsen, E.2007 Numerical simulations of non-spherical bubble collapse with applications to shockwave lithotripsy. PhD thesis, California Institute of Technology, Pasadena, CA.
Johnsen, E. & Colonius, T. 2006 Implementation of WENO schemes in compressible multicomponent flow problems. J. Comput. Phys. 219, 715732.
Johnsen, E. & Colonius, T. 2009 Numerical simulations of non-spherical bubble collapse. J. Fluid Mech. 629, 231262.
Joseph, D. D., Belanger, J. & Beavers, G. S. 1999 Breakup of a liquid drop suddenly exposed to a high-speed airstream. Intl J. Multiphase Flow 25, 12631303.
Kapila, A. K., Menikoff, R., Bdzil, J. B., Son, S. F. & Stewart, D. S. 2001 Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations. Phys. Fluids 13 (10), 30023024.
Khosla, S., Smith, C. E. & Throckmorton, R. P. 2006 Detailed understanding of drop atomization by gas crossflow using the volume of fluid method. In 19th Annual Conference on Liquid Atomization and Spray Systems. ILASS.
Lane, W. R. 1951 Shatter of drops in streams of air. Ind. Engng Chem. 43 (6), 13121317.
Liu, Z. & Reitz, R. D. 1997 An analysis of the distortion and breakup mechanisms of high speed liquid drops. Intl J. Multiphase Flow 23 (4), 631650.
Meng, J. C.2016 Numerical simulations of droplet aerobreakup. PhD thesis, California Institute of Technology, Pasadena, CA.
Meng, J. C. & Colonius, T. 2015 Numerical simulations of the early stages of high-speed droplet breakup. Shock Waves 25 (4), 399414.
Mohseni, K. & Colonius, T. 2000 Numerical treatment of polar coordinate singularities. J. Comput. Phys. Note 157, 787795.
Murrone, A. & Guillard, H. 2005 A five equation reduced model for compressible two phase flow problems. J. Comput. Phys. 202, 664698.
Pelanti, M. & Shyue, K. M. 2014 A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259, 331357.
Perigaud, G. & Saurel, R. 2005 A compressible flow model with capillary effects. J. Comput. Phys. 209, 139178.
Pilch, M. & Erdman, C. A. 1987 Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop. Intl J. Multiphase Flow 13 (6), 741757.
Quan, S. & Schmidt, D. P. 2006 Direct numerical study of a liquid droplet impulsively accelerated by gaseous flow. Phys. Fluids 18, 102103.
Quirk, J. J. & Karni, S. 1996 On the dynamics of a shock-bubble interaction. J. Fluid Mech. 318, 129163.
Ranger, A. A. & Nicholls, J. A. 1968 Aerodynamic shattering of liquid drops. In AIAA 6th Aerospace Sciences Meeting. AIAA.
Saurel, R., Petitpas, F. & Berry, R. A. 2009 Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures. J. Comput. Phys. 228, 16781712.
Simpkins, P. G. & Bales, E. L. 1972 Water-drop response to sudden accelerations. J. Fluid Mech. 55, 629639.
Stapper, B. E. & Samuelsen, G. S. 1990 An experimental study of the breakup of a two-dimensional liquid sheet in the presence of co-flow air shear. In AIAA 28th Aerospace Sciences Meeting. AIAA.
Takayama, K. & Itoh, K.1986 Unsteady drag over cylinders and aerofoils in transonic shock tube flows. Tech. Rep. vol. 51. Institute of High Speed Mechanics, Tohoku University, Sendai, Japan.
Tanno, H., Itoh, K., Saito, T., Abe, A. & Takayama, K. 2003 Interaction of a shock with a sphere suspended in a vertical shock tube. Shock Waves 13, 191200.
Theofanous, T. G. 2011 Aerobreakup of Newtonian and viscoelastic liquids. Annu. Rev. Fluid Mech. 43, 661690.
Theofanous, T. G. & Li, G. J. 2008 On the physics of aerobreakup. Phys. Fluids 20, 052103.
Theofanous, T. G., Li, G. J. & Dinh, T. N. 2004 Aerobreakup in rarefied supersonic gas flows. Trans. ASME J. Fluid Engng 126, 516527.
Theofanous, T. G., Mitkin, V. V., Ng, C. L., Chang, C. H., Deng, X. & Sushchikh, S. 2012 The physics of aerobreakup. Part II. Viscous liquids. Phys. Fluids 24, 022104.
Wadhwa, A. R., Magi, V. & Abraham, J. 2007 Transient deformation and drag of decelerating drops in axisymmetric flows. Phys. Fluids 19, 113301.
Xiao, F., Dianat, M. & McGuirk, J. J. 2014 Large eddy simulation of single droplet and liquid jet primary breakup using a coupled level set/volume of fluid method. Atomiz. Sprays 24 (4), 281302.
Zaleski, S., Li, J. & Succi, S. 1995 Two-dimensional Navier–Stokes simulation of deformation and breakup of liquid patches. Phys. Rev. Lett. 75 (2), 244247.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 47
Total number of PDF views: 417 *
Loading metrics...

Abstract views

Total abstract views: 676 *
Loading metrics...

* Views captured on Cambridge Core between 29th November 2017 - 22nd August 2018. This data will be updated every 24 hours.