Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-26T17:44:25.992Z Has data issue: false hasContentIssue false
  • English
  • Français

Drop impact into a deep pool: vortex shedding and jet formation

Published online by Cambridge University Press:  02 January 2015

G. Agbaglah ,
M.-J. Thoraval Open the ORCID record for M.-J. Thoraval [Opens in a new window] ,
S. T. Thoroddsen ,
L. V. Zhang ,
K. Fezzaa  and
R. D. Deegan
G. Agbaglah*
Affiliation:
Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA
M.-J. Thoraval
Affiliation:
Division of Physical Sciences and Engineering & Clean Combustion Research Center, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, 7500 AE Enschede, The Netherlands
S. T. Thoroddsen
Affiliation:
Division of Physical Sciences and Engineering & Clean Combustion Research Center, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia
L. V. Zhang
Affiliation:
Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA
K. Fezzaa
Affiliation:
X-Ray Science Division, Argonne National Laboratory, Argonne, IL 60439, USA
R. D. Deegan
Affiliation:
Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

One of the simplest splashing scenarios results from the impact of a single drop on a deep pool. The traditional understanding of this process is that the impact generates an axisymmetric sheet-like jet that later breaks up into secondary droplets. Recently it was shown that even this simplest of scenarios is more complicated than expected because multiple jets can be generated from a single impact event and there are transitions in the multiplicity of jets as the experimental parameters are varied. Here, we use experiments and numerical simulations of a single drop impacting on a deep pool to examine the transition from impacts that produce a single jet to those that produce two jets. Using high-speed X-ray imaging methods we show that vortex separation within the drop leads to the formation of a second jet long after the formation of the ejecta sheet. Using numerical simulations we develop a phase diagram for this transition and show that the capillary number is the most appropriate order parameter for the transition.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops Drops and Bubbles: Drops and Bubbles
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 764 , 10 February 2015 , R1
Check for updates
Copyright
© 2014 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

Agbaglah, G. & Deegan, R. D. 2014 Growth and instability of the liquid rim in the crown splash regime. J. Fluid Mech. 752, 485–496.Google Scholar
Agbaglah, G., Delaux, S., Fuster, D., Hoepffner, J., Josserand, C., Popinet, S., Ray, P., Scardovelli, R. & Zaleski, S. 2011 Parallel simulation of multiphase flows using octree adaptivity and the volume-of-fluid method. C. R. Méc. 339, 194–207.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Castrejón-Pita, A., Castrejón-Pita, J. & Hutchings, I. 2012 Experimental observation of von Kármán vortices during drop impact. Phys. Rev. E 86, 045301.Google Scholar
Cossali, G. E., Coghe, A. & Marengo, M. 1997 Impact of a single drop on a wetted solid surface. Exp. Fluids 22 (6), 463–472.Google Scholar
Deegan, R. D., Brunet, P. & Eggers, J. 2008 Complexities of splashing. Nonlinearity 21 (1), C1–C11.CrossRefGoogle Scholar
Fezzaa, K. & Wang, Y. J. 2008 Ultrafast x-ray phase-contrast imaging of the initial coalescence phase of two water droplets. Phys. Rev. Lett. 100 (10), 104501.Google Scholar
Fuster, D., Agbaglah, G., Josserand, C., Popinet, S. & Zaleski, S. 2009 Numerical simulation of droplets, bubbles and waves: state of the art. Fluid Dyn. Res. 41 (6), 065001.Google Scholar
Howison, S. D., Ockendon, J. R., Oliver, J. M., Purvis, R. & Smith, F. T. 2005 Droplet impact on a thin fluid layer. J. Fluid Mech. 542, 1–23.Google Scholar
Josserand, C. & Zaleski, S. 2003 Droplet splashing on a thin liquid film. Phys. Fluids 15 (6), 1650–1657.Google Scholar
Kiger, K. T. & Duncan, J. H. 2012 Air-entrainment mechanisms in plunging jets and breaking waves. Annu. Rev. Fluid Mech. 44, 563–596.Google Scholar
Kolinski, J. M., Rubinstein, S. M., Mandre, S., Brenner, M. P., Weitz, D. A. & Mahadevan, L. 2012 Skating on a film of air: drops impacting on a surface. Phys. Rev. Lett. 108, 074503.Google Scholar
Leal, L. G. 1989 Vorticity transport and wake structure for bluff bodies at finite Reynolds number. Phys. Fluids A1, 124–131.Google Scholar
Moore, M. R., Ockendon, H., Ockendon, J. R. & Oliver, J. M. 2014 Capillary and viscous perturbations to Helmholtz flows. J. Fluid Mech. 742, R1. doi:10.1017/jfm.2014.39.Google Scholar
Oguz, H. N. & Prosperetti, A. 1989 Surface-tension effects in the contact of liquid surfaces. J. Fluid Mech. 203, 149–171.Google Scholar
Popinet, S. 2003 Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190 (2), 572–600.Google Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228 (16), 5838–5866.Google Scholar
Rioboo, R., Bauthier, C., Conti, J., Voue, M. & De Coninck, J. 2003 Experimental investigation of splash and crown formation during single drop impact on wetted surfaces. Exp. Fluids 35 (6), 648–652.Google Scholar
Thoraval, M.-J., Takehara, K., Etoh, T. G., Popinet, S., Ray, P., Josserand, C., Zaleski, S. & Thoroddsen, S. T. 2012 von Karman vortex street within an impacting drop. Phys. Rev. Lett. 108 (26), 264506.Google Scholar
Thoraval, M.-J., Takehara, K., Etoh, T. G. & Thoroddsen, S. T. 2013 Drop impact entrapment of bubble rings. J. Fluid Mech. 724, 234–258.Google Scholar
Thoroddsen, S. T. 2002 The ejecta sheet generated by the impact of a drop. J. Fluid Mech. 451, 373–381.Google Scholar
Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2003 Air entrapment under an impacting drop. J. Fluid Mech. 478, 125–134.CrossRefGoogle Scholar
Thoroddsen, S. T., Thoraval, M. J., Takehara, K. & Etoh, T. G. 2011 Droplet splashing by a slingshot mechanism. Phys. Rev. Lett. 106 (3), 034501.Google Scholar
Tryggvason, G., Scardovelli, R. & Zaleski, S. 2011 Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge University Press.Google Scholar
Wang, A. B. & Chen, C. C. 2000 Splashing impact of a single drop onto very thin liquid films. Phys. Fluids 12 (9), 2155–2158.Google Scholar
Weiss, D. A. & Yarin, A. L. 1999 Single drop impact onto liquid films: neck distortion, jetting, tiny bubble entrainment, and crown formation. J. Fluid Mech. 385, 229–254.CrossRefGoogle Scholar
Worthington, A. M. 1882 On impact with a liquid surface. Proc. Phys. Soc. Lond. 34, 217–230.Google Scholar
Xu, L., Zhang, W. W. & Nagel, S. R. 2005 Drop splashing on a dry smooth surface. Phys. Rev. Lett. 94, 184505.Google Scholar
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159–192.Google Scholar
Yarin, A. L. & Weiss, D. A. 1995 Impact of drops on solid-surfaces—self-similar capillary waves, and splashing as a new-type of kinematic discontinuity. J. Fluid Mech. 283, 141–173.Google Scholar
Zhang, L. V., Brunet, P., Eggers, J. & Deegan, R. D. 2010 Wavelength selection in the crown splash. Phys. Fluids 22 (12), 122105.Google Scholar
Zhang, L. V., Toole, J., Fezzaa, K. & Deegan, R. D. 2012a Evolution of the ejecta sheet from the impact of a drop with a deep pool. J. Fluid Mech. 690, 5–15.Google Scholar
Zhang, L. V., Toole, J., Fezzaa, K. & Deegan, R. D. 2012b Splashing from drop impact into a deep pool: multiplicity of jets and the failure of conventional scaling. J. Fluid Mech. 703, 402–413.Google Scholar

Agbaglah et al. supplementary movie

Experimental movie showing the formation of a rolled up vortex sheet

Download Agbaglah et al. supplementary movie(Video)
Video 691.6 KB

Agbaglah et al. supplementary movie

Numerical simulation showing a smooth one jet regime for We=700 and Re=500

Download Agbaglah et al. supplementary movie(Video)
Video 1.9 MB

Agbaglah et al. supplementary movie

Numerical simulation showing the vortex shedding in the two jets regime for We=500 and Re=3500

Download Agbaglah et al. supplementary movie(Video)
Video 2 MB

Agbaglah et al. supplementary movie

Numerical simulation showing the bumping regime for We=700 and Re=4000

Download Agbaglah et al. supplementary movie(Video)
Video 1.9 MB