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The water entry of multi-droplet streams and jets

Published online by Cambridge University Press:  16 April 2018

Nathan B. Speirs ,
Zhao Pan ,
Jesse Belden  and
Tadd T. Truscott Open the ORCID record for Tadd T. Truscott [Opens in a new window]
Nathan B. Speirs
Affiliation:
Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84322, USA
Zhao Pan
Affiliation:
Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84322, USA
Jesse Belden
Affiliation:
Naval Undersea Warfare Center Division Newport, 1176 Howell Street, Newport, RI 02841, USA
Tadd T. Truscott*
Affiliation:
Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84322, USA
*
†Email address for correspondence: taddtruscott@gmail.com
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Abstract

Water entry has been studied for over a century, but few studies have focused on multiple droplets impacting on a liquid bath sequentially. We connect multi-droplet streams, jets and solid objects with physical-based scaling arguments that emphasize the intrinsically similar cavities. In particular, the cavities created by the initial impact of both droplet streams and jets on an initially quiescent liquid pool exhibit the same types of cavity seal as hydrophobic spheres at low Bond number, some of which were previously unseen for jets and droplet streams. Low-frequency droplet streams exhibit an additional three new cavity seal types unseen for jets or solid spheres that can be predicted with a new non-dimensional frequency. The cavity depth and cavity velocity for both droplet and jet impact are rationalized by an energy scaling analysis and the Bernoulli equation.

JFM classification

Drops and Bubbles: Drops and Bubbles Interfacial Flows (free surface): Interfacial Flows (free surface) Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 1084 - 1111
Copyright
© Cambridge University Press 2018. This is a work of the U.S. Government and is not subject to copyright protection in the United States. 

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References

Aristoff, J. M. & Bush, J. W. M. 2009 Water entry of small hydrophobic spheres. J. Fluid Mech. 619, 45–78.10.1017/S0022112008004382Google Scholar
Bick, A. G., Ristenpart, W. D., van Nierop, E. A. & Stone, H. A. 2010 Bubble formation via multidrop impacts. Phys. Fluids 22 (4), 042105.10.1063/1.3397851Google Scholar
Birkhoff, G. & Zarantonello, E. H. 1957 Jets, Wakes, and Cavities (Series in Applied Mathematics and Mechanics), vol. 2. Academic Press.Google Scholar
Bouwhuis, W., Huang, X., Chan, C. U., Frommhold, P. E., Ohl, C.-D., Lohse, D., Snoeijer, J. H. & van der Meer, D. 2016 Impact of a high-speed train of microdrops on a liquid pool. J. Fluid Mech. 792, 850–868.10.1017/jfm.2016.105Google Scholar
Cole, D.2007 The splashing morphology of liquid–liquid impacts. PhD thesis, James Cook University.Google Scholar
Coleman, H. W. & Steele, W. G. 2009 Experimentation, Validation, and Uncertainty Analysis for Engineers. Wiley.10.1002/9780470485682Google Scholar
Duclaux, V., Caillé, F., Duez, C., Ybert, C., Bocquet, L. & Clanet, C. 2007 Dynamics of transient cavities. J. Fluid Mech. 591, 1–19.10.1017/S0022112007007343Google Scholar
Engel, O. G. 1966 Crater depth in fluid impacts. J. Appl. Phys. 37 (4), 1798–1808.10.1063/1.1708605Google Scholar
Engel, O. G. 1967 Initial pressure, initial flow velocity, and the time dependence of crater depth in fluid impacts. J. Appl. Phys. 38 (10), 3935–3940.10.1063/1.1709044Google Scholar
Franz, G. J. 1959 Splashes as sources of sound in liquids. J. Acoust. Soc. Am. 31 (8), 1080–1096.10.1121/1.1907831Google Scholar
Hurd, R., Fanning, T., Pan, Z., Mabey, C., Bodily, K., Hacking, K., Speirs, N. & Truscott, T. 2015 Matryoshka cavity. Phys. Fluids 27 (9), 091104.10.1063/1.4930902Google Scholar
Kersten, B., Ohl, C. D. & Prosperetti, A. 2003 Transient impact of a liquid column on a miscible liquid surface. Phys. Fluids 15 (3), 821–824.10.1063/1.1542614Google Scholar
Kiger, K. T. & Duncan, J. H. 2012 Air-entrainment mechanisms in plunging jets and breaking waves. Annu. Rev. Fluid Mech. 44 (1), 563–596.10.1146/annurev-fluid-122109-160724Google Scholar
Leng, L. J. 2001 Splash formation by spherical drops. J. Fluid Mech. 427, 73–105.10.1017/S0022112000002500Google Scholar
Lin, S. P. & Reitz, R. D. 1998 Drop and spray formation from a liquid jet. Annu. Rev. Fluid Mech. 30 (1), 85–105.10.1146/annurev.fluid.30.1.85Google Scholar
Lorenceau, É., Quéré, D. & Eggers, J. 2004 Air entrainment by a viscous jet plunging into a bath. Phys. Rev. Lett. 93, 254501.10.1103/PhysRevLett.93.254501Google Scholar
Mansoor, M. M., Marston, J. O., Vakarelski, I. U. & Thoroddsen, S. T. 2014 Water entry without surface seal: extended cavity formation. J. Fluid Mech. 743, 295–326.10.1017/jfm.2014.35Google Scholar
Marston, J. O., Truscott, T. T., Speirs, N. B., Mansoor, M. M. & Thoroddsen, S. T. 2016 Crown sealing and buckling instability during water entry of spheres. J. Fluid Mech. 794, 506–529.10.1017/jfm.2016.165Google Scholar
May, A. & Woodhull, J. C. 1948 Drag coefficients of steel spheres entering water vertically. J. Appl. Phys. 19 (12), 1109–1121.10.1063/1.1715027Google Scholar
Morton, D., Rudman, M. & Jong-Leng, L. 2000 An investigation of the flow regimes resulting from splashing drops. Phys. Fluids 12 (4), 747–763.10.1063/1.870332Google Scholar
Oguz, H. N. & Prosperetti, A. 1990 Bubble entrainment by the impact of drops on liquid surfaces. J. Fluid Mech. 219, 143–179.10.1017/S0022112090002890Google Scholar
Oguz, H. N., Prosperetti, A. & Kolaini, A. R. 1995 Air entrapment by a falling water mass. J. Fluid Mech. 294, 181–207.10.1017/S0022112095002850Google Scholar
Oguz, H. N., Prosperetti, A. & Lezzi, A. M. 1992 Examples of air entraining flows. Phys. Fluids A 4 (4), 649–651.10.1063/1.858281Google Scholar
Qu, X., Goharzadeh, A., Khezzar, L. & Molki, A. 2013 Experimental characterization of air-entrainment in a plunging jet. Exp. Therm. Fluid Sci. 44, 51–61.10.1016/j.expthermflusci.2012.05.013Google Scholar
Ray, B., Biswas, G. & Sharma, A. 2015 Regimes during liquid drop impact on a liquid pool. J. Fluid Mech. 768, 492–523.10.1017/jfm.2015.108Google Scholar
Rodriguez, F. & Mesler, R. 1988 The penetration of drop-formed vortex rings into pools of liquid. J. Colloid Interface Sci. 121 (1), 121–129.10.1016/0021-9797(88)90414-6Google Scholar
Soh, W. K., Khoo, B. C. & Yuen, W. Y. D. 2005 The entrainment of air by water jet impinging on a free surface. Exp. Fluids 39 (3), 498–506.10.1007/s00348-005-0965-9Google Scholar
Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2003 Air entrapment under an impacting drop. J. Fluid Mech. 478, 125–134.10.1017/S0022112002003427Google Scholar
Truscott, T. T., Epps, B. P. & Belden, J. 2014 Water entry of projectiles. Annu. Rev. Fluid Mech. 46 (1), 355–378.10.1146/annurev-fluid-011212-140753Google Scholar
Truscott, T. T., Epps, B. P. & Techet, A. H. 2012 Unsteady forces on spheres during free-surface water entry. J. Fluid Mech. 704, 173–210.10.1017/jfm.2012.232Google Scholar
Worthington, A. M. & Cole, R. S. 1900 Impact with a liquid surface studied by the aid of instantaneous photography. Phil. Trans. R. Soc. Lond. A 194, 175–199.Google Scholar
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159–192.10.1146/annurev.fluid.38.050304.092144Google Scholar
Zhu, Y., Oğuz, H. N. & Prosperetti, A. 2000 On the mechanism of air entrainment by liquid jets at a free surface. J. Fluid Mech. 404, 151–177.10.1017/S0022112099007090Google Scholar

Speirs et al. supplementary movie 1

Supplemental movie for Fig. 10a – deep seal for droplets A cavity formed by a multi-droplet stream with higher Bo and We pinches off in a deep seal (f = 1500 Hz, Us = 6.59 m s-1, dd = 2.17 mm, We* = 1,309, Bo* = 0.64, and Mt = 16.9). Pinch-off occurs approximately halfway between the free-surface and cavity bottom. Movie played back at 1/200 of real speed.

Download Speirs et al. supplementary movie 1(Video)
Video 3.4 MB

Speirs et al. supplementary movie 2

Supplemental movie for Fig. 10b – deep seal for jets A cavity formed by a jet at a moderate Bo pinches off in a deep seal (Us = 7.09 m s-1, dj = 0.71 mm, We = 527, and Bo = 0.068). Because Bo is relatively small for this jet impact, we still observe the downward moving capillary wave near the surface seen for shallow seal. Pinch-off occurs approximately halfway between the free-surface and cavity bottom. Movie played back at 1/200 of real speed.

Download Speirs et al. supplementary movie 2(Video)
Video 1.3 MB

Speirs et al. supplementary movie 3

Supplemental movie for Fig. 7a – sub-cavity 1 collapse Sub-cavity 1 collapse. For Mt < 1, the second droplet impacts the cavity after sub-cavity 1 has begun to collapse. Sub-cavity 1 continues to collapse after impact separating sub-cavity 2 from the surface. Parameters of the impact event are as follows: f = 80 Hz, Us = 1.77 m s-1, dd =3.08 mm, We* = 77, Bo* = 0.4, and Mt = 0.88. Movie played back at 1/200 of real speed.

Download Speirs et al. supplementary movie 3(Video)
Video 404.9 KB

Speirs et al. supplementary movie 4

Supplemental movie for Fig. 7b – sub-cavity 2 collapse Sub-cavity 2 collapse. For 1 <Mt<4, the cavity is still expanding when each successive droplet impacts thus, enabling the cavity to grow larger in the vertical direction (f = 300 Hz, Us = 1.80 m s-1, dd = 2.18 mm, We* = 56, Bo* = 0.21, and Mt = 1.55). The cavity collapse occurs between the bottom of sub-cavity 1 and the bottom of sub-cavity 2. Movie played back at 1/200 of real speed.

Download Speirs et al. supplementary movie 4(Video)
Video 952.3 KB

Speirs et al. supplementary movie 5

Supplemental movie for Fig. 8a – sub-cavity dome over Sub-cavity dome over at low Mt. When Mt<4 and We* ≲ 350 splash crowns form at the base of each sub-cavity and sometimes dome over. When Mt is at the lower end of this range the cavity fully pinches off at the dome over position detaining further droplets from entering into the lower portion of the cavity (f = 100 Hz, Us = 4.41 m/s, dd = 3.42 mm, We* = 527, Bo* = 0.52, and Mt = 1.84). Movie played back at 1/200 of real speed.

Download Speirs et al. supplementary movie 5(Video)
Video 3.1 MB

Speirs et al. supplementary movie 6

Supplemental movie for Fig. 8b – sub-cavity dome over at higher Mt Sub-cavity dome over at higher Mt. As Mt →4 droplets break through the sub-cavity dome overs reopening the cavity and preventing a full pinch-off (f = 200 Hz, Us = 5.45 m/s, dd = 3.76 mm, We* = 886, Bo* = 0.63, and Mt = 3.27). Movie played back at 1/200 of real speed.

Download Speirs et al. supplementary movie 6(Video)
Video 4.5 MB

Speirs et al. supplementary movie 7

Supplemental movie for Fig. 9a – shallow seal for droplets A cavity created by a multi-droplet stream pinches off with a shallow seal for small Bo* (f = 6000 Hz, Us = 6.39 m/s, dd = 0.39 mm, We* = 223, Bo* = 0.021, and Mt = 39.7). Movie played back at 1/200 of real speed.

Download Speirs et al. supplementary movie 7(Video)
Video 247.8 KB

Speirs et al. supplementary movie 8

Supplemental movie for Fig. 9b – shallow seal for jets A cavity created by a jet experiences first shallow and then deep seal (Us = 5.78 m s-1, dj = 0.41 mm, We = 190, and Bo = 0.023). After shallow seal pinch-off, the jet is perturbed and begins to break up into a droplet stream from the Rayleigh-Plateau instability. Movie played back at 1/200 of real speed.

Download Speirs et al. supplementary movie 8(Video)
Video 676.4 KB

Speirs et al. supplementary movie 9

Supplemental movie for Fig. 12a – surface seal for droplets The splash crown (not shown) of a cavity created by a multi-droplet stream domes over resulting in surface seal which is followed by deep seal (f = 2500 Hz, Us = 7.51 m s-1, dd = 2.06 mm, We* = 1,616, Bo* = 0.5796, and Mt = 28). Movie played back at 1/200 of real speed.

Download Speirs et al. supplementary movie 9(Video)
Video 4.1 MB

Speirs et al. supplementary movie 10

Supplemental movie for Fig. 12b – surface seal for jets The splash crown (not shown) of a cavity created by a jet domes over resulting in surface seal which is followed by deep seal (Us = 9.69 m s-1, dj = 0.71 mm, We = 921, and Bo = 0.068). Movie played back at 1/200 of real speed.

Download Speirs et al. supplementary movie 10(Video)
Video 802.3 KB