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On similarity solutions occurring in the theory of interactive laminar boundary layers

Published online by Cambridge University Press:  26 April 2006

Philipp Gittler
Philipp Gittler
Affiliation:
Institute of Fluid Dynamics and Heat Transfer, Technical University Vienna, Wiedner Hauptstr. 7, A-1040 Wien, Austria
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Abstract

A theoretical investigation of similarity solutions for interactive laminar boundary layers is presented. The questions of uniqueness and of the appearance of homogeneous eigensolutions are discussed. The similarity solutions yielding the asymptotic behaviour of the nonlinear triple-deck equations in the far field can be used either to improve the development of computational schemes or to check the accuracy of numerical results. A special similarity solution governed by a modified Falkner-Skan boundary-value problem determines the shape of a wall generating the largest possible deflection of a laminar boundary layer in supersonic flow if separation is to be avoided. Increasing the controlling parameter of this special pressure distribution (for both supersonic and subsonic flows) beyond a cutoff value leads to a global breakdown of the interacting laminar-boundary-layer approach which cannot be removed or avoided.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 244 , November 1992 , pp. 131 - 147
Copyright
© 1992 Cambridge University Press

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References

Abramowitz, M. & Stegun J. A. 1970 Handbook of Mathematical Functions. Dover.
Bodonyi R. J., Welch W. J. C., Duck, P. W. & Tadjfar M. 1989 A numerical study of the interaction between unsteady free-stream disturbances and localized variations in surface geometry. J. Fluid Mech. 209, 285–308.Google Scholar
Brown, S. N. & Stewartson K. 1970 Trailing edge stall. J. Fluid Mech. 42, 561–584.Google Scholar
Burggraf, O. R. & Duck P. W. 1981 Spectral computations of triple-deck flows. In Proc. Symp. on Physical and Numerical Aspects of Aerodynamic Flows (ed. T. Cebeci). California State University, Long Beach.
Daniels P. G. 1974 Numerical and asymptotic solutions for the supersonic flow near the trailing edge of a flat plate. Q. J. Mech. Appl. Maths 27, 175–191.Google Scholar
Gajjar, J. & Smith F. T. 1983 On hypersonic self-induced separation, hydraulic jumps and boundary layers with algebraic growth. Mathematika 30, 77–93.Google Scholar
Gittler Ph. 1984 Laminare Wechselwirkungsvorgänge am schiebenden Flügel bei Über-schallströmung. Z. Angew. Math. Mech. 64, T198–200.Google Scholar
Gittler Ph. 1985 Dreidimensionale Wechselwirkungsvorgänge bei laminaren Grenzschichten. dissertation TU Wien, pp. 1–142.
Gittler, Ph. & Kluwick A. 1987 Triple-deck solutions for supersonic flows past flared cylinders. J. Fluid Mech. 179, 469–487.Google Scholar
Gittler, Ph. & Kluwick A. 1989 Interacting laminar boundary layers in quasi-two-dimensional flow. Fluid Dyn. Res. 5, 29–47.Google Scholar
Kluwick A. 1987 Interacting boundary layers. Z. Angew. Math. Mech. 67 (4), T3–13.Google Scholar
Kluwick A., Gittler, Ph. & Bodonyi R. J. 1984 Viscous-inviscid interactions on axisymmetric bodies in supersonic flow. J. Fluid Mech. 140, 281–301.Google Scholar
Kluwick A., Gittler, Ph. & Bodonyi R. J. 1985 Freely interacting boundary layers on bodies of revolution. Q. J. Mech. Appl. Maths 38, 575–588.Google Scholar
Libby, P. A. & Fox H. 1963 Some perturbation solutions in laminar boundary-layer theory. J. Fluid Mech. 17, 433–449.Google Scholar
Libby, P. A. & Liu T. M. 1967 Further solutions of the Falkner-Skan equation. AIAA J. 5, 1040–1042.Google Scholar
Lighthill M. J. 1953 On boundary layers and upstream influence II. Supersonic flows without separation Proc. R. Soc. Lond. A 217, 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. 1983 Boundary-layer interaction theory. Trans. ASME E: J. Appl. Mech. 50, 1104–1113Google Scholar
Neiland V. Ya. 1969 Towards a theory of separation of the laminar boundary layer in a supersonic stream. Izv. Akad. Nauk. SSSR, Mekh. Zhidk. Gaza 4, 53–57Google Scholar
Rizetta D., Burggraf, O. & Jenson R. 1978 Triple-deck solutions for viscous supersonic and hypersonic flow past corners. J. Fluid Mech. 89, 535–552.Google Scholar
Smith F. T. 1973 Laminar flow over a small jump on a flat plate. J. Fluid Mech. 57, 803–824.Google Scholar
Smith F. T. 1977 The laminar separation of an incompressible fluid streaming past a smooth surface Proc. R. Soc. Lond. A 356, 433–463.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. & Bodonyi, R. J. 1985 On short scale inviscid instabilities in flow past surface-mounted obstacles and other non-parallel motions. Aeronaut. J. 84, 205–212.Google Scholar
Smith, F. T. & Khorrami A. F. 1991 The interactive breakdown in supersonic ramp flow. J. Fluid Mech. 224, 197–215.Google Scholar
Smith, F. T. & Merkin J. H. 1982 Triple-deck solutions for subsonic flow past humps, steps, concave or convex corners and wedged trailing edges. Computers Fluids 10, 7–25.Google Scholar
Stewartson K. 1969 On the flow near the trailing edge of a flat plate. Mathematika 16, 106–121.Google Scholar
Stewartson K. 1970 On laminar boundary layers near corners. Q. J. Mech. Appl. Maths 23, 137–152.Google Scholar
Stewartson K. 1971 On laminar boundary layers near corners. Q. J. Mech. Appl. Maths 24, 387–389.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. & Williams P. G. 1973 On self-induced separation II. Mathematika 20, 98–108.Google Scholar
Stratford B. S. 1954 Flow in the laminar boundary layer near separation. Aeronaut. Res. Counc. Rep. & Mem. 3002.Google Scholar