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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
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
Corresponding
E-mail address:

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.

Type
JFM Papers
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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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 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 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 405 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 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 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 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 248 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 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 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 KB
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