Advertisement

Stability and separation of freely interacting boundary layers

  • Oleg S. Ryzhov
  • Vladimir I. Zhuk
Contributed Papers
Part of the Lecture Notes in Physics book series (LNP, volume 141)

Abstract

The triple-deck theory to describe boundary-layer free interaction and separation is carefully investigated from the viewpoint of how it predicts stability properties of a viscous flow. The linearized version of this theory gives the same results as the linear stability theory based on the Orr-Sommerfeld equation if the flow is incompressible and the wave number of small disturbances goes to zero. Hence, a rather general criterion results to fix limits for a subsonic boundary layer to be stable. On the contrary, the linear approximation to the triple-deck theory leads to discouraging conclusions when the velocity of the oncoming stream exceeds the speed of sound, since it fails to reveal the boundary-layer instability. The Prandtl equations with a self-induced pressure gradient included are used to formulate a nonlinear approach for elucidating stability properties of freely inter acting boundary layers both for subsonic and supersonic cases. The shock-wave boundary-layer interaction and separation on a moving wall is numerically studied, the formation of two recirculation bubbles being the most striking feature. With the shock strength increasing, both bubbles tend to divide into smaller vortex cells whence the nonsteady process of velocity field “breathing” stems.

Keywords

Internal Wave Linear Stability Theory Recirculation Bubble Interact Boundary Layer Prandtl Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Lin, C. C. 1955. The theory of hydrodynamic stability. Cambridge Univ. Press.Google Scholar
  2. Messiter, A. F. 1970. Boundary-layer flow near the trailing edge of a flat plate. SIAM J. Appl. Math., Vol. 8, N1: 241–257.CrossRefGoogle Scholar
  3. Neiland, V. Ya. 1969. Contribution to the theory of laminar boundary-layer separation in supersonic flow. Izv. AN SSSR, Mekh. Zhidk. i Gaza, N4: 53-57 (in Russian).Google Scholar
  4. Smith, F. T. 1979. On the non-parallel flow stability of the Blasius boundary layer. Proc. R. Soc. London, Ser. A, Vol. 366, N1724: 91–109.Google Scholar
  5. Stewartson, K. and Williams, P. G. 1969. Self-induced separation. Proc. R. Soc. London, Ser. A, Vol. 312, N1509:181–206.Google Scholar
  6. Williams, J. C., III. 1977. Incompressible boundary-layer separation. Ann. Rev. Fluid Mech., Vol. 9: 113–144.CrossRefGoogle Scholar
  7. Zhuk, V.I. and Ryzhov, O. S. 1979. On solutions of a dispersion relation from the theory of free interaction of a boundary layer. Dokl. AN SSSR, Vol. 247, N5: 1085–1088 (in Russian).Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Oleg S. Ryzhov
    • 1
  • Vladimir I. Zhuk
    • 1
  1. 1.Computing CenterAcademy of SciencesMoscowUSSR

Personalised recommendations