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A uniformly asymptotic solution for incompressible flow past thin sharp-edged aerofoils at zero incidence

Published online by Cambridge University Press:  24 October 2008

A. F. Sheer
A. F. Sheer
Affiliation:
Royal Holloway College, Englefield Green, Surrey
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Extract

Expansions obtained from classical subsonic thin-aerofoil theory break down in the neighbourhood of the aerofoil edges. At sharp edges the method of matched asymptotic expansions fails to remedy this. Here this failure is explained, and in the case of incompressible flow past a symmetric aerofoil at zero incidence it is shown that by proper choice of the dependent variable an expansion may be obtained which is uniformly asymptotic. Finally, the case of a circular-arc aerofoil is considered in more detail.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 1 , July 1971 , pp. 135 - 155
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

1Bollheimer, L. and Weissinger, J.An application of the ‘PLK’ method to conformal mapping and thin airfoil theory. Z. Flugwiss. 16 (1968), 6.Google Scholar
2Caratheodory, C.Conformal representation, 2nd ed. (Cambridge University Press, 1952.)Google Scholar
3Caratheodory, C.Theory of functions. (New York, Chelsea, 1954.)Google Scholar
4Geer, J. F. and Keller, J. B.Uniformly asymptotic solutions for potential flow round a thin airfoil and the electrostatic potential about a thin conductor. SIAM J. Appl. Math. 16 (1968), 75.CrossRefGoogle Scholar
5Hoogstraaten, H. W.Uniformly valid approximations in two-dimensional subsonic thin airfoil theory. J. Engineering Math. 1 (1967), 51.CrossRefGoogle Scholar
6Lighthill, M. J.A new approach to thin aerofoil theory. Aero. Quart. 3 (1951), 193.CrossRefGoogle Scholar
7Milne-Thompson, L. M.Theoretical hydrodynamics, 4th ed. (New York, Macmillan, 1960.)Google Scholar
8Protter, M. H. and Weinberger, H. F.Maximum principles in differential equations. (Englefield Cliffs N. J., Prentice-Hall, 1967.)Google Scholar
9Van Dyke, M. D.Perturbation methods in fluid mechanics. (New York, Academic Press, 1964.)Google Scholar