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Water entry of deformable spheres

  • Randy C. Hurd (a1), Jesse Belden (a2), Michael A. Jandron (a2), D. Tate Fanning (a3), Allan F. Bower (a4) and Tadd T. Truscott (a1)...

Abstract

When a rigid body collides with a liquid surface with sufficient velocity, it creates a splash curtain above the surface and entrains air behind the sphere, creating a cavity below the surface. While cavity dynamics has been studied for over a century, this work focuses on the water entry characteristics of deformable elastomeric spheres, which has not been studied. Upon free surface impact, an elastomeric sphere deforms significantly, giving rise to large-scale material oscillations within the sphere resulting in unique nested cavities. We study these phenomena experimentally with high-speed imaging and image processing techniques. The water entry behaviour of deformable spheres differs from rigid spheres because of the pronounced deformation caused at impact as well as the subsequent material vibration. Our results show that this deformation and vibration can be predicted from material properties and impact conditions. Additionally, by accounting for the sphere deformation in an effective diameter term, we recover previously reported characteristics for time to cavity pinch off and hydrodynamic force coefficients for rigid spheres. Our results also show that velocity change over the first oscillation period scales with the dimensionless ratio of material shear modulus to impact hydrodynamic pressure. Therefore, we are able to describe the water entry characteristics of deformable spheres in terms of material properties and impact conditions.

Copyright

Corresponding author

Email addresses for correspondence: randyhurd@gmail.com, taddtruscott@gmail.com

References

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JFM classification

Type Description Title
VIDEO
Movies

Hurd et al. supplementary movie 1
A sphere deforms significantly as it enters the water (G∞ = 6.70 kPa, D = 51 mm, U0 = 5.3 m/s and ρs = 1070 kg/m3) creating a subsurface cavity. After the initial deformation, the sphere oscillates between oblate and prolate shapes, eventually creating a second cavity within the first. Pinch-off occurs within this second, smaller cavity. The entry event is shown from both a top view and side view.

 Video (6.5 MB)
6.5 MB
VIDEO
Movies

Hurd et al. supplementary movie 2
A sphere deforms significantly as it impacts and rebounds from a flat horizontal surface (G∞= 6.70 kPa, D = 51 mm, U0≈ 5 m/s and ρs = 1070 kg/m3). After impact the sphere oscillates between oblate and prolate shapes.

 Video (2.1 MB)
2.1 MB
VIDEO
Movies

Hurd et al. supplementary movie 3
A rigid sphere enters the water forming a subsurface cavity (G∞ = 5.66E5 kPa, D = 51 mm and U0 = 6.5 m/s and ρs= 1070 kg/m3). The cavity pinches-off with a deep seal event.

 Video (4.3 MB)
4.3 MB
VIDEO
Movies

Hurd et al. supplementary movie 4
A deformable sphere enters the water forming a subsurface cavity (G∞ = 70.2 kPa, D = 51 mm, U0 = 6.5 m/s and ρs = 1070 kg/m3). The cavity pinches-off with a deep seal event, very similar to a rigid sphere.

 Video (7.0 MB)
7.0 MB
VIDEO
Movies

Hurd et al. supplementary movie 5
A deformable sphere enters the water forming a subsurface cavity (G∞ = 6.70 kPa, D = 51 mm, U0= 6.5 m/s and ρs = 1070 kg/m3). Pinch-off occurs within the second cavity formed.

 Video (4.8 MB)
4.8 MB
VIDEO
Movies

Hurd et al. supplementary movie 6
A deformable sphere enters the water forming a subsurface cavity (G∞ = 1.12 kPa, D = 51 mm, U0 = 6.5 m/s and ρs= 1070 kg/m3). Pinch-off occurs within the second cavity formed.

 Video (4.6 MB)
4.6 MB
VIDEO
Movies

Hurd et al. supplementary movie 7
For the largest and most compliant spheres tested (G∞ = 1.12 kPa, D = 100 mm, U0 = 6.5 m/s and ρs = 1070 kg/m3) the sphere decelerates more rapidly, occupying the space where pinch-off would occur. The attached cavity recedes upward along the sphere and pinch-off occurs at the top.

 Video (7.2 MB)
7.2 MB

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