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Hypersonic boundary-layer separation on a cold wall

Published online by Cambridge University Press:  26 April 2006

R. M. Kerimbekov ,
A. I. Ruban  and
J. D. A. Walker
R. M. Kerimbekov
Affiliation:
Central Aerohydrodynamic Institute, Zhukovsky-3, Moscow Region, 140160, Russia
A. I. Ruban
Affiliation:
Central Aerohydrodynamic Institute, Zhukovsky-3, Moscow Region, 140160, Russia
J. D. A. Walker
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015, USA
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Abstract

An asymptotic theory of laminar hypersonic boundary-layer separation for large Reynolds number is described for situations when the surface temperature is small compared with the stagnation temperature of the inviscid external gas flow. The interactive boundary-layer structure near separation is described by well-known tripledeck concepts but, in contrast to the usual situation, the displacement thickness associated with the viscous sublayer is too small to influence the external pressure distribution (to leading order) for sufficiently small wall temperature. The present interaction takes place between the main part of the boundary layer and the external flow and may be described as inviscid–inviscid. The flow in the viscous sublayer is governed by the classical boundary-layer equations and the solution develops a singularity at the separation point. A main objective of this study is to show how the singularity may be removed in different circumstances.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 274 , 10 September 1994 , pp. 163 - 195
Copyright
© 1994 Cambridge University Press

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References

Adamson, T. C. & Messiter, A. F. 1980 Analysis of two-dimensional interactions between shock waves and boundary layers. Ann. Rev. Fluid Mech. 12, 103–138.Google Scholar
Brown, S. N., Cheng, H. K. & Lee, C. J. 1990 Inviscid—viscous interaction on triple-deck scales in a hypersonic flow with strong wall cooling. J. Fluid Mech. 220, 309–337.Google Scholar
Brown, S. N. & Stewartson, K. 1983 On an integral equation of marginal separation. SIAM J. Appl. Maths 43, 1119–1126.Google Scholar
Cassel, K. 1993 The effect of interaction on boundary-layer separation and breakdown. PhD thesis, Dept. of Mechanical Engineering and Mechanics, Lehigh University.
Chapman, D. R., Kuehn, D. M. & Larson, H. K. 1958 Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition. NACA Tech. Rep. 1356, pp. 419–460.
Goldstein, S. 1948 On laminar boundary-layer flow near a position of separation. Q. J. Mech. Appl. Maths 1, 43–69.Google Scholar
Hartree, D. R. 1939 A solution of the laminar boundary-layer equation for retarded flow. Aeronaut. Res. Coun. Rep. Memo. 2426 (issued 1949).
Howarth, L. 1938 On the solution of the laminar boundary layer equations. Proc. R. Soc. Lond. A 164, 547–579.Google Scholar
Jensen, R., Burggraf, O. R. & Rizzetta, D. P. 1975 Asymptotic solution for the supersonic viscous flow past a compression corner. In Proc. 4th Intl Conf. on Numerical Methods in Fluid Dynamics (ed. R. D. Richtmyer). Lecture Notes in Physics, vol. 35, pp. 218–224. Springer.
Lagerstrom, P. A. 1975 Solutions of the Navier—Stokes equation at large Reynolds number. SIAM J. Appl. Maths 28, 202–214.Google Scholar
Landau, L. D. & Lifschitz, E. M. 1944 Mechanics of Continuous Media. Moscow: Gostechizdat (in Russian).
Lighthill, M. J. 1953 On boundary layers and upstream influence. II. Supersonic flows without separation. Proc. R. Soc. Lond. A 217, 1131, 478–507.Google Scholar
Messiter, A. F. 1970 Boundary-layer flow near the trailing edge of a flat plate. SIAM J. Appl. Maths 18, 241–257.Google Scholar
Messiter, A. F. 1979 Boundary-layer separation. In Proc. 8th US Natl Congr. Appl. Mech., pp. 157–179. Western Periodicals, North Hollywood, California.
Messiter, A. F., 1983 Boundary-layer interaction theory. Trans. ASME E: J. Appl. Mech., 50, 1104–1113.Google Scholar
Messiter, A. F., Matarrese, M. D. & Adamson, T. C. 1991 Strip blowing from a wedge at hypersonic speeds. AIAA Paper 91-0032.
Neiland, V. Ya., 1969 On the theory of laminar boundary layer separation in supersonic flow. Izv. Akad. Nauk SSSR, Mech. Zhid. Gaza No. 4, 53–57.Google Scholar
Neiland, V. Ya., 1973 Peculiarities of boundary-layer separation on a cooled body and its interaction with a hypersonic flow. Izv. Akad. Nauk SSSR, Mech. Zhid. Gaza No. 6, 99–109.Google Scholar
Neiland, V. Ya., 1974 Asymptotic problems of the viscous supersonic flow theory. TsAGI Trans. No. 1529.Google Scholar
Neiland, V. Ya., 1981 Asymptotic theory for separation and interaction of a boundary layer with supersonic gas flow. Adv. Mech. 4, 3–62.Google Scholar
Neiland, V. Ya., & Sokolov, L. A. 1975 On the asymptotic theory of incipient separation in compression ramp hypersonic flow on cooled body for a weak hypersonic interaction regime. Uchen. Zap. TsAGI, 6 No. 3, 25–34.Google Scholar
Pearson, H., Holliday, J. B. & Smith, S. F. 1958 A theory of the cylindrical ejector supersonic propelling nozzle. J. Aeronaut. Soc. 62, 756–761.Google Scholar
Prandtl, L. 1904 Über Flüssigkeitsbewegung bei sehr Kleiner Reiburg. Verb. III Intern. Math. Kongr., Heidelberg; Leipzig, pp. 484–491. Teubner.
Ruban, A. I. 1978 Numerical solution of the asymptotic problem for unsteady laminar boundary separation in supersonic flow. Zh. Vychiesl. Mat. & Mat. Phys. 18 (5), 1253–1265.Google Scholar
Ruban, A. I. 1981 Singular solution for boundary layer equations with continuous extension downstream of zero skin friction point. Izv. Akad. Nauk SSSR, Mech. Zhid. Gaza No. 6. 42–52.Google Scholar
Ruban, A. I. 1982 Asymptotic theory for short separation bubbles on the leading edge of thin airfoil. Izv. Akad. Nauk SSSR, Mech. Zhid. Gaza No. 1, 42–51.Google Scholar
Smith, F. T. 1982 On the high Reynolds number theory of laminar flows. IMA J. Appl. Maths 28, 207–281.Google Scholar
Smith, F. T., Brighton, P. W. M., Jackson, P. S. & Hunt, J. C. R. 1981 On boundary-layer flow past two-dimensional obstacles. J. Fluid Mech. 113, 123–152.Google Scholar
Smith, F. T. & Daniels, P. G. 1981 Removal of Goldstein's singularity at separation in flow past obstacles in wall layers. J. Fluid Mech. 110, 1–37.Google Scholar
Stewartson, K. 1970 Is the singularity at separation removable? J. Fluid Mech. 44, 347–364.Google Scholar
Stewartson, K. 1974 Multistructured boundary layers on flat plates and related bodies. Adv. Appl. Mech. 14, 145–239.Google Scholar
Stewartson, K. 1981 D’Alembert's paradox. SIAM Rev. 23, 308–343.Google Scholar
Stewartson, K., Smith, F. T. & Kaups, K. 1982 Marginal separation. Stud. Appl. Maths 67, 45–61.Google Scholar
Stewartson, K. & Williams, P. G. 1969 Self-induced separation. Proc. R. Soc. Lond. A 312, 181–206.Google Scholar
Sychev, V. V. 1972 On laminar separation. Izv. Akad. Nauk SSSR, Mech. Zhid. Gaza No. 3, 47–59.Google Scholar
Sychev, V. V., Ruban, A. I., Syzhev, Vik. V., & Korolev, G. L. 1987 Asymptotic Theory for Separated Flows. Moscow: Nauka.
Townend, L. H. 1991 Research and design for hypersonic aircraft. Phil. Trans. R. Soc. Lond. A 335, 201–224.Google Scholar
Walberg, G. D. 1991 Hypersonic flight experience. Phil. Trans. R. Soc. Lond. A 335, 91–119.Google Scholar
Werle, M. J. & Davis, R. T. 1972 Incompressible laminar boundary layers on a parabola at angle of attack: a study of the separation point. Trans. ASME E: J. Appl. Mech. 39, 7–12.Google Scholar
Zhikharev, C. N. 1993 Separation phenomenon in hypersonic flow with strong wall cooling: subcritical regime. Theoret. Comput. Fluid Dyn. 4, 209–226.Google Scholar