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Subsonic potential flow past a circle and the transonic controversy

Published online by Cambridge University Press:  17 February 2009

M. D. Van Dyke  and
A. J. Guttmann
M. D. Van Dyke
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, California 94305, U.S.A.
A. J. Guttmann
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle, N.S.W. 2308.
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Abstract

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The Mach-number series expansion of the potential function for the two-dimensional flow of an inviscid, compressible, perfect, diatomic gas past a circular cylinder is obtained to 29 terms. Analysis of this expansion allows the critical Mach number, at which flow first becomes locally sonic, to be estimated as M* = 0.39823780 ± 0.00000001. Analysis also permits the following estimate of the radius of convergence of the series for the maximum velocity to be made: Mc = 0.402667605 ± 0.00000005, though we have been unable to determine the nature of the singularity of M = Mc. Since Mc exceeds M* by some 1.1%, it follows that this particular “airfoil” can possess a continuous range of shock-free potential flows above the critical Mach number. This result hopefully resolves a 70-year old controversy.

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 3 , January 1983 , pp. 243 - 261
Copyright
Copyright © Australian Mathematical Society 1983

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