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An asymptotic two-layer model for supersonic turbulent boundary layers

Published online by Cambridge University Press:  26 April 2006

J. He ,
J. Y. Kazakia  and
J. D. A. Walker
J. He
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
J. Y. Kazakia
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
J. D. A. Walker
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
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Abstract

An asymptotic analysis of the compressible turbulent boundary-layer equations is carried out for large Reynolds numbers and mainstream Mach numbers of O(1). A self-consistent two-layer asymptotic structure is described wherein the time-mean velocity and total enthalpy are logarithmic within the overlap zone but in terms of the Howarth–Dorodnitsyn variable; the proposed structure leads to a compressible law of the wall for high-speed turbulent flows with surface heat transfer. Simple outer-region algebraic turbulence models are formulated to reflect the effects of compressibility. To test the proposed asymptotic structure and turbulence models, a set of self-similar outer-region profiles for velocity and total enthalpy is obtained for constant-pressure flow and for constant wall temperature; these are combined with wall-layer profiles to form a set of composite profiles valid across the entire boundary layer. A direct comparison with experimental data shows good agreement over a wide range of conditions for flows with and without surface heat transfer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 295 , 25 July 1995 , pp. 159 - 198
Copyright
© 1995 Cambridge University Press

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