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A new method for treating supersonic flow past nearly plane wings

Published online by Cambridge University Press:  28 March 2006

Myrna Lewin  and
Robert A. Schmeltzer
Myrna Lewin
Affiliation:
North American Aviation, Los Angeles Division, Los Angeles, California Present address: Courant Institute of mathematical Sciences, New York University.
Robert A. Schmeltzer
Affiliation:
North American Aviation, Los Angeles Division, Los Angeles, California Present address: Bell Telephone Laboratories, Holmdel, New Jersey.
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Abstract

Function-theoretic techniques are used for determining the supersonic flow past a wing of infinite length having a straight leading edge. The problem is reduced to a set of dual integral equations which are solved by function - theoretic methods. This approach is shown to be useful for treating more general - type leading edges yielding closed - form solutions which heretofore have been unobtainable. The general solutions obtained here are shown to be in complete agreement with previous solutions for the flow at large distances downstream on the aerofoil. For a wing of infinite span, the solution reduces to the well - known perturbation potential for a distribution of sources in a horizontal plane.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 17 , Issue 2 , October 1963 , pp. 305 - 313
Copyright
© 1963 Cambridge University Press

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References

Gunn, J. C. 1947 Linearized supersonic aerofoil theory. Phil. Trans. A, 240, 327–73.Google Scholar
Hadamard, J. 1923 Lectures on Cauchy's problem in Linear Partial Differential Equations. New Haven: Yale University Press.
Lomax, H., Heaslet, M. A. & Fuller, F. B. 1951 Integrals and integral equations in linearized wing theory. N.A.C.A. Rep. no. 1054.Google Scholar
Muskhelishvili, N. I. 1946 Singular Integral Equations, 2nd edn. J. R. M. Radok.
Puckett, A. E. 1946 Supersonic wave drag of thin aerofoils. J. Aero. Sci., 13, 475–85.Google Scholar
Stewartson, K. 1950 Supersonic flow over an inclined wing of zero aspect ratio. Proc. Camb. Phil. Soc., 46, 307–15.Google Scholar
Ward, G. N. 1955 Linearized Theory of Steady High-speed Flow. Cambridge University Press.