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Theory of optimum shapes in free-surface flows. Part 2. Minimum drag profiles in infinite cavity flow

Published online by Cambridge University Press:  29 March 2006

Arthur K. Whitney
Arthur K. Whitney
Affiliation:
California Institute of Technology, Pasadena, California Present address: Lockheed Palo Alto Research Laboratory, Lockheed Missiles and Space Co., Palo Alto, California.
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Abstract

The problem considered here is to determine the shape of a symmetric two-dimensional plate so that the drag of this plate in infinite cavity flow is a minimum. With the flow assumed steady and irrotational, and the effects due to gravity ignored, the drag of the plate is minimized under the constraints that the frontal width and wetted arc-length of the plate are fixed. The extremization process yields, by analogy with the classical Euler differential equation, a pair of coupled nonlinear singular integral equations. Although analytical and numerical attempts to solve these equations prove to be unsuccessful, it is shown that the optimal plate shapes must have blunt noses. This problem is next formulated by a method using finite Fourier series expansions, and optimal shapes are obtained for various ratios of plate arc-length to plate width.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 55 , Issue 3 , 10 October 1972 , pp. 457 - 472
Copyright
© 1972 Cambridge University Press

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References

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