Whitney, Arthur K. (1972) Theory of optimum shapes in free-surface flows. Part 2. Minimum drag profiles in infinite cavity flow. Journal of Fluid Mechanics, 55 (3). pp. 457-472. ISSN 0022-1120. doi:10.1017/S0022112072001958. https://resolver.caltech.edu/CaltechAUTHORS:20120724-100549334
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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.
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| Additional Information: | © 1972 Cambridge University Press. Received September 8 1971; Revised July 6 1972. Published Online March 29 2006. This paper is based on part of the author's doctoral research which was supported by the National Science Foundation and carried out at the California Institute of Technology under Professor T. Y. Wu, whose interest and encouragement is gratefully acknowledged. The present work was sponsored by the Naval Ship System Command General Hydrodynamics Research and Development Center and the Office of Naval Research, under contract 220(51). | |||||||||
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| Issue or Number: | 3 | |||||||||
| DOI: | 10.1017/S0022112072001958 | |||||||||
| Record Number: | CaltechAUTHORS:20120724-100549334 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120724-100549334 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 32667 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 24 Jul 2012 21:26 | |||||||||
| Last Modified: | 09 Nov 2021 21:29 |
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