A Problem in Potential Flow with a Free Surface

Author: Trilling, Leon

Year: 1947

Degree: Engineer's thesis

Advisor: Millikan, Clark Blanchard

Committee Member: Unknown, Unknown

Option: Aeronautics

DOI: 10.7907/CA87-ZG47

Abstract

The present paper concerns itself with the determination of impact pressure and force which act on a body when it hits a horizontal fluid surface at any angle at a high speed.

It is assumed that only the hydrodynamic force has any effect and also, that the impact is so short that the effect of the fluid splash is negligible. Under those conditions, it is possible to linearize the boundary condition of the flow and to divide the force and velocity vectors into vertical and horizontal components. The problem in the vertical direction then becomes identical with that of the motion of a body submerged in an infinite fluid, and is easily solved for bodies of simple shape. The problem in the horizontal direction resolves itself into a problem of potential flow with a symmetric discontinuity along the free surface, so that the free surface may be replaced by a symmetric configuration with velocity components opposite and equal to those in the actual fluid.

Under those conditions, two simple two-dimensional configurations are studied; an infinite elliptic semi-cylinder and an infinite flat plate. The analysis is carried out in terms of conformal transformations. Three simple three-dimensional problems are also solved: that of a sphere, an ellipsoid of revolution and a general ellipsoid. The method here is that of three dimensional harmonic analysis.

In conclusion, a specific example is given: the drag components on a sphere which hits the surface at 45° are calculated; the results are compared to experimental data and show fair agreement with them.

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