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Interaction between a weak oblique shock wave and a turbulent boundary layer in purely supersonic flow

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The paper deals with the interaction of a weak oblique shock and a turbulent boundary layer at a flat plate at purely supersonic speeds. Except for a small region where nonlinear transonic effects are of importance analytical expressions for the pressure- and skin friction distributions are derived.

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References

  1. Ackeret, J., Feldmann, F., Rott, N.: Untersuchung an Verdichtungsstößen und Grenzschichten in schnell bewegten Gasen. Mitteilungen aus dem Inst. für Aerodynamik, ETH Zürich, Nr. 10, 1946.

  2. Adamson, T. C., jr., Feo, A.: Interaction between a shock wave and a turbulent boundary layer in transonic flow. SIAM J. Appl. Math.29, 121–145 (1975).

    Google Scholar 

  3. Adamson, T. C., jr.: The structure of shock wave — boundary layer interactions in transonic flow, in: Symposium transonicum II (Oswatitsch, K., Rues, D., eds.). Berlin-Heidelberg-New York: Springer 1975.

    Google Scholar 

  4. Adamson, T. C., jr., Messiter, A. F.: Analysis of two-dimensional interactions between shock waves and boundary layers. Ann. Rev. Fluid Mech.12, 103–138 (1980).

    Google Scholar 

  5. Barry, F. W., Shapiro, A. H., Neumann, E. P.: The interaction of a shock wave with boundary layers on a flat surface. J. Aero. Sci.18, 229–238 (1951).

    Google Scholar 

  6. Bohning, R., Zierep, J.: Der senkrechte Verdichtungsstoß an der gekrümmten Wand unter Berücksichtigung der Reibung. ZAMP27, 225–240 (1976).

    Google Scholar 

  7. Bohning, R., Zierep, J.: Bedingung für das Einsetzen der Ablösung der turbulenten Grenzschicht an der gekrümmten Wand mit senkrechtem Verdichtungsstoß. ZAMP29, 190–198 (1978).

    Google Scholar 

  8. Bush, W. B., Fendell, F. E.: Asymptotic analysis of turbulent channel and boundary layer flow. J. Fluid Mech.56, 657–681 (1972).

    Google Scholar 

  9. Cebeci, T., Smith, A. M. O.: Analysis of turbulent boundary layers. New York: Academic Press 1974.

    Google Scholar 

  10. Coles, D. E.: The law of the wake in the turbulent boundary layer. J. Fluid Mech.1, 191–226 (1956).

    Google Scholar 

  11. Gadd, G. E., Holder, D. W., Regan, J. D.: An experimental investigation of the interaction between shock waves and boundary layers. Proc. Roy. Soc.A 226, 227–253 (1954).

    Google Scholar 

  12. Green, J. E.: Reflexion of an oblique shock wave by a turbulent boundary layer. J. Fluid Mech.40, 81–95 (1970).

    Google Scholar 

  13. Henderson, L. F.: The reflexion of a shock wave at a rigid wall in the presence of a boundary layer. J. Fluid Mech.30, 699–722 (1967).

    Google Scholar 

  14. Inger, G. R., Mason, W. H.: Analytical analysis of transonic normal shock — turbulent boundary — layer interactions. AIAA J.14, 1266–1272 (1976).

    Google Scholar 

  15. Kluwick, A.: Stationäre, laminare wechselwirkende Reibungsschichten. Z. Flugwiss. Weltraumforsch.3, 157–174 (1979).

    Google Scholar 

  16. Liepman, H. W.: The interaction between boundary layer and shock waves in transonic flow. J. Aero. Sci.13, 623–637 (1946).

    Google Scholar 

  17. Lighthill, M. J.: On boundary layers and upstream influence. II: Supersonic flows without separation. Proc. Royal Soc.A 217, 478–507 (1953).

    Google Scholar 

  18. Liou, M. S., Adamson, T. C., Jr.: Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. Part II: Wall shear stress. ZAMP31, 227–246 (1980).

    Google Scholar 

  19. Maise, G., McDonald, H.: Mixing length and kinematic eddy viscosity in a compressible boundary layer. AIAA J.6, 73–79 (1968).

    Google Scholar 

  20. Mellor, G. L.: The large Reynolds number asymptotic theory of turbulent boundary layers. Int. J. Eng. Sci.10, 851–873 (1972)

    Google Scholar 

  21. Melnik, R. E., Grossman, B.: Analysis of the interaction of a weak normal shock wave with a turbulent boundary layer. AIAA Paper, No. 74-598 (1974).

  22. Messiter, A. F.: Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds, part I: Pressure distribution. ZAMP31, 204–226 (1980).

    Google Scholar 

  23. Millikan, C. B.: A critical discussion of turbulent flows in channels and circular tubes. Proc. 5th Int. Cong. Appl. Mech., pp. 386–392, 1933.

  24. Müller, E. A.: Theoretische Untersuchungen über die Wechselwirkung zwischen einer einfallenden kleinen Störung und der Grenzschicht bei schnell strömenden Gasen. Diss. Universität Göttingen (1953).

  25. Prandtl, L.: Über die ausgebildete Turbulenz. ZAMM5, 136–139 (1925).

    Google Scholar 

  26. Smith, F. T.: On the high Reynolds number theory of laminar flows. IMA J. Appl. Math.28, 207 (1982).

    Google Scholar 

  27. Stewartson, K., Williams, P. G.: Self-induced separation. Proc. Roy. Soc.A 312, 181–206 (1969).

    Google Scholar 

  28. Stewartson, K.: Multistructured boundary layers on flat plates and related bodies. In: Advanced in applied mechanics, Vol. 14, pp. 145–239. New York: Academic Press (1974).

    Google Scholar 

  29. Stewartson, K.: High Reynolds number flows. In: Approximation methods for Navier-Stokes problems, Proc. of IUTAM Symposium at the University of Paderborn, p. 305 (1979).

  30. Van Driest, E. R.: Turbulent boundary layer in compressible fluids. J. Aero. Sci.18, 145–160 (1951).

    Google Scholar 

  31. Van Kármán, Th.: Mechanische Ähnlichkeit und Turbulenz. Nachr. Ges. Wiss. Göttingen, Math. Phys. Klasse58 (1930).

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Kluwick, A., Stross, N. Interaction between a weak oblique shock wave and a turbulent boundary layer in purely supersonic flow. Acta Mechanica 53, 37–56 (1984). https://doi.org/10.1007/BF01176249

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