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Bilateral estimates of the critical Mach number for some classes of carrying wing profiles

Published online by Cambridge University Press:  17 February 2009

F. G. Avkhadiev  and
A. M. Elizarov
F. G. Avkhadiev
Affiliation:
Chebotarev Institute of Mathematics and Mechanics, Kazan State University, University St. 17, Kazan 420008, Tatarstan, Russia.
A. M. Elizarov
Affiliation:
Chebotarev Institute of Mathematics and Mechanics, Kazan State University, University St. 17, Kazan 420008, Tatarstan, Russia.
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Abstract

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A problem of estimation of the critical Mach number for a class of carrying wing profiles with a fixed theoretical angle of attack is considered. The Chaplygin gas model is used to calculate the velocity field of the flow. The original problem is reduced to a special minimax problem. A solution is constructed for an extended class of flows including multivalent ones, hence M* is estimated from above. For a fixed interval [0, β0], β0 ≅ 3π/8, an estimate of M* is given from below.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 4 , April 2001 , pp. 494 - 503
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Aul'chenko, S. M., “Variational method of subsonic airfoils design”, J. Appl. Mech. Tecn. Phys. 4 (1992) 90–93, (in Russian).Google Scholar
[2]Avkhadiev, F. G., Elizarov, A. M. and Fokin, D. A., “Estimates for critical Mach number under isoperimetrical constraints”, European J. Appl. Math. 6 (1995) 385–398.CrossRefGoogle Scholar
[3]Bers, L., Mathematical aspects of subsonic and transonic gas dynamics (John Wiley and Sons, New York, 1958).Google Scholar
[4]Brutyan, M. A. and Lyapunov, S. V., “Optimization of plane symmetrical body shape to increase the critical Mach number”, Tr. TSIAGI 12 (1981) 10–22, (in Russian).Google Scholar
[5]Elizarov, A. M., Il'inskiy, N. B. and Potashev, A. V., Mathematical methods of airfoils design (inverse boundary-value problems of aerohydrodynamics) (Wiley, Berlin, 1997) p. 280.Google Scholar
[6]Gilbarg, D. and Shiffman, M., “On bodies achieving extreme values of critical Mach number. I”, J. Ration. Mech and Analysis 3 (1954) 209–230.Google Scholar
[7]Golusin, G. M., Geometric theory of functions of a complex variable, Transl. Math. Monographs 26 (American Mathematical Society, Providence, RI, 1969) p. 676.CrossRefGoogle Scholar
[8]Kraĭko, A. N., “Plane and axial-symmetric configurations flowed with the maximal critical Mach number”, Prikl. Mat. Mekh. 51 (1987) 941–950, (in Russian).Google Scholar
[9]Loewner, C., “Some bounds for the critical free stream Mach number of a compressible flow around an obstacle”, in Studies in Math. and Mech. presented to R. von Mises, (Academic Press, New York, 1954).Google Scholar
[10]Stepanov, G. Yu., Hydrodynamics of turbomachine grids, (in Russian) (Physmathguiz, Moscow, 1962).Google Scholar