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Numerical simulation of the aerobreakup of a water droplet

Published online by Cambridge University Press:  29 November 2017

Jomela C. Meng Open the ORCID record for Jomela C. Meng [Opens in a new window]  and
Tim Colonius
Jomela C. Meng*
Affiliation:
California Institute of Technology, Pasadena, CA 91125, USA
Tim Colonius
Affiliation:
California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: jomela.meng@caltech.edu
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Abstract

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.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 835 , 25 January 2018 , pp. 1108 - 1135
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Copyright
© 2017 Cambridge University Press 

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References

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), 2371–2378.CrossRefGoogle Scholar
Allaire, G., Clerc, S. & Kokh, S. 2002 A five-equation model for the simulation of interfaces between compressible fluids. J. Comput. Phys. 181, 577–616.CrossRefGoogle Scholar
Batchelor, G. K. 1987 The stability of a large gas bubble rising through liquid. J. Fluid Mech. 184, 399–422.CrossRefGoogle Scholar
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.Google Scholar
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, 946–990.CrossRefGoogle Scholar
Chen, H. 2008 Two-dimensional simulation of stripping breakup of a water droplet. AIAA J. 46 (5), 1135–1143.CrossRefGoogle Scholar
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.Google Scholar
Coralic, V. & Colonius, T. 2013 Shock-induced collapse of a bubble inside a deformable vessel. Eur. J. Mech. (B/Fluids) 40, 64–74.CrossRefGoogle ScholarPubMed
Coralic, V. & Colonius, T. 2014 Finite-volume WENO scheme for viscous compressible multicomponent flows. J. Comput. Phys. 274, 95–121.CrossRefGoogle ScholarPubMed
Engel, O. G. 1958 Fragmentation of waterdrops in the zone behind an air shock. J. Res. Natl Bur. Stand. 60 (3), 245–280.CrossRefGoogle Scholar
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), 63–68.CrossRefGoogle Scholar
Guildenbecher, D. R., López-Rivera, C. & Sojka, P. E. 2009 Secondary atomization. Exp. Fluids 46, 371–402.CrossRefGoogle Scholar
Han, J. & Tryggvason, G. 2001 Secondary breakup of axisymmetric liquid drops. Part II. Impulsive acceleration. Phys. Fluids 13 (6), 1554–1565.CrossRefGoogle Scholar
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), 1070–1080.CrossRefGoogle Scholar
Harlow, F. H. & Amsden, A. A.1971 Fluid dynamics. Tech. Rep. LA-4700. LASL.Google Scholar
Hinze, J. O. 1949 Critical speeds and sizes of liquid globules. Appl. Sci. Res. A1, 273–288.CrossRefGoogle Scholar
Hsiang, L. P. & Faeth, G. M. 1992 Near-limit drop deformation and secondary breakup. Intl J. Multiphase Flow 18 (5), 635–652.CrossRefGoogle Scholar
Hsiang, L. P. & Faeth, G. M. 1995 Drop deformation and breakup due to shock wave and steady disturbances. Intl J. Multiphase Flow 21 (4), 545–560.CrossRefGoogle Scholar
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.Google Scholar
Igra, D. & Takayama, K. 2001b Numerical simulation of shock wave interaction with a water column. Shock Waves 11, 219–228.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
Jalaal, M. & Mehravaran, K. 2014 Transient growth of droplet instabilities in a stream. Phys. Fluids 26, 012101.CrossRefGoogle Scholar
Johnsen, E.2007 Numerical simulations of non-spherical bubble collapse with applications to shockwave lithotripsy. PhD thesis, California Institute of Technology, Pasadena, CA.Google Scholar
Johnsen, E. & Colonius, T. 2006 Implementation of WENO schemes in compressible multicomponent flow problems. J. Comput. Phys. 219, 715–732.CrossRefGoogle Scholar
Johnsen, E. & Colonius, T. 2009 Numerical simulations of non-spherical bubble collapse. J. Fluid Mech. 629, 231–262.CrossRefGoogle ScholarPubMed
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, 1263–1303.CrossRefGoogle Scholar
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), 3002–3024.CrossRefGoogle Scholar
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.Google Scholar
Lane, W. R. 1951 Shatter of drops in streams of air. Ind. Engng Chem. 43 (6), 1312–1317.CrossRefGoogle Scholar
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), 631–650.CrossRefGoogle Scholar
Meng, J. C.2016 Numerical simulations of droplet aerobreakup. PhD thesis, California Institute of Technology, Pasadena, CA.Google Scholar
Meng, J. C. & Colonius, T. 2015 Numerical simulations of the early stages of high-speed droplet breakup. Shock Waves 25 (4), 399–414.CrossRefGoogle Scholar
Mohseni, K. & Colonius, T. 2000 Numerical treatment of polar coordinate singularities. J. Comput. Phys. Note 157, 787–795.CrossRefGoogle Scholar
Murrone, A. & Guillard, H. 2005 A five equation reduced model for compressible two phase flow problems. J. Comput. Phys. 202, 664–698.CrossRefGoogle Scholar
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, 331–357.CrossRefGoogle Scholar
Perigaud, G. & Saurel, R. 2005 A compressible flow model with capillary effects. J. Comput. Phys. 209, 139–178.CrossRefGoogle Scholar
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), 741–757.CrossRefGoogle Scholar
Quan, S. & Schmidt, D. P. 2006 Direct numerical study of a liquid droplet impulsively accelerated by gaseous flow. Phys. Fluids 18, 102103.CrossRefGoogle Scholar
Quirk, J. J. & Karni, S. 1996 On the dynamics of a shock-bubble interaction. J. Fluid Mech. 318, 129–163.CrossRefGoogle Scholar
Ranger, A. A. & Nicholls, J. A. 1968 Aerodynamic shattering of liquid drops. In AIAA 6th Aerospace Sciences Meeting. AIAA.Google Scholar
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, 1678–1712.CrossRefGoogle Scholar
Simpkins, P. G. & Bales, E. L. 1972 Water-drop response to sudden accelerations. J. Fluid Mech. 55, 629–639.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
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, 191–200.CrossRefGoogle Scholar
Theofanous, T. G. 2011 Aerobreakup of Newtonian and viscoelastic liquids. Annu. Rev. Fluid Mech. 43, 661–690.CrossRefGoogle Scholar
Theofanous, T. G. & Li, G. J. 2008 On the physics of aerobreakup. Phys. Fluids 20, 052103.CrossRefGoogle Scholar
Theofanous, T. G., Li, G. J. & Dinh, T. N. 2004 Aerobreakup in rarefied supersonic gas flows. Trans. ASME J. Fluid Engng 126, 516–527.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Wadhwa, A. R., Magi, V. & Abraham, J. 2007 Transient deformation and drag of decelerating drops in axisymmetric flows. Phys. Fluids 19, 113301.CrossRefGoogle Scholar
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), 281–302.CrossRefGoogle Scholar
Zaleski, S., Li, J. & Succi, S. 1995 Two-dimensional Navier–Stokes simulation of deformation and breakup of liquid patches. Phys. Rev. Lett. 75 (2), 244–247.CrossRefGoogle ScholarPubMed