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Estimates for critical Mach number under isoperimetric constraints1

Published online by Cambridge University Press:  26 September 2008

F. G. Avkhadiev ,
A. M. Elizarov  and
D. A. Fokin
A. M. Elizarov
Affiliation:
Chebotarev Institute of Mathematics and Mechanics, Kazan State University, Tatarstan, Kazan 420008, Russia
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Abstract

The problem of maximization of the critical Mach number in a subsonic flow of an ideal gas is considered. The Chaplygin gas approximation and the integral representation of the solution of the inverse boundary-value problem of aerohydrodynamics are used to reduce the problem to a special minimax one. The exact solution of the latter is obtained on the basis of the Lindelöf principle. An upper estimate for the critical Mach number is obtained. The results are generalized for the case of airfoil cascades. Some open problems are described.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 5 , October 1995 , pp. 385 - 398
Copyright
Copyright © Cambridge University Press 1995

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References

[1]Aulchenko, S. M. 1992 Variational method of subsonic airfoils design. J. Appl. Mech. Teen. Phys. (4), 90–93 (Russian).Google Scholar
[2]Bers, L. 1958 Mathematical Aspects of Subsonic and Transonic Gas Dynamics. John Wiley.Google Scholar
[3]Elizarov, A. M., Il'Inskiy, N. B. & Potashev, A. V. 1994 Inverse Boundary-value Problems of Aerohydrodynamics. Fizmatlit, Moscow (in Russian).Google Scholar
[4]Gilbarg, D. & Shiffman, M. 1954 On bodies achieving extreme values of critical Mach number, 1. J. Ration. Mech and Analysis 3(2), 209–230.Google Scholar
[5]Golusin, G. M. 1969 Geometric theory of functions of a complex variable. Translations of mathematical monographs 26. American Mathematical Society, Providence, RI.CrossRefGoogle Scholar
[6]Haslinger, J. & Neittaanmäki, P. 1988 Finite Element Approximation for Optimal Shape Design: Theory and application. John Wiley.Google Scholar
[7]Loewner, C. 1954 Some bounds for the critical free stream Mach number of a compressible flow around an obstacle. Studies in Math. and Mech. presented to R. von Mises. Academic Press.Google Scholar
[8]Milne-Thompson, L. M. 1960 Theoretical Hydrodynamics. St. Martin's Press, New York.Google Scholar
[9]Pironneau, O. 1984 Optimal shape design for elliptic systems. Springer Lecture Notes in Computational Physics. Springer-Verlag.CrossRefGoogle Scholar
[10]Stepanov, G. Y. 1962 Hydrodynamics of Turbomachine Lattices. Fizmatgiz, Moscow (in Russian).Google Scholar