An Asymptotic Theory of Supersonic Turbulent Interactions in a Compression Corner

  • R. E. Melnik
  • R. L. Cusic
  • M. J. Siclari
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (MANUTECH)


In this paper we present a theoretical analysis of the interaction of an unseparated supersonic turbulent boundary layer with a shallow two-dimensional compression corner. In these flows the pressure rises in two stages: an abrupt, nearly discontinuous jump, followed by a more gradual rise to the inviscid wedge value far downstream. The downstream flow in the gradual part of the pressure rise is now fairly well understood. In 1969, Roshko and Thomke [1] and later Elfstrom [2] showed that this could be accurately predicted with a simple inviscid rotational flow model, provided that a suitable cut-off or slip velocity was applied to the initial velocity profile and adjusted to match the steep part of the pressure rise. Later, in 1984, Agrawal and Messiter [3] developed a rational asymptotic theory for this problem based on the limits of small wedge angle and large Reynolds number. Their approach is closely related to asymptotic theories previously developed for other turbulent interaction problems in Refs. [4–11]. Agrawal and Messiter [3] showed that their theory could predict the gradual part of the pressure rise without the need to introduce an empirical slip velocity. Unfortunately, their theory was singular at the corner and could not describe the flow in the steep part of the pressure rise. In the present paper we briefly describe a new asymptotic theory that applies to the near corner region covering the steep part of the pressure rise.


Shock Wave Mach Number Turbulent Boundary Layer Pressure Rise Asymptotic Theory 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Roshko, A. and Thomke, G.J., “Supersonic, Turbulent Boundary-layer Interaction with a Compression Corner at Very High Reynolds Number,” Proc USAF ARL Symp on Viscous Interaction Phenomena in Supersonic and Hypersonic Flow, Univ of Dayton Press, Dayton, OH (1969) 109–138.Google Scholar
  2. 2.
    Elfstrom, G.M., “Turbulent Hypersonic Flow at a Wedge-compression Corner,” J. Fluid Mech, 53 (1972) 113–127.CrossRefADSGoogle Scholar
  3. 3.
    Agrawal, S. and Messiter, A.F., “Turbulent Boundary-layer Interaction with a Shock Wave in a Compression Corner,” J. Fluid Mech, 143, (1984) 23–46.CrossRefMATHADSGoogle Scholar
  4. 4.
    Melnik, R.E. and Grossman, B., “Analysis of the Interaction of a Weak Normal Shock Wave with a Turbulent Boundary Layer,” AIAA Paper 74–598 (1978).Google Scholar
  5. 5.
    Adamson, T.C. and Feo, A., “Interaction between a Shock Wave and a Turbulent Boundary Layer in Transonic Flow,” SIAM J. Appl Maths, 29 (1975) 121–145.CrossRefMATHADSGoogle Scholar
  6. 6.
    Messiter, A.F., “Interaction Between a Normal Shock Wave and a Turbulent Boundary Layer at High Transonic Speeds. Part I: Pressure Distribution,” Z. angew Math. Phys, 31 (1980) 204–226.CrossRefMATHGoogle Scholar
  7. 7.
    Melnik, R.E., “Turbulent Interactions on Airfoils at Transonic Speeds — Recent Developments,” AGARD CP 291 Paper 10 (1981).Google Scholar
  8. 8.
    Adamson, T.C. and Messiter, A.F., “Analysis of Two-dimensional Interactions Between Shock Waves and Boundary Layers,” Annual Rev of Fluid Mech, 12, Annual Reviews Inc, Palo Alto, CA (1980) 103–139.Google Scholar
  9. 9.
    Melnik, R.E., Chow, R.R., Mead, H.R. and Jameson, A., “An Improved Viscid/inviscid Interaction Procedure for Transonic Flow Over Airfoils,” NASA CR-3805 (1985).Google Scholar
  10. 10.
    Melnik, R.E. and Grossman, B., “On Turbulent Viscidinviscid Interaction at a Wedge Shaped Trailing Edge,” Proc of Symp on Numerical and Physical Aspects of Aerodynamic Flows, I Springer-Verlag, New York (1982) 211–235.Google Scholar
  11. 11.
    Sykes, R.L., “An Asymptotic Theory for Incompressible Turbulent Boundary-layer Flow Over a Small Hump,” J. Fluid Mech, 101 (1980) 647–670.CrossRefMATHADSMathSciNetGoogle Scholar
  12. 12.
    Murman, E.M. and Cole, J.D., “Calculation of Plane Steady Transonic Flows,” AIAA J., 9 (1971) 114–121.CrossRefMATHADSGoogle Scholar
  13. 13.
    Settles, G. S., Fitzpatrick, T. J., and Bogdonoff, S.M., “Detailed Study of Attached and Separated Compression Corner Flow Fields in High Reynolds Number Supersonic Flow,” AIAA J., 17 (1979) 579–585.CrossRefADSGoogle Scholar
  14. 14.
    Cusic, R., “An Asymptotic Theory of Turbulent Boundary Layer Interaction in a Compression Corner at Supersonic Speeds,” PhD thesis, Univ of Colorado, Boulder (to be submitted).Google Scholar
  15. 15.
    Melnik, R.E., Cusic, R.L., and Siclari, M.J., “An Asymptotic Theory of Supersonic Turbulent Interactions in a Compression Corner,” Grumman Corporate Research Center, to be published (November 1985).Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1986

Authors and Affiliations

  • R. E. Melnik
    • 1
  • R. L. Cusic
    • 2
  • M. J. Siclari
    • 1
  1. 1.Grumman CorporationUSA
  2. 2.University of ColoradoUSA

Personalised recommendations