Advertisement

Review of Linear Compressible Stability Theory

  • Leslie M. Mack
Part of the ICASE NASA LaRC Series book series (ICASE/NASA)

Summary

A review is given of some aspects of the linear compressible stability theory. Major attention is given to the inviscid theory and the additional solutions that arise when there is a region of supersonic flow relative to the phase velocity. For highly cooled flat-plate boundary layers at Mach number 5.8, the unstable region includes supersonic outgoing waves. A previously unknown neutral incoming wave has also been found. An example of viscous multiple solutions is given, along with calculations of higher viscous discrete modes and the compressible counterpart of the Squire mode.

Keywords

Mach Number Phase Velocity Incoming Wave Discrete Mode Compressible Boundary Layer 
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.

Reference

  1. 1.
    Lees, L. and Lin, C.C., Investigation of the Stability of the Laminar Boundary Layer in a Compressible Fluid. NACA Technical Note No. 1115, 1946.zbMATHGoogle Scholar
  2. 2.
    Mack, L.M., Boundary-Layer Stability Theory, Document No. 900–277, Rev. A, Jet Propulsion Laboratory, Pasadena, CA, 1969.Google Scholar
  3. 3.
    Mack, L.M., Boundary-Layer Linear Stability Theory, in “Special Course on Stability and Transition of Laminar Flow,” AGARD Report No. 709, pp. 3–1 to 3–81, 1984.Google Scholar
  4. 4.
    Gapnov, S.A. and Maslov, A.A., Propagation of Disturbances in Compressible Fluids (in Russian), Akademia Nauk, Siberian Branch, Novosibirsk, USSR, 1980.Google Scholar
  5. 5.
    Lees, L. and Gold, H., Stability of Laminar Boundary Layers and Wakes at Hypersonic Speeds: Part I. Stability of Laminar Wakes, in “Proceedings of International Symposium on Fundamental Phenomenon in Hypersonic Flow,” pp. 310–337, Cornell Univ. Press, 1964.Google Scholar
  6. 6.
    Brown, W.B., Exact Numerical Solutions of the Complete Linearized Equations for the Stability of Compressible Boundary Layers, Norair Report No. NOR-62–15, Northrop Aircraft Inc., Hawthorne, CA 1962.Google Scholar
  7. 7.
    Mack, L.M., Stability of the Compressible Laminar Boundary Layer According to a Direct Numerical Solution, in AGARDograph 97, Part I, pp. 329–362, 1965.Google Scholar
  8. 8.
    Gropengiesser, H., Beitrag zur Stabilitat freier Grenzschichten in kompressiblen Medien, Report DLR FB 69–25, Deutsche Luft- und Raumfahrt, 1969 (also available as NASA Technical Translation F-12, 786, Washington, D.C., 1970).Google Scholar
  9. 9.
    Mack, L.M., Linear Stability and the Problem of Supersonic Boundary-Layer Transition, AIAA J., Vol. 13, pp. 278–289, 1975.ADSCrossRefGoogle Scholar
  10. 10.
    Mack, L.M., A Numerical Method for the Prediction of High-Speed Boundary-Layer Transition Using Linear Theory, in “Proceedings of Conference on Aerodynamic Analyses Requiring Advanced Computers,” NASA SP-347, 1975.Google Scholar
  11. 11.
    Nayfeh, A.H. and El-Hady, N.M., Nonparallel Stability of Compressible Boundary Layer Flows, Rep. No. VPI-E-79.13, Engineering Science and Mechanics Dept., Virginia Polytechnic and State Univ., Blacksburg, VA, 1980.Google Scholar
  12. 12.
    Gaponov, S.A., The Influence of Flow Non-parallelism on Disturbance Development in the Supersonic Boundary Layer in “Proceedings of the Eighth Canadian Congress of Applied Mechanics,” pp. 673–674, 1981.Google Scholar
  13. 13.
    Drazin, P.G. and Davey, A., Shear Layer Instability of an Inviscid Compressible Fluid: Part 3, J. Fluid Mech., Vol. 82, Part 2, pp. 255–260, 1977.ADSzbMATHCrossRefGoogle Scholar
  14. 14.
    Mack, L.M., On the Stability of the Boundary Layer on a Transonic Swept Wing, AIAA Paper No. 79–0264, 1979.Google Scholar
  15. 15.
    Lekoudis, S., Stability of Three-Dimensional Boundary Layers over Wings with Suction, AIAA Paper No. 79–0265, 1979.Google Scholar
  16. 16.
    Malik, M.R., COSAL — A Black-Box Compressible Stability Analysis Code for Transition Prediction in Three-Dimensional Boundary Layers, NASA CR-165925, 1982.Google Scholar
  17. 17.
    Herbert, Th., Subharmonic Three-Dimensional Disturbances in Unstable Plane Shear Flows, AIAA Paper No. 83–1759, 1983.Google Scholar
  18. 18.
    Herbert, Th., Analysis of the Subharmonic Route to Transition in Boundary Layers, AIAA Paper No. 84–0009, 1984.Google Scholar
  19. 19.
    Squire, H.B., On the Stability of Three-Dimensional Disturbance of Viscous Flow Between Parallel Walls, Proc. Roy. Soc. A, Vol. 142, pp. 621–628, 1933.ADSzbMATHCrossRefGoogle Scholar
  20. 20.
    Tam, C.K.W. and Morris, P.J., The Radiation of Sound by the Instability Waves of a Compressible Plane Turbulent Shear Layer, J. Fluid Mech., Vol. 98, Part 2, pp. 349–381, 1980.MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. 21.
    El-Hady, N.M., On the Effect of Boundary-Layer Growth on the Stability of Compressible Flows, unpublished, 1981.Google Scholar
  22. 22.
    Mack, L.M., Computation of the Stability of the Laminar Boundary Layer, in “Methods of Computational Physics” (B. Alder, S. Fernbach and M. Rotenberg, eds.), Vol. 4, pp. 247–299, Academic Press, NY, 1965.Google Scholar
  23. 23.
    Lees, L., The Stability of the Laminar Boundary Layer in a Compressible Fluid, NACA Technical Report No. 876, 1947.Google Scholar
  24. 24.
    Mack, L.M., A Numerical Study of the Temporal Eigenvalue Spectrum of the Blasius Boundary Layer, J. Fluid Mech., Vol. 79, pp. 497–520, 1976.ADSCrossRefGoogle Scholar
  25. 25.
    Petrov, G.V., Stability of Thin Viscous Shock Layer on a Wedge in Hypersonic Flow of a Perfect Gas, in “Laminar-Turbulent Transition” (V.V. Kozlov, ed.), Proceedings of 2nd IUTAM Symposium, pp. 487–493, Springer, Berlin, 1984.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Leslie M. Mack

There are no affiliations available

Personalised recommendations