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On parachutes of optimum shape in a subsonic gas flow

Published online by Cambridge University Press:  01 February 2007

D. V. MAKLAKOV ,
A. M. ELIZAROV  and
R. R. SHARIPOV
D. V. MAKLAKOV
Affiliation:
Chebotarev Institute of Mathematics and Mechanics, Kazan State University, Universitetskaya, 17, Kazan, 420008, Russia email: Dmitri.Maklakov@ksu.ru, Elizarov@ksu.ru
A. M. ELIZAROV
Affiliation:
Chebotarev Institute of Mathematics and Mechanics, Kazan State University, Universitetskaya, 17, Kazan, 420008, Russia email: Dmitri.Maklakov@ksu.ru, Elizarov@ksu.ru
R. R. SHARIPOV
Affiliation:
Kazan State Architectural–Building University, 1, Zelenaya str., 420043 Kazan, Russia
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Abstract

In this paper the problem of finding the impermeable parachute of optimum shape in a subsonic gas flow has been solved. The effects of compressibility have been taken into account out by making use of ideas of Chaplygin's approximate method. A formula for the drag coefficient has been deduced and by comparison with exact solutions it has been demonstrated that for bluff bodies its related error is no more than 0.5% for any Mach number at infinity less than unity. On the basis of the formula a functional for the drag force has been constructed and its global maximum has been found analytically. It has been shown that the optimum shape is slightly affected by compressibility.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 18 , Issue 1 , February 2007 , pp. 81 - 102
Copyright
Copyright © Cambridge University Press 2007

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References

[1]Chaplygin, S. A. (1933) On gas jets. Complete Works 2, Leningrad: AN SSSR, 3–90 (in Russian).Google Scholar
[2]Elizarov, A. M., Il'inskiy, N. B. & Potashev, A. V. (1997) Mathematical Methods of Airofoil Design. Inverse Boundary–Value Problems of Aerohydrodynamics. Berlin, Akademy Verlag.Google Scholar
[3]Gurevich, M. I. (1979) The theory of jets in an ideal fluid. Moscow, Nauka (in Russian).Google Scholar
[4]Iacob, C. (1933) Sur quelques problemes concernant l'ecoulement des fluides parfaits compressibles. C.R. Acad. Sci., Paris 197, 125–127.Google Scholar
[5]Lavrentieff, M. (1938) Sur certaines propriétés des functions univalentes et leurs application à la théories des sillages. Mat. Sbornik 46, 391–458.Google Scholar
[6]Maklakov, D. V. (1988) The maximum resistance of a curvilinear obstacle subjected to the action of free jets with separation. Sov. Phys., Dokl 33 (1), 11–13 (translation from 1988 Dokl. Akad. Nauk SSSR 298 (3), 574–577).Google Scholar
[7]Maklakov, D. V. & Uglov, A. N. (1995) On the maximum drag of a curved plate in flow with a wake. Europ. J. Appl. Math. 6 (5), 517–527.CrossRefGoogle Scholar
[8]Maklakov, D. V. (1997) Nonlinear problems of hydrodynamics of potential flows with unknown boundaries. Moskva, Yanus-K (in Russian).Google Scholar
[9]Maklakov, D. V. (1999) A note on the optimum profile of a sprayless planing surface. J. Fluid Mech. 384, 281–292.CrossRefGoogle Scholar
[10]Maklakov, D. V. 2004 Some remarks on the exact solution for an optimal impermeable parachute problem. J. Computational & Appl. Math. 166 (2), 591–596.CrossRefGoogle Scholar
[11]Maklakov, D. V. (2005) On deflectors of optimum shape. J. Fluid Mech. 540, 175–187.CrossRefGoogle Scholar
[12]Serrin, J. (1953) On plane and axially symmetric free boundary problems. J. Rat. Mech. Anal. 2, 563–575.Google Scholar
[13]Stepanov, G. Yu. (1962) Hydrodynamics of turbine cascades. Moscow, FizMatGiz (in Russian).Google Scholar
[14]Sungurtsev, Yu. V. (1989) Plane jet flows of gas. Moscow, Moscow State University (in Russian).Google Scholar
[15]Whitney, A. K. (1972) Theory of optimum shapes in free-surface flows. Part 2: Minimum drag profiles in infinite cavity flow. J. Fluid. Mech. 55 457–472.CrossRefGoogle Scholar
[16]Wu, T. Y. & Whitney, A. K. (1972) Theory of optimum shapes in free-surface flows. Part 1: Optimum profile on sprayless planing surface. J. Fluid. Mech. 55, 439–455.CrossRefGoogle Scholar