Skip to main content
Log in

Unsteady viscous supersonic flow over a short flap

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The method of matched asymptotic expansions is used to investigate the unsteady flow over a short flap deflected through an angle of order R−1/4 in a supersonic stream in a characteristic time ∼ R−1/4. The length of the flap and the pressure difference at the trailing edge are assumed to be such that an interaction region is formed near the flap for which the asymptotic description in the limit R → ∞ is analogous to the description of the flow in the neighborhood of the trailing edge of an oscillating plate [7]. A numerical method is proposed for calculating the unsteady flow and the heat fluxes in the viscous wall layer. The results of calculations make it possible to estimate the influence of the viscous interaction in unsteady flows on the aerodynamic coefficients of control elements of aircraft and the distribution of the heat fluxes over the surface of the body.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature cited

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

  2. V. Ya. Neiland, “Theory of separation of a laminar boundary layer in a supersonic stream,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 53 (1969).

    Google Scholar 

  3. K. Stewartson and P. G. Wilson, “Self-induced separation,” Proc. R. Soc. London Ser. A312, 181 (1969).

    Google Scholar 

  4. V. Ya. Neiland, “Asymptotic problems in the theory of viscous supersonic flows,” Tr. TsAGI, No. 1529, 125 (1974).

    Google Scholar 

  5. P. G. Daniels, “Numerical and asymptotic solutions for the supersonic flow near the trailing edge of a flat plate,” Q. J. Mech. Appl. Math.,27, 175 (1974).

    Google Scholar 

  6. P. G. Daniels, “Numerical and asymptotic solutions for the supersonic flow near the trailing edge of a flat plate at incidence,” J. Fluid Mech.,63, 641 (1974).

    Google Scholar 

  7. P. G. Daniels, “The flow about the trailing edge of a supersonic oscillating aerofoil,” J. Fluid Mech., No. 3, 541 (1975).

    Google Scholar 

  8. W. Schneider, “Upstream propagation of unsteady disturbances in supersonic boundary layers,” J. Fluid Mech.,63, 465 (1974).

    Google Scholar 

  9. O. S. Ryzhov and E. D. Terent'ev, “Unsteady boundary layer with self-induced pressure,” Prikl. Mat. Mekh.,41, 1007 (1977).

    Google Scholar 

  10. A. I. Ruban, “Numerical solution of a local asymptotic problem on unsteady separation of a laminar boundary layer in a supersonic stream,” Zh. Vychisl. Mat. Mat. Fiz.,18, 1253 (1978).

    Google Scholar 

  11. J. E. Carter, “Solutions for laminar boundary layers with separation and reattachment,” AIAA Paper, No. 583, 11 (1974).

    Google Scholar 

  12. J. M. Klineberg and J. L. Steger, “On laminar boundary-layer separation,” AIAA Paper, No. 94, p. 17 (1974).

    Google Scholar 

  13. R. Jenson, O. R. Burggraf, and D, P. Rizzetta, “Asymptotic solution for supersonic viscous flow past a compression corner,” Lect. Notes Phys.,35, 218 (1975).

    Google Scholar 

  14. A. I. Ruban, “Numerical method of solving a free interaction problem,” Uch. Zap. TsAGI,7, 45 (1976).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 111–118, July–August, 1981.

I am grateful to V. Ya. Neiland for valuable advice in a discussion of the work.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kazakov, A.V. Unsteady viscous supersonic flow over a short flap. Fluid Dyn 16, 579–585 (1981). https://doi.org/10.1007/BF01094603

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01094603

Keywords

Navigation