Free Surface Penetration of Inverted Right Circular Cones at Low Froude Number

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Virginia Tech

In this thesis the impact of inverted cones on a liquid surface is studied. It is known that with the right combination of velocity, geometry, and surface treatment, a cavity of air can be formed behind an impacting body and extended for a considerable distance. Other investigators have shown that the time and depth of the cone when this cavity collapses and seals follows a different power law for flat objects such as disks, then it does for slender objects such as cylinders. Intuitively it can be expected that a more slender body will have less drag and that the streamlined shape will not push the fluid out of it's way at impact to the same extent as a more blunt body, therefore forming a smaller cavity behind it. With a smaller initial cavity, the time and depth of it's eventual collapse can be expected to be less than that of a much more blunt object, such as a flat disk.

To study this, a numerical model has been developed to simulate cones with the same base radius but different angles impacting on a liquid surface over a range of velocities, showing how the seal depth, time at cavity seal, and drag forces change. In order to ensure the numerical model is accurate, it is compared with experimental data including high speed video and measurements made of the force with time.

It is expected that the results will fall inside the power law exponents reported by other authors for very blunt objects such as disks on one end of the spectrum, and long slender cylinders on the other. Furthermore, we expect that the drag force exerted on the cones will become lower as the L/D of the cone is increased.

boundary element method, free surface penetration, interfacial flow, water entry, Laplace's equation