Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Hypersonic flow past a rectangular profile through which gas is blown strongly

  • 24 Accesses

Abstract

In the present paper, we consider the hypersonic flow past a rectangular profile and the end of a cylinder when there is strong distributed blowing of gas through their flat front parts. The injected gas is assumed to be inviscid, and the pressure on the contact surface which separates the exterior flow and the blowing layer is determined in accordance with Newton's formula. The use of perturbation theory in the case of a thin blowing layer has made it possible to obtain limit problems for different flow regions, and the analytic solution and subsequent asymptotic matching of these problems yield the form of the contact surface and the distribution of the pressure on the body. It is shown that the drag of the body depends nonmonotonically on the flow rate of the blown gas. The optimal blowing parameters and the corresponding minimal drag are determined.

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    É. A. Gershbein and G. A. Tirskii, “Flow of a viscous heat conducting multicomponent gas in a shock layer in the neighborhood of a nose cone in the case of intensive blowing,” Nauchn. Tr. Inst. Mekh. Mosk. Univ., No. 1, 46 (1970).

  2. 2.

    V. P. Stulov, “Strong blowing on the surface of a blunt body in a supersonic stream,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 89 (1972).

  3. 3.

    M. M. Gilinskii and M. G. Lebedev, “Calculation of strong blowing on a blunt body and a profile,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No.1, 117 (1977).

  4. 4.

    M. A. Koval', “Experimental and theoretical investigation of strong blowing into a supersonic stream,” Dissertation for Candidate's Degree [in Russian], State University, Moscow (1978).

  5. 5.

    N. S. Matveeva and V. Ya. Neiland, “Strong blowing on a body of finite length in a supersonic stream,” Uch. Zap. TsAGI,1, 13 (1970).

  6. 6.

    V. A. Levin, “Strong blowing on the surface of a body in a supersonic gas stream,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 97 (1973).

  7. 7.

    I. I. Vigdorovich and V. A. Levin, “Strong blowing of fluid in a supersonic stream from the surface of a plate of finite length,” in: Nonequilibrium Flows of Gas and Optimal Shapes of Bodies in Supersonic Streams [in Russian], Izd. Mosk. Un., Moscow (1978), p. 51.

  8. 8.

    A. N. Osiptsov, “Blowing from the end of a cylinder into a hypersonic gas stream,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 192 (1979).

  9. 9.

    I. I. Vigdorovich, “Strong blowing of fluid into a hypersonic stream from the surface of a plate of finite length,” Prikl. Mat. Mekh.,43, 829 (1979).

  10. 10.

    I. I. Vigdorovich, “Blowing of fluid into a supersonic stream through a permeable surface,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 108 (1980).

  11. 11.

    M. A. Koval', V. P. Stulov, and A. I. Shvets, “Experimental investigation of supersonic flow over blunt bodies with strong distributed blowing,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 84 (1978).

  12. 12.

    G. G. Chernyi, Gas Flows at High Supersonic Velocities [in Russian], Fizmatgiz, Moscow (1959), p. 220.

  13. 13.

    V. V. Lunev, Hypersonic Aerodynamics [in Russian], Mashinostroenie, Moscow (1975), p. 327.

  14. 14.

    M. D. Van Dyke, Perturbation Methods in Fluid Mechanics, New York (1964).

  15. 15.

    W. R. Wasow, Asymptotic Expansions for Ordinary Differential Equations, New York (1965).

  16. 16.

    I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York and London (1965) (the reference is to p. 1100 of the Russian original published by Fizmatgiz, Moscow (1963)).

  17. 17.

    V. A. Ditkin and A. P. Prudnikov, Operator Calculus [in Russian], Vysshaya Shkola, Moscow (1966), p. 405.

  18. 18.

    Yu. A. Brychkov and A. P. Prudnikov, Integral Transforms of Generalized Functions [in Russian], Nauka, Moscow (1977), p. 287.

  19. 19.

    N. E. Kochin, I. A. Kibel', and N. V. Roze, Theoretical Hydrodynamics, New York (1964).

  20. 20.

    F. I. Frankl', “Chaplygin problems for mixed subsonic and supersonic flows,” Izv. Akad. Nauk SSSR, Ser. Mat.,9, 121 (1945).

  21. 21.

    I. G. Petrovskii, Lectures on Partial Differential Equations [in Russian], Fizmatgiz, Moscow (1961), p. 400.

  22. 22.

    L. I. Sedov, Two-Dimensional Problems of Hydrodynamics and Aerodynamics [in Russian], Nauka, Moscow (1966), p. 448.

  23. 23.

    Yu. V. Rudnev, “On some mixed problems of gas dynamics,” in: Theoretical Hydrodynamics, No. 2 [in Russian], Oborongiz, Moscow (1955), p. 143.

  24. 24.

    V. V. Golubev, Lectures on the Analytic Theory of Differential Equations, Gostekhizdat, Moscow-Leningrad (1950), p. 436.

Download references

Author information

Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 154–166, January–February, 1982.

I thank V. A. Levin for interest in the work and valuable discussions.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Vigdorovich, I.I. Hypersonic flow past a rectangular profile through which gas is blown strongly. Fluid Dyn 17, 127–138 (1982). https://doi.org/10.1007/BF01090710

Download citation

Keywords

  • Perturbation Theory
  • Contact Surface
  • Flow Region
  • Front Part
  • Limit Problem