Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-22T06:52:00.140Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baldwin, B. S. & Lomax, H. 1978 Thin-layer approximation and algebraic model for turbulent separated flows. AIAA Paper 78–257.
Bartlett, R. P., Edwards, A. J., Harvey, J. K. & Hillier, R. 1979 Pitot pressure and total temperature measurements in a hypersonic turbulent boundary layer at M = 9. I. C. Aero. Rep 79–01.
Burggraf, O. R. 1962 The compressibility transformation and the turbulent boundary-layer equations. J. Aerospace Sci. 29, 434–439.Google Scholar
Carvin, C. 1988 Etude experimentale d'une couche limite turbulente supersonique fortement chauffee. PhD thesis, Université d'Aix Marseille
Carvin, C., Debieve, J. F. & Smits, A. J. 1988 The near-wall temperature profile of turbulent boundary layers. AIAA Paper 88–0136.
Cebeci, T. & Smith, A. M. O. 1974 Analysis of Turbulent Boundary Layers. Academic.
Coles, D. 1964 The turbulent boundary layer in a compressible fluid. Adv. Appl. Mech. 1, 1–51.Google Scholar
Crawford, M. E. & Kays, W. M. 1980 Convective Heat and Mass Transfer. McGraw-Hill.
Crocco, L. 1963 Transformations of the compressible turbulent boundary layer with heat exchange. AIAA J. 1, 2723–2731.Google Scholar
Degani, A. T., Smith, F. T. & Walker, J. D. A. 1992 The three-dimensional turbulent boundary layer near a plane of symmetry. J. Fluid Mech. 234, 329–360.Google Scholar
Degani, A. T., Smith, F. T. & Walker, J. D. A. 1993 The structure of a three-dimensional turbulent boundary layer. J. Fluid Mech. 250, 43–68.Google Scholar
Degani, A. T. & Walker, J. D. A. 1993 Computation of attached three-dimensional turbulent boundary. J. Comput. Phys. 109, 202–214.Google Scholar
Degani, A. T., Walker, J. D. A., Ersoy, S. & Power, G. 1991 On the application of algebraic turbulence models to high Mach number flows. AIAA Paper 90–0616.
Fendell, F. E. 1972 Singular perturbation and turbulent shear flow near walls. J. Astro. Sci. 20, 129–165.Google Scholar
Fernholz, H. H. & Finley, P. J. 1977 A critical compilation of compressible turbulent boundary layer data. AGARD-AG-223.
Fernholz, H. H. & Finley, P. J. 1980 A critical commentary on mean flow data for two-dimensional compressible turbulent boundary layers. AGARD-AG-253.
Fernholz, H. H. & Finley, P. J. 1981 A further compilation of compressible boundary layer data with a survey of turbulence data. AGARD-AG-263.
Fischer, M. C. & Maddalon, D. V. 1971 Experimental laminar, transitional and turbulent boundary-layer profiles on a wedge at local Mach number 6.5 and comparisons with theory. NASA TN D-6462.
Gates, D. F. 1973 Measurements of upstream history effects in compressible turbulent boundary layers. NOL TR 73–152.
He, J. 1993 Asymptotic structure of supersonic turbulent boundary layers. PhD thesis, Lehigh University, Bethlehem, PA.
He, J., Kazakia, J. Y. & Walker, J. D. A. 1990 Embedded function methods for supersonic boundary layers. AIAA Paper 90–0306.
He, J., Kazakia, J. Y., Ruban, A. I. & Walker, J. D. A. 1992 An algebraic model for dissipation in supersonic boundary layers. AIAA Paper 92–0311.
He, J. & Walker, J. D. A. 1995 A note on the Baldwin–Lomax model. Trans. ASME I: J. Fluids Engng (in press).Google Scholar
Horstman, C. C. & Owen, F. K. 1972 Turbulent properties of a compressible boundary layer. AIAA J. 10, 1418.Google Scholar
Johnson, J. A. & King, L. S. 1985 A mathematically simple turbulence closure model for attached and separated turbulent boundary layers. AIAA J. 23, 1684–1692.Google Scholar
Keener, E. R. & Hopkins, E. J. 1972 Turbulent boundary layer profiles on a nonadiabatic flat plate at Mach number 6.5. NASA TN D-6907.
Keyes, F. G. 1952 The heat conductivity, viscosity, specific heat and Prandtl number for thirteen gases. Project Squid TR 37. MIT, Cambridge, MA.
Kline, S. J., Cantwell, B. J. & Lilley, G. M. 1981 The 1980-81 AFOSR—HTTM-Stanford Conference on Complex Turbulent Flows: Comparison of Computation and Experiments, vols. I—III. Thermosciences Division, Stanford University.
Kussoy, I. & Horstman, K. C. 1991 Documentation of two- and three-dimensional shock-wave/turbulent boundary-layer interaction flows at Mach 8.2. NASA Tech. Memo. 103838.
Mabey, D. G., Meier, H. U. & Sawyer, K. G. 1974 Experimental and theoretical studies of the boundary layer on a flat plate at Mach numbers from 2.5 to 4.5. RAE/TR 74127.
Maise, G. & McDonald, H. 1968 Mixing length and kinematic eddy viscosity in a compressible boundary layer. AIAA J. 6, 73–80.Google Scholar
Mellor, G. L. 1972 The large Reynolds number asymptotic theory of turbulent boundary layers. Int. J. Engng Sci 10, 851–873.Google Scholar
Mellor, G. L. & Gibson, D. M. 1966 Equilibrium turbulent boundary layers. J. Fluid Mech. 24, 225–253.Google Scholar
Rotta, J. C. 1960 Turbulent boundary layers with heat transfer in compressible flow. AGARD Rep. 251.
Samuels, R. D., Peterson, J. B. & Adcock, J. B. 1967 Experimental investigation of the turbulent boundary layer at a Mach number of 6 with heat transfer at high Reynolds numbers. NASA TN D-3858.
Smith, C. R., Walker, J. D. A., Haidari, A. H. & Sobrun, U. 1991 On the dynamics of near-wall turbulence. Phil. Trans. R. Soc. Lond. A 336, 131–175.Google Scholar
Stalmach, C. J. 1958 Experimental investigation of the surface impact probe method of measuring local skin friction at supersonic speeds. University of Texas DRL-410, CF 2675.
Stewartson, K. 1964 The Theory of Laminar Boundary Layers in Compressible Fluids. Oxford University Press.
Stone, D. R. & Gary, A. M. 1972 Discrete sonic jets used as boundary layer trips at Mach numbers of 6 and 8.5. NASA TN D-6802.
Talcott, N. A. & Kumar, A. 1985 Two-dimensional viscous simulation of inlet/diffuser flows with terminal shocks. J. Propulsion 1, 103–108.Google Scholar
Van Driest, E. R. 1951 Turbulent boundary layer in compressible fluids. J. Aero. Sci. 18, 145–161.Google Scholar
Viegas, J. R., Rubesin, M. W. & Horstman, C. C. 1985 On the use of wall functions as boundary conditions for two-dimensional separated compressible flows. AIAA Paper 85-0180.
Voisinet, L. P. & Lee, R. E. 1972 Measurements of a Mach 4.9 zero pressure gradient turbulent boundary layer with heat transfer. NOL TR 72–232.
Walker, J. D. A., Abbott, D. E., Scharnhorst, R. K. & Weigand, G. G. 1989 Wall layer model for the velocity profile in turbulent flows. AIAA J. 27, 140–149.Google Scholar
Walker, J. D. A. & Scharnhorst, R. K. 1986 The Ξ function. Dept Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania, Rep. FM-9; Air Force Office of Scientific Research, AFOSR-TR-1715TR (available NTIS-AD-A188680).
Walker, J. D. A., Scharnhorst, R. K. & Weigand, G. G. 1986 Wall layer models for the calculation of velocity and heat transfer in turbulent boundary layers. AIAA Paper 86–0213.
Walker, J. D. A., Werle, M. J. & Ece, M. C. 1987 An embedded function approach for turbulent flow prediction. AIAA J. 29, 1810–1818.Google Scholar
Watson, R. D., Harris, J. E. & Anders, J. B. 1973 Measurements in a transitional/turbulent Mach 10 boundary layer at high Reynolds numbers. AIAA Paper 73–165.
Weigand, G. G. 1978 Forced convection in a two-dimensional nominally steady turbulent boundary layer. PhD thesis, Purdue University.
White, F. M. 1992 Viscous Fluid Flow. McGraw-Hill.
White, F. M. & Christoph, G. H. 1972 Simple theory for two-dimensional compressible turbulent boundary layer. Trans. ASME J. Basic Engng 94, 636–642.Google Scholar
Winter, K. G. & Gaudet, L. 1973 Turbulent boundary-layer studies at high Reynolds numbers at Mach numbers between 0.2 and 2.8. ARC R & M 3712.
Young, F. L. 1965 Experimental investigation of the effects of surface roughness on compressible turbulent boundary layer skin friction and heat transfer. University of Texas Rep. DRL-532, AD 621 085.