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Rebound and jet formation of a fluid-filled sphere
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10.1063/1.4771985
/content/aip/journal/pof2/24/12/10.1063/1.4771985
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/12/10.1063/1.4771985

Figures

Image of FIG. 1.
FIG. 1.

Jet formation within a partially fluid-filled sphere. m = 173 g, dia = 8 cm.

Image of FIG. 2.
FIG. 2.

Progression of a urethane sphere filled with 20% water dropped from a height of 10 cm (m = 207 g, dia = 8 cm). The time in milliseconds is marked above each image. The moment of greatest sphere deformation upon the first impact is marked as t = 0 ms. The apex of the first rebound is marked at t = 130 ms. Dark lines indicate where the second and third impacts occur. The apex of the second rebound occurs at t = 340 ms. After the first impact, the fluid climbs up the sides of the sphere and forms a large cavity in the center. On the second impact, this cavity collapses forming a large jet in the center. On the third impact, the flow becomes completely disorganized (Video 1) (enhanced online). [URL: http://dx.doi.org/10.1063/1.4771985.1]10.1063/1.4771985.1

Image of FIG. 3.
FIG. 3.

The experimental setup used to observe the dynamics of a partially fluid filled sphere.

Image of FIG. 4.
FIG. 4.

Comparison of fluid motion with different volumes and physical properties within a urethane sphere. All sequences included are dropped from 20 cm. The moment of greatest sphere deformation upon the first impact is marked as t = 0 ms. Dark bars indicate the second and third impacts. (a) Sequence of an empty sphere (Video 2) m = 125 g. (b) Sequence of a sphere 20% filled with isopropyl alcohol (Video 3) m = 196 g. (c) Sequence of a sphere 20% filled with water (Video 4) m = 207 g. (d) Sequence of a sphere 70% filled with water (Video 5) m = 425 g. (e) Sequence of a sphere 20% filled with glycerin (Video 6) m = 249 g. All spheres shown have a diameter of 8 cm (enhanced online). [URL: http://dx.doi.org/10.1063/1.4771985.2] [URL: http://dx.doi.org/10.1063/1.4771985.3] [URL: http://dx.doi.org/10.1063/1.4771985.4] [URL: http://dx.doi.org/10.1063/1.4771985.5] [URL: http://dx.doi.org/10.1063/1.4771985.6]10.1063/1.4771985.210.1063/1.4771985.310.1063/1.4771985.410.1063/1.4771985.510.1063/1.4771985.6

Image of FIG. 5.
FIG. 5.

Rebound trajectories vs time for several cases of a sphere partially filled with water: empty sphere, 10%, 30%, 50%, 70%, 90%, and 100% filled sphere. The 30% filled sphere experiences the greatest rebound suppression of any case dropped from 20 cm (compare to Fig. 4). (a) Trials dropped from 10 cm. (b) Trials dropped from 20 cm. (c) Trials dropped from 30 cm.

Image of FIG. 6.
FIG. 6.

Rebound trajectories vs time for trials of water, isopropyl alcohol, and glycerin filled to 10%–40% of interior volume in comparison with that of an empty sphere. Trials are dropped from 20 cm (compare to Fig. 4). (a) 10% filled. (b) 20% filled. (c) 30% filled. (d) 40% filled.

Image of FIG. 7.
FIG. 7.

Comparison of fluid motion with different volumes and physical properties within an acrylic sphere. All sequences included are dropped from 20 cm. The moment of first impact is marked as t = 0 ms. Dark bars indicate the second and third impacts. (a) Sequence of an empty acrylic sphere (Video 7). m = 50 g. (b) Sequence of an acrylic sphere 30% filled with water (Video 8). m = 192 g. (c) Sequence of an acrylic sphere 70% filled with water (Video 9). m = 387 g. All spheres shown have a diameter of 8 cm (enhanced online). [URL: http://dx.doi.org/10.1063/1.4771985.7] [URL: http://dx.doi.org/10.1063/1.4771985.8] [URL: http://dx.doi.org/10.1063/1.4771985.9]10.1063/1.4771985.710.1063/1.4771985.810.1063/1.4771985.9

Image of FIG. 8.
FIG. 8.

Rebound trajectories vs time for trials of partially filled acrylic spheres with water: empty sphere, 30% filled sphere, 70% filled sphere, and 100% filled sphere. Trials are dropped from 20 cm (compare to Fig. 7). Again we see that an interior fill of 30% mitigates the rebound best from that drop height. Inconsistencies in tracking the motion of the sphere due to overexposure were approximated with a quadratic fit, hence the gaps in the data replaced by dotted lines.

Image of FIG. 9.
FIG. 9.

Images of the first rebound for a 30% filled urethane sphere with an initially disturbed free surface (vortex) dropped from 20 cm above the ground. The vortex collapses during the first rebound (t = 25 ms) forming a large jet that mitigates the rebound height. m = 250 g, dia = 8 cm (Video 10) (enhanced online). [URL: http://dx.doi.org/10.1063/1.4771985.10]10.1063/1.4771985.10

Image of FIG. 10.
FIG. 10.

Images of a 70% filled acrylic sphere that was initially elongated before release, resulting in small oscillations afterward (same set as Fig. 7(c)). A jet is formed as each of the small dimpled disturbances collapse after impact. m = 387 g, dia = 8 cm (Video 11) (enhanced online). [URL: http://dx.doi.org/10.1063/1.4771985.11]10.1063/1.4771985.11

Image of FIG. 11.
FIG. 11.

Images of the first rebound for two 60% filled urethane spheres rolling off of a 30% inclined plane (not shown) from 10 cm above the ground. m = 377 g, dia = 8 cm. (a) Released with an initially rotating vortical-like flow (Video 12). The vortex collapses during the first rebound (t = 23 ms) forming a large jet that mitigates the rebound height. (b) Released after the flow came to rest yielding a much larger rebound (Video 13) (enhanced online). [URL: http://dx.doi.org/10.1063/1.4771985.12] [URL: http://dx.doi.org/10.1063/1.4771985.13]10.1063/1.4771985.1210.1063/1.4771985.13

Image of FIG. 12.
FIG. 12.

This image is formed by combining a single pixel line from the center of the sphere from each image in the set of Fig. 2, where the left side is t = −120 ms and the right is t = 536 ms.

Image of FIG. 13.
FIG. 13.

The position, velocity, and acceleration of both the sphere (Y relative to ground) and interior fluid (Y j relative to the sphere). Position, velocity, and acceleration of the jet are forced to zero after jet formation (t > 280 ms).

Image of FIG. 14.
FIG. 14.

(a) A physical model of the rebound reduction of a partially filled sphere where two spheres collide after one impacts the ground altering their momentum. (b) The momentum of the sphere and jet after the second impact normalized by the combined momentum of the sphere and jet before impact for both the model and experimental data.

Image of FIG. 15.
FIG. 15.

A free body diagram of a partially fluid-filled sphere. At the initial position, (PE0), m tot is suspended above a flat, rigid surface at the initial height h 0. As the sphere rises from the first impact (), a parabolic cavity forms. At the apex of the first rebound, (PE1), the cavity is fully formed and the energy of the system is once again stored in the potential of m tot at h 1. The kinetic energy of m tot approaching the second impact is transferred to the collapse of the cavity and kinetic energy contained in m f l . The result of this energy transfer is the formation of the jet () and reduced rebound height, h 2.

Image of FIG. 16.
FIG. 16.

Non-dimensional energy loss vs percentage of interior volume filled for trials of (a) urethane spheres partially filled with water and (b) urethane spheres partially filled with isopropyl alcohol. Empty markers denote the energy loss to the fluid occurring after the first impact, while the filled markers represent the loss after the second impact. The results are scaled by the amount of energy available to the sphere before first and second impact, Mgh 0 and Mgh 1, respectively.

Image of FIG. 17.
FIG. 17.

Non-dimensional energy loss vs percentage of interior volume filled for acrylic spheres that are partially filled with water. Scaling and marker representation are the same as in Fig. 16. Dotted lines are included to assist in observing the behavior of the system as more fluid is added.

Tables

Generic image for table
Table I.

Summary of independent parameters varied in the experiment.

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/content/aip/journal/pof2/24/12/10.1063/1.4771985
2012-12-27
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Rebound and jet formation of a fluid-filled sphere
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/12/10.1063/1.4771985
10.1063/1.4771985
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