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Gelatine cavity dynamics of high-speed sphere impact

  • Akihito Kiyama (a1) (a2), Mohammad M. Mansoor (a3), Nathan B. Speirs (a3), Yoshiyuki Tagawa (a1) (a2) and Tadd T. Truscott (a3)...

Abstract

We investigate the impact and penetration of a solid sphere passing through gelatine at various impact speeds up to $143.2~\text{m}~\text{s}^{-1}$ . Tests were performed with several concentrations of gelatine. Impacts for low elastic Froude number $\mathit{Fr}_{e}$ , a ratio between inertia and gelatine elasticity, resulted in rebound. Higher $\mathit{Fr}_{e}$ values resulted in penetration, forming cavities with prominent surface textures. The overall shape of the cavities resembles those observed in water-entry experiments, yet they appear in a different order with respect to increasing inertia: rebound, quasi-seal, deep-seal, shallow-seal and surface-seal. Remarkably, similar to the $We$ $Bo$ phase diagram in water-entry experiments, the elastic Froude number $\mathit{Fr}_{e}$ and elastic Grashof number $\mathit{Gr}_{e}$ (a ratio between gravity and gelatine elasticity) classify all five different phenomena into distinguishable regimes. We find that $\mathit{Fr}_{e}$ can be a good indicator to describe the cavity length $H$ , particularly in the shallow-seal regime. Finally, the evolution of cavity shape, pinch-off depth, and lower cavity radius are investigated for different $\mathit{Fr}_{e}$ values.

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Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Email addresses for correspondence: tagawayo@cc.tuat.ac.jp, taddtruscott@gmail.com

References

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JFM classification

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Type Description Title
VIDEO
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Kiyama et al. supplementary movie 1
Surface-seal in water (We~4.1×104, Bo~6.8×10-1).

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Kiyama et al. supplementary movie 2
Surface-seal in 1wt% gelatin (Fre~1.9×104, Gre~3.3×10-1).

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Kiyama et al. supplementary movie 3
Shallow-seal in 2wt% gelatin (Fre ~4.0×103, Gre ~5.5×10-2).

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Kiyama et al. supplementary movie 4
Shallow-seal in 3wt% gelatin (Fre ~1.4×103, Gre ~2.3×10-2).

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Kiyama et al. supplementary movie 5
Shallow-seal in 5wt% gelatin (Fre ~1.9×102, Gre ~4.1×10-3).

 Video (1.0 MB)
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Kiyama et al. supplementary movie 6
Quasi-seal in 10wt% (Fre ~5.9×101, Gre ~1.3×10-3).

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Kiyama et al. supplementary movie 7
Rebound in 2wt% gelatin (Fre ~1.8×101, Gre ~5.5×10-2).

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1.7 MB
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Kiyama et al. supplementary movie 8
Surface-seal in 2wt% gelatin (Fre ~1.5×104, Gre ~5.5×10-2).

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Kiyama et al. supplementary movie 9
Cavity shape after closure in 3wt% gelatin (an extended version of Movie 4).

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Kiyama et al. supplementary material
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Gelatine cavity dynamics of high-speed sphere impact

  • Akihito Kiyama (a1) (a2), Mohammad M. Mansoor (a3), Nathan B. Speirs (a3), Yoshiyuki Tagawa (a1) (a2) and Tadd T. Truscott (a3)...

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