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Viscous-inviscid interactions on axisymmetric bodies of revolution in supersonic flow

Published online by Cambridge University Press:  20 April 2006

A. Kluwick
Affiliation:
Institut für Strömungslehre und Wärmeübertragung, Technische Universität Wien, Wiedner Hauptstrasse 7, A-1040 Vienna, Austria
P. Gittler
Affiliation:
Institut für Strömungslehre und Wärmeübertragung, Technische Universität Wien, Wiedner Hauptstrasse 7, A-1040 Vienna, Austria
R. J. Bodonyi
Affiliation:
Department of Mathematical Sciences, Indiana University - Purdue University at Indianapolis, 1125 East 38th Street, Indianapolis, Indiana 46223

Abstract

Using the method of matched asymptotic expansions, the interaction between axisymmetric laminar boundary layers and inviscid supersonic external flows is investigated in the limit of large Reynolds numbers. The resulting triple-deck equations are solved numerically for two different cases of body shapes: a cylinder-cone configuration and a configuration consisting of two concentric cylinders which are connected by a smooth curve. Solutions to the linearized as well as the fully nonlinear equations are presented.

Type
Research Article
Copyright
© 1984 Cambridge University Press

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References

Brilliant, H. M. & Adamson, T. C. 1973 Shock-wave-boundary-layer interactions in laminar transonic flow. AIAA Paper 73–239.Google Scholar
Burggraf, O. R. & Duck, P. 1981 Spectral computation of triple deck flows. In Proc. 1st Symp. on Physical and Numerical Aspects of Aerodynamic Flows, California State University, Long Beach.
Cooley, J. W. & Tukey, J. W. 1965 Math. Comp. 19, 297.
Duck, P. 1984 The effect of a surface discontinuity on an axisymmetric boundary layer. Q. J. Mech. Appl. Maths (in press).Google Scholar
Gittler, P. 1984 Laminare Wechselwirkungsvorgaenge am schiebenden Fluegel bei Ueberschall-stroemung. Z. angew. Math. Mech. 64, T108 (in press).Google Scholar
Huang, M. & Inger, G. R. 1983 Application of the triple-deck theory of viscous-inviscid interactions to bodies of revolution. J. Fluid Mech. 129, 427.Google Scholar
Kluwick, A. 1979 Stationaere, laminare wechselwirkende Reibungsschichten. Z. Flugwiss. Weltraumf. 3, 157.Google Scholar
Lighthill, M. J. 1945 Supersonic flow past bodies of revolution. ARC R&M 2003.Google Scholar
Lighthill, M. J. 1953 On boundary layers and upstream influence II. Supersonic flow without separation. Proc. R. Soc. Lond. A 217, 478.Google Scholar
Lighthill, M. J. 1958 An Introduction to Fourier Analysis and Generalized Functions. Cambridge University Press.
Messiter, A. F. 1970 Boundary layer flow near the trailing edge of a flat plate. SIAM J. Appl. Maths 18, 241.Google Scholar
Messiter, A. F. 1978 Boundary layer separation. In Proc. 8th US Natl Congr. Appl. Mech., p. 157.
Messiter, A. F. 1983 Boundary layer interaction theory. Trans. ASME E: J. Appl. Mech. (to appear).Google Scholar
Oswatitsch, K. 1958 Die Abloesebedingung von Grenzschichten. In Grenzschichtforschung (ed. H. Goertler), p. 357. Springer.
Rizzetta, D., Burggraf, O. & Jenson, R. 1978 Triple-deck solutions for viscous supersonic and hypersonic flows past corners. J. Fluid Mech. 89, 535.Google Scholar
Rosenhead, L. 1963 Laminar Boundary Layers. Oxford University Press.
Smith, F. T. 1976 Pipeflows distorted by nonsymmetric indentation or branching. Mathematika 23, 62.Google Scholar
Smith, F. T. 1982 On the high Reynolds number theory of laminar flows. IMA J. Appl. Maths 28, 207.Google Scholar
Smith, F. T., Sykes, R. I. & Brighton, P. W. M. 1977 A two-dimensional boundary layer encountering a three-dimensional hump. J. Fluid Mech. 83, 163.Google Scholar
Stewartson, K. 1955 The asymptotic boundary layer on a circular cylinder in axial incompressible flow. Q. Appl. Maths 13, 113.Google Scholar
Stewartson, K. 1969 On the flow near the trailing edge of a flat plate II. Mathematika 16, 106.Google Scholar
Stewartson, K. 1970a On supersonic boundary layers near convex corners. Proc. R. Soc. Lond. A 319, 289.Google Scholar
Stewartson, K. 1970b On laminar boundary layers near corners. Q. J. Mech. Appl. Maths 23, 137.Google Scholar
Stewartson, K. 1971 On laminar boundary layers near corners: corrections and an addition. Q. J. Mech. Appl. Maths 24, 387.Google Scholar
Stewartson, K. 1974 Multistructured boundary layers on flat plates and related bodies. Adv. Applied Mech. 14, 145.Google Scholar
Stewartson, K. 1980 High Reynolds number flows. In Approximation Methods for Navier-Stokes Problems (ed/ R. Rautmann), p. 505. Springer.
Stewartson, K. 1981 D'Alembert's Paradox. SIAM Rev. 23, 308.Google Scholar
Stewartson, K. & Williams, P. G. 1969 Self-induced separation. Proc. R. Soc. Lond. A 312, 181.Google Scholar
Sykes, R. I. 1980 On three-dimensional boundary layer flow over surface irregularities. Proc. R. Soc. Lond. A 373, 311.Google Scholar
Vatsa, V. N. & Werle, M. J. 1977 Quasi-three-dimensional laminar boundary-layer separations in supersonic flow. Trans. ASME I: J. Fluids Engng 99, 634.Google Scholar
Ward, G. N. 1948 The approximate external and internal flow past a quasi-cylindrical tube moving at supersonic speeds. Q. J. Mech. Appl. Maths 1, 225.Google Scholar
Ward, G. N. 1955 Linearized Theory of Steady High Speed Flow. Cambridge University Press.