Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-06-23T11:56:38.517Z Has data issue: false hasContentIssue false

On the formation and recurrent shedding of ligaments in droplet aerobreakup

Published online by Cambridge University Press:  07 October 2020

Benedikt Dorschner*
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA91125, USA
Luc Biasiori-Poulanges
Affiliation:
Institut Pprime, CNRS UPR 3346 – Université de Poitiers – ISAE-ENSMA, 1 avenue Clément Ader, 86961Futuroscope, France
Kevin Schmidmayer
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA91125, USA
Hazem El-Rabii*
Affiliation:
Institut Pprime, CNRS UPR 3346 – Université de Poitiers – ISAE-ENSMA, 1 avenue Clément Ader, 86961Futuroscope, France
Tim Colonius
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA91125, USA
*
Email addresses for correspondence: bdorschn@caltech.edu, hazem.elrabii@cnrs.pprime.fr
Email addresses for correspondence: bdorschn@caltech.edu, hazem.elrabii@cnrs.pprime.fr

Abstract

The breakup of water droplets when exposed to high-speed gas flows is investigated using both high-magnification shadowgraphy experiments as well as fully three-dimensional numerical simulations, which account for viscous as well as capillary effects. After thorough validation of the simulations with respect to the experiments, we elucidate the ligament formation process and the effect of surface tension. By Fourier decomposition of the flow field, we observe the development of specific azimuthal modes, which destabilize the liquid sheet surrounding the droplet. Eventually, the liquid sheet is ruptured, which leads to the formation of ligaments. We further observe the ligament formation and shedding to be a recurrent process. While the first ligament shedding weakly depends on the Weber number, subsequent shedding processes seem to be driven primarily by inertia and the vortex shedding in the wake of the deformed droplet.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by 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

REFERENCES

Abgrall, R. & Karni, S. 2001 Computations of compressible multifluids. J. Comput. Phys. 169 (2), 594623.CrossRefGoogle Scholar
Achenbach, E. 1974 Vortex shedding from spheres. J. Fluid Mech. 62 (2), 209221.CrossRefGoogle Scholar
Allison, P. M., McManus, T. A. & Sutton, J. A. 2016 Quantitative fuel vapor/air mixing imaging in droplet/gas regions of an evaporating spray flow using filtered rayleigh scattering. Opt. Lett. 41 (6), 10741077.CrossRefGoogle ScholarPubMed
Baer, M. R. & Nunziato, J. W. 1986 A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. Intl J. Multiphase Flows 12, 861889.CrossRefGoogle Scholar
Ball, G. J., Howell, B. P., Leighton, T. G. & Schofield, M. J. 2000 Shock-induced collapse of a cylindrical air cavity in water: a free-lagrange simulation. Shock Waves 10 (4), 265276.CrossRefGoogle Scholar
Biasiori-Poulanges, L. & El-Rabii, H. 2019 High-magnification shadowgraphy for the study of drop breakup in a high-speed gas flow. Opt. Lett. 44 (23), 58845887.CrossRefGoogle Scholar
Bolleddula, D. A., Berchielli, A. & Aliseda, A. 2010 Impact of a heterogeneous liquid droplet on a dry surface: application to the pharmaceutical industry. Adv. Colloid Interface Sci. 159 (2), 144159.CrossRefGoogle ScholarPubMed
Cao, X. K., Sun, Z. G., Li, W. F., Liu, H. F. & Yu, Z. H. 2007 A new breakup regime of liquid drops identified in a continuous and uniform air jet flow. Phys. Fluids 19 (5), 057103.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover.Google Scholar
Chen, H. & Liang, S. M. 2008 Flow visualization of shock/water column interactions. Shock Waves 17 (5), 309321.CrossRefGoogle Scholar
Chou, W. H., Hsiang, L. P. & Faeth, G. M. 1997 Temporal properties of drop breakup in the shear breakup regime. Intl J. Multiphase Flow 23 (4), 651669.CrossRefGoogle Scholar
Cocchi, J. P. & Saurel, R. 1997 A Riemann problem based method for the resolution of compressible multimaterial flows. J. Comput. Phys. 137 (2), 265298.CrossRefGoogle Scholar
Coralic, V. & Colonius, T. 2014 Finite-volume WENO scheme for viscous compressible multicomponent flows. J. Comput. Phys. 274, 95121.CrossRefGoogle ScholarPubMed
Dorschner, B., Schmidmayer, K., Biasiori-Poulanges, L., El-Rabii, H. & Colonius, T. 2019 Shock-induced atomization of water droplets. Bull. Am. Phys. Soc. 64.Google Scholar
Eckhoff, R. K. 2016 Explosion Hazards in the Process Industries. Gulf Professional Publishing.Google Scholar
Faeth, G. M., Hsiang, L. P. & Wu, P. K. 1995 Structure and breakup properties of sprays. Intl J. Multiphase Flow 21, 99127.CrossRefGoogle Scholar
Fishburn, B. D. 1974 Boundary layer stripping of liquid drops fragmented by Taylor instability. Acta Astronaut. 1 (9–10), 12671284.CrossRefGoogle Scholar
Fuster, D. 2019 A review of models for bubble clusters in cavitating flows. Flow Turbul. Combust. 102, 497536.CrossRefGoogle Scholar
Garrick, D. P. 2016 Numerical modeling of atomization in compressible flow. PhD thesis, Iowa State University.Google Scholar
Gelfand, B. E. 1996 Droplet breakup phenomena in flows with velocity lag. Prog. Energy Combust. Sci. 22 (3), 201265.CrossRefGoogle Scholar
Gel'fand, B. E., Gubin, S. A. & Kogarko, S. M. 1974 Various forms of drop fractionation in shock waves and their special characteristics. J. Engng Phys. 27 (1), 877882.CrossRefGoogle Scholar
Guildenbecher, D. R., López-Rivera, C. & Sojka, P. E. 2009 Secondary atomization. Exp. Fluids 46 (3), 371.CrossRefGoogle Scholar
Guildenbecher, D. R., López-Rivera, C. & Sojka, P. E. 2011 Droplet deformation and breakup. In Handbook of Atomization and Sprays, pp. 145–156. Springer.CrossRefGoogle Scholar
Han, J. & Tryggvason, G. 1999 Secondary breakup of axisymmetric liquid drops. I. Acceleration by a constant body force. Phys. Fluids 11 (12), 36503667.CrossRefGoogle Scholar
Han, J. & Tryggvason, G. 2001 Secondary breakup of axisymmetric liquid drops. II. Impulsive acceleration. Phys. Fluids 13 (6), 15541565.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), 10701080.CrossRefGoogle Scholar
Harper, E. Y., Grube, G. W. & Chang, I. D. 1972 On the breakup of accelerating liquid drops. J. Fluid Mech. 52 (3), 565591.CrossRefGoogle Scholar
Hinze, J. O. 1955 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1 (3), 289295.CrossRefGoogle Scholar
Hirahara, H. & Kawahashi, M. 1992 Experimental investigation of viscous effects upon a breakup of droplets in high-speed air flow. Exp. Fluids 13 (6), 423428.CrossRefGoogle Scholar
Hsiang, L. P. & Faeth, G. M. 1992 Near-limit drop deformation and secondary breakup. Intl J. Multiphase Flow 18 (5), 635652.CrossRefGoogle Scholar
Hsiang, L. P. & Faeth, G. M. 1993 Drop properties after secondary breakup. Intl J. Multiphase Flow 19 (5), 721735.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), 545560.CrossRefGoogle Scholar
Hwang, S. S., Liu, Z. & Reitz, R. D. 1996 Breakup mechanisms and drag coefficients of high-speed vaporizing liquid drops. Atomiz. Sprays 6 (3), 353–376.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 (2177), 20140930.Google Scholar
Jalaal, M. & Mehravaran, K. 2012 Fragmentation of falling liquid droplets in bag breakup mode. Intl J. Multiphase Flow 47, 115132.CrossRefGoogle Scholar
Jalaal, M. & Mehravaran, K. 2014 Transient growth of droplet instabilities in a stream. Phys. Fluids 26 (1), 012101.CrossRefGoogle Scholar
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 (6), 12631303.CrossRefGoogle Scholar
Kapila, A., Menikoff, R., Bdzil, J., Son, S. & Stewart, D. 2001 Two-phase modeling of DDT in granular materials: reduced equations. Phys. Fluids 13, 30023024.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-Americas), Toronto, Canada.Google Scholar
Kim, D., Desjardins, O., Herrmann, M. & Moin, P. 2006 Toward two-phase simulation of the primary breakup of a round liquid jet by a coaxial flow of gas. In Center for Turbulence Research Annual Research Briefs, vol. 185. Stanford University.Google Scholar
Kim, H. J. & Durbin, P. A. 1988 Observations of the frequencies in a sphere wake and of drag increase by acoustic excitation. Phys. Fluids 31 (11), 32603265.CrossRefGoogle Scholar
Krzeczkowski, S. A. 1980 Measurement of liquid droplet disintegration mechanisms. Intl J. Multiphase Flow 6 (3), 227239.CrossRefGoogle Scholar
Kulkarni, V. & Sojka, P. E. 2014 Bag breakup of low viscosity drops in the presence of a continuous air jet. Phys. Fluids 26 (7), 072103.CrossRefGoogle Scholar
Labousse, M. & Bush, J. W. M. 2015 Polygonal instabilities on interfacial vorticities. Eur. Phys. J. E 38 (10), 113.CrossRefGoogle ScholarPubMed
Lane, W. R. 1951 Shatter of drops in streams of air. Ind. Engng Chem. 43 (6), 13121317.CrossRefGoogle Scholar
Lee, C. H. & Reitz, R. D. 1999 Modeling the effects of gas density on the drop trajectory and breakup size of high-speed liquid drops. Atomiz. Sprays 9 (5), 497–517.Google Scholar
Lee, C. H. & Reitz, R. D. 2000 An experimental study of the effect of gas density on the distortion and breakup mechanism of drops in high speed gas stream. Intl J. Multiphase Flow 26 (2), 229244.CrossRefGoogle Scholar
Lee, C. S. & Reitz, R. D. 2001 Effect of liquid properties on the breakup mechanism of high-speed liquid drops. Atomiz. Sprays 11 (1), 1–19.Google Scholar
Lefebvre, A. H. & McDonell, V. G. 2017 Atomization and Sprays. CRC.CrossRefGoogle Scholar
Liu, T. G., Khoo, B. C. & Yeo, K. S. 2003 Ghost fluid method for strong shock impacting on material interface. J. Comput. Phys. 190 (2), 651681.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), 631650.CrossRefGoogle Scholar
Liu, N., Wang, Z., Sun, M., Deiterding, R. & Wang, H. 2019 Simulation of liquid jet primary breakup in a supersonic crossflow under adaptive mesh refinement framework. Aerospace Sci. Technol. 91, 456473.CrossRefGoogle Scholar
Liu, N., Wang, Z., Sun, M., Wang, H. & Wang, B. 2018 Numerical simulation of liquid droplet breakup in supersonic flows. Acta Astronaut. 145, 116130.CrossRefGoogle Scholar
Liu, W., Yuan, L. & Shu, C. W. 2011 A conservative modification to the ghost fluid method for compressible multiphase flows. Commun. Comput. Phys. 10 (4), 785806.CrossRefGoogle Scholar
Magarvey, R. H. & Taylor, B. W. 1956 Free fall breakup of large drops. J. Appl. Phys. 27 (10), 11291135.CrossRefGoogle Scholar
Marcotte, F. & Zaleski, S. 2019 Density contrast matters for drop fragmentation thresholds at low Ohnesorge number. Phys. Rev. Fluids 4 (10), 103604.CrossRefGoogle Scholar
Marmottant, P. & Villermaux, E. 2004 On spray formation. J. Fluid Mech. 498, 73111.CrossRefGoogle Scholar
Matas, J.-P. 2015 Inviscid versus viscous instability mechanism of an air–water mixing layer. J. Fluid Mech. 768, 375387.CrossRefGoogle Scholar
Meng, J. C. 2016 Numerical simulations of droplet aerobreakup. PhD thesis, California Institute of Technology.Google Scholar
Meng, J. C. & Colonius, T. 2014 Numerical simulations of the early stages of high-speed droplet breakup. Shock Waves 25, 399414.CrossRefGoogle Scholar
Meng, J. C. & Colonius, T. 2018 Numerical simulation of the aerobreakup of a water droplet. J. Fluid Mech. 835, 11081135.CrossRefGoogle Scholar
Pan, S., Han, L., Hu, X. & Adams, N. A. 2018 A conservative interface-interaction method for compressible multi-material flows. J. Comput. Phys. 371, 870895.CrossRefGoogle Scholar
Périgaud, G. & Saurel, R. 2005 A compressible flow model with capillary effects. J. Comp. Phys. 209, 139178.CrossRefGoogle Scholar
Pilch, M. & Erdman, C. A. 1987 Use of breakup time data and velocity history to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop. Intl J. Multiphase Flow 13, 741757.CrossRefGoogle Scholar
Pishchalnikov, Y. A., Behnke-Parks, W. M., Schmidmayer, K., Maeda, K., Colonius, T., Kenny, T. W. & Laser, D. J. 2019 High-speed video microscopy and numerical modeling of bubble dynamics near a surface of urinary stone. J. Acoust. Soc. Am. 146, 516531.CrossRefGoogle Scholar
Ranger, A. A. & Nicholls, J. A. 1969 Aerodynamic shattering of liquid drops. AIAA J. 7 (2), 285290.Google Scholar
Rayleigh, Lord 1882 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. s1–14 (1), 170177.CrossRefGoogle Scholar
Reinecke, W. & Waldman, G. 1975 Shock layer shattering of cloud drops in reentry flight. In 13th Aerospace Sciences Meeting, p. 152.Google Scholar
Sakamoto, H. & Haniu, H. 1990 A study on vortex shedding from spheres in a uniform flow. J. Fluids Engng 112 (4), 386392.CrossRefGoogle Scholar
Saurel, R. & Pantano, C. 2018 Diffuse-interface capturing methods for compressible two-phase flows. Annu. Rev. Fluid Mech. 50, 105130.CrossRefGoogle 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 (5), 16781712.CrossRefGoogle Scholar
Schmidmayer, K., Bryngelson, S. H. & Colonius, T. 2020 a An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics. J. Comput. Phys. 402, 109080.CrossRefGoogle Scholar
Schmidmayer, K., Petitpas, F. & Daniel, E. 2019 Adaptive Mesh refinement algorithm based on dual trees for cells and faces for multiphase compressible flows. J. Comput. Phys. 388, 252278.CrossRefGoogle Scholar
Schmidmayer, K., Petitpas, F., Daniel, E., Favrie, N. & Gavrilyuk, S. L. 2017 A model and numerical method for compressible flows with capillary effects. J. Comput. Phys. 334, 468496.CrossRefGoogle Scholar
Schmidmayer, K., Petitpas, F., Le Martelot, S. & Daniel, E. 2020 b ECOGEN: an open-source tool for multiphase, compressible, multiphysics flows. Comput. Phys. Commun. 251, 107093.CrossRefGoogle Scholar
Shraiber, A. A., Podvysotsky, A. M. & Dubrovsky, V. V. 1996 Deformation and breakup of drops by aerodynamic forces. Atomiz. Sprays 6 (6), 667692.CrossRefGoogle Scholar
Shyue, K. M. & Xiao, F. 2014 An Eulerian interface sharpening algorithm for compressible two-phase flow: the algebraic THINC approach. J. Comput. Phys. 268, 326354.CrossRefGoogle Scholar
Simpkins, P. G. & Bales, E. L. 1972 Water-drop response to sudden accelerations. J. Fluid Mech. 55 (04), 629639.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 28th Aerospace Sciences Meeting, p. 461. AIAA.Google Scholar
Theofanous, T. G. 2011 Aerobreakup of Newtonian and viscoelastic liquids. Annu. Rev. Fluid Mech. 43, 661690.CrossRefGoogle Scholar
Theofanous, T. G. & Li, G. J. 2008 On the physics of aerobreakup. Phys. Fluids 20 (5), 052103.CrossRefGoogle Scholar
Theofanous, T. G., Li, G. J. & Dinh, T. N. 2004 Aerobreakup in rarefied supersonic gas flows. J. Fluids Engng 126 (4), 516527.CrossRefGoogle Scholar
Thévand, N., Daniel, E. & Loraud, J. C. 1999 On high-resolution schemes for solving unsteady compressible two-phase dilute viscous flows. Intl J. Numer. Meth. Fluids 31 (4), 681702.3.0.CO;2-K>CrossRefGoogle Scholar
Toro, E. F. 1997 Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer Verlag.CrossRefGoogle Scholar
Van Leer, B. 1977 Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow. J. Comput. Phys. 23 (3), 263275.CrossRefGoogle Scholar
Wadhwa, A. R., Magi, V. & Abraham, J. 2007 Transient deformation and drag of decelerating drops in axisymmetric flows. Phys. Fluids 19 (11), 113301.CrossRefGoogle Scholar
Wang, C., Chang, S., Wu, H. & Xu, J. 2014 Modeling of drop breakup in the bag breakup regime. Appl. Phys. Lett. 104 (15), 154107.CrossRefGoogle Scholar
Wierzba, A. 1990 Deformation and breakup of liquid drops in a gas stream at nearly critical weber numbers. Exp. Fluids 9 (1-2), 5964.CrossRefGoogle Scholar
Zandian, A., Sirignano, W. A. & Hussain, F. 2019 Vorticity dynamics in a spatially developing liquid jet inside a co-flowing gas. J. Fluid Mech. 877, 429470.CrossRefGoogle Scholar
Zhao, H., Liu, H. F., Li, W. F. & Xu, J. L. 2010 Morphological classification of low viscosity drop bag breakup in a continuous air jet stream. Phys. Fluids 22 (11), 114103.CrossRefGoogle Scholar
Zhao, H., Liu, H. F., Xu, J. L., Li, W. F. & Lin, K. F. 2013 Temporal properties of secondary drop breakup in the bag-stamen breakup regime. Phys. Fluids 25 (5), 054102.CrossRefGoogle Scholar