Skip to main content
Log in

Numerical solution of the problem of the mixing of the boundary layers shed from the trailing edge of a wing

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

During the mixing of viscous incompressible flows with different velocities, in the vicinity of a trailing edge an interaction region with a three-layer structure is formed, similar to that in the case of symmetric shedding with equal velocities. The boundary layers developing on the upper and lower sides of the airfoil form a viscous mixing layer, or vortex sheet, which separates the flows downstream of the trailing edge. The boundary value problem corresponding to the flow in the viscous sublayer in the vicinity of the trailing edge of a flat plate is solved for high Reynolds numbers using an efficient numerical method for solving the equations of asymptotic interaction theory.

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

References

  1. V. Ya. Neiland, “Theory of laminar boundary layer separation in supersonic flow,” Fluid Dynamics, 4, No. 4, 38 (1969).

    Google Scholar 

  2. K. Stewartson and P.G. Williams, “Self-induced separation,” Proc. Roy. Soc. London. Ser. A, 312, No. 1509, 181 (1969).

    ADS  MATH  Google Scholar 

  3. K. Stewartson, “On the flow near the trailing edge of a flat plate,” Mathematika, 16, Pt. 1, No. 31, 106 (1969).

    Article  Google Scholar 

  4. A. F. Messiter, “Boundary layer flow near the trailing edge on a flat plate,” SIAM J. Appl. Math., 18, 241 (1970).

    Article  MATH  Google Scholar 

  5. V. Ya. Neiland, V. V. Bogolepov, G. N. Dudin, and I. I. Lipatov, Asymptotic Theory of Supersonic Viscous Flows [in Russian], Fizmatlit, Moscow (2003).

    Google Scholar 

  6. Vic. V. Sychev, V. V. Sychev, A. I. Ruban, and G. L. Korolev, Asymptotic Theory of Separated Flows, Cambridge Univ. Pres, Cambridge (1998).

    MATH  Google Scholar 

  7. C. E. Jobe and O.R. Burggfaf, “The numerical solution of the asymptotic equations of trailing edge flow,” Proc. Roy. Soc. London. Ser. A, 340, No. 1620, 91 (1974).

    ADS  MATH  Google Scholar 

  8. A. I. Ruban, “Asymptotic theory of the flow near the trailing edge of a thin airfoil,” Uch. Zap. TsAGI, 8, No. 1, 6 (1977).

    Google Scholar 

  9. S. N. Brown and K. Stewartson, “Trailing-edge stall,” J. Fluid Nech., 42, 561 (1970).

    Article  ADS  MATH  Google Scholar 

  10. R. Chow and R. E. Melnik, “Numerical solution of the triple-deck equations for laminar trailing-edge stall,” in: Lecture Notes in Physics. Vol. 59, Springer, Berlin (1976), p. 135.

    Google Scholar 

  11. G. L. Korolev, “Contribution to the theory of thin-profile trailing edge separation,” Fluid Dynamics, 24, No. 4, 534 (1989).

    Article  MathSciNet  Google Scholar 

  12. G. G. Daniels, “Viscous mixing at a trailing edge,” Quart. J. Mech. Appl. Math., 30, 319 (1977).

    MathSciNet  MATH  Google Scholar 

  13. S. Goldstein, “Concerning some solutions of the boundary layer equations in hydrodynamics,” Proc. Camb. Phil. Soc., 36, 1 (1930).

    Article  Google Scholar 

  14. M.A. Kravtsova, V. B. Zametaev, and A. I. Ruban, “An effective numerical method for solving viscous-inviscid interaction problems,” Phil. Trans. Roy. Soc. London. Ser. A, 363, No. 1830, 1157 (2005).

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Authors

Additional information

__________

Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2006, pp. 160–173.

Original Russian Text Copyright © 2006 by Zametaev and Kravtsova.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zametaev, V.B., Kravtsova, M.A. Numerical solution of the problem of the mixing of the boundary layers shed from the trailing edge of a wing. Fluid Dyn 41, 817–829 (2006). https://doi.org/10.1007/s10697-006-0098-8

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10697-006-0098-8

Keywords

Navigation