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A transformation for compressible turbulent boundary layers with air injection

Published online by Cambridge University Press:  28 March 2006

L. O. F. Jeromin
L. O. F. Jeromin
Affiliation:
Engineering Department, University of Cambridge
Now at Messer Griesheim GmbH, Frankfurt/Main, Germany.
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Abstract

The transformation proposed by Coles for correlating the compressible turbulent boundary layer on a solid surface with a given incompressible layer has been extended to the case of a porous surface with air injection. However, unlike Coles's work, the new transformation does not use the empirical concept of the sublayer to define one of the transformation parameters. Instead this parameter can be defined in terms of the stream function at the wall, and so is directly related to the injection rate. The present paper concerns the transformation for the boundary layer with constant pressure and zero heat transfer, but the possibility of extending the transformation to flows with pressure gradients and heat transfer is mentioned briefly.

Comparison with experiments shows that the new transformation successfully relates cf, θ and the fully turbulent part of the velocity profile with their corresponding incompressible values for a wide range of Mach numbers and injection rates.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 31 , Issue 1 , 8 January 1968 , pp. 65 - 94
Copyright
© 1968 Cambridge University Press

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References

Baronti, P. O. & Libby, P. A. 1966 Velocity profiles in turbulent compressible boundary layers AIAA J. 4, 193–202.Google Scholar
Black, T. J. & Sarnecki, A. J. 1958 The turbulent boundary layer with suction or injection. British ARC R. & M. no. 3387.Google Scholar
Coles, D. 1962 The turbulent boundary layer in a compressible fluid. The RAND Corp. Santa Monica Calif. R-403-Pr. Also Phys. Fluids, 7, 1403.Google Scholar
Crocco, L. 1963 Transformations of the compressible turbulent boundary layer with heat exchange AIAA J. 1, 2723–2731.Google Scholar
Czarnecki, K. R. & Sinclair, A. R. 1955 An investigation of the effects of heat transfer on boundary layer transition on a parabolic body of revolution (NACA RM 10) at a Mach number of 1.61. NACA Rept. no. 1240.Google Scholar
Danberg, J. F. 1960 Measurements of the characteristics of the compressible turbulent boundary layer with air injection. NAVORD Rept. no. 6683. Aerodyn. Res. Rept. no. 67.Google Scholar
Danberg, J. F. 1964 Characteristics of the turbulent boundary layer with heat and mass transfer at M = 6.7, NOL TR, 46–99. Aerodynamic Res. Rept. no. 228.Google Scholar
Dorrance, W. H. & Dore, F. J. 1954 The effect of mass transfer on the compressible turbulent boundary layer skin friction and heat transfer. J. Aero/Space Sci. 21, 404–410.Google Scholar
Dutton, R. A. 1957 The velocity distribution of a turbulent boundary layer along a flat plate. ARC C.P. no. 453.Google Scholar
Dutton, R. A. 1958 The effect of distributed suction on the development of turbulent boundary layers. ARC no. 20,036.Google Scholar
Eber, G. R. 1952 Recent investigations of temperature recovery and heat transfer on cones and cylinders in axial flow at the NOL Aeroballistic Wind Tunnel. J. Aero/Space Sci. 19, 303.Google Scholar
Higgins, R. N. & Pappas, C. C. 1951 An experimental investigation of the effect of surface heating on boundary layer transition on a flat plate in supersonic flow. NACATN no. 2351.Google Scholar
Jeromin, L. O. F. 1966a The compressible turbulent boundary layer with fluid injection. Ph.D. Thesis, University of Cambridge.
Jeromin, L. O. F. 1966b An experimental investigation of the compressible turbulent boundary layer with air injection. ARC no. 28,549, ARC R. & M. 3526.Google Scholar
Ludwieg, H. & Tillmann, W. 1950 Investigations of the wall shearing stress in turbulent boundary layers. NACA TM no. 1285.Google Scholar
Mager, A. 1962 Transformation of the compressible turbulent boundary layer. J. Aero/Space Sci. 25, 305–311.Google Scholar
McQuaid, J. 1966 Incompressible turbulent boundary layers with distributed injection. Ph.D. Thesis, University of Cambridge.
Mickley, H. S. & Davies, R. S. 1957 Momentum transfer for flow over a flat plate with blowing. NACA TN no. 4017.Google Scholar
Pappas, C. C. & Okuno, A. F. 1960 Measurements of skin friction of the compressible turbulent boundary layer on a cone with foreign gas injection. J. Aero/Space Sci. 27, 321.Google Scholar
Romanenko, P. N. & Kharchenko, V. N. 1963 The effect of transverse mass flow on heat transfer and friction drag in a turbulent flow of compressible gas along an arbitrarily shaped surface Int. J. Heat Mass Transfer, 6, 727–738.CrossRefGoogle Scholar
Rosenbaum, H. 1966 Turbulent compressible boundary layer on a flat plate with heat transfer and mass diffusion AIAA J. 4, 1548–1556.Google Scholar
Rubesin, M. W. 1956 The influence of surface injection on heat transfer and skin friction associated with the high speed turbulent boundary layer. NACA R. & M. A 55 L 13.Google Scholar
Rubesin, M. W. 1959 An analytical estimation of the effect of transpiration cooling on heat transfer and skin friction characteristics of a compressible, turbulent boundary layer. NACA TN no. 3341.Google Scholar
Rubesin, M. W., Maydew, R. C. & Varga, S. A. 1951 An analytical and experimental investigation of the skin friction of the turbulent boundary layer on a flat plate at supersonic speeds. NACA TN no. 2305.Google Scholar
Scherrer, R. 1951 Comparison of theoretical and experimental heat transfer characteristics of bodies of revolution at supersonic speeds. NACA, Rept. 1055.Google Scholar
Schlichting, H. 1960 Boundary Layer Theory, 4th edition. New York: McGraw-Hill Book Company.
Schultz-Grunow, F. 1941 Neues Widerstandsgeretz für glatte Platten. Luftfahrtforschung 17, 239, 1940; NACA TM no. 986, 1941.Google Scholar
Smith, D. W. & Walker, J. H. 1958 Skin friction measurements in incompresible flow. NACA TN no. 4231.Google Scholar
Spalding, D. B., Auslander, D. M. & Sundaram, T. R. 1964 The calculation of heat and mass transfer through the turbulent boundary layer on a flat plate at high Mach numbers, with and without chemical reaction. Supersonic Flow, Chemical Processes and Radioactive Transfer, pp. 211–276. Edited D. B. Olfe and V. Zakkay. Oxford: Pergamon Press.
Spence, D. A. 1960 Distributions of velocity, enthalpy and shear stress in the compressible turbulent boundary layer on a flat plate J. Fluid Mech. 8, 368–387.Google Scholar
Stevenson, T. N. 1963 A law of the wall for turbulent boundary layers with suction or injection. The College of Aeronautics, Cranfield. CoA Rept. Aero no. 166.Google Scholar
Tendeland, T. & Okuno, A. F. 1956 The effect of fluid injection on the compressible turbulent boundary layer—the effect on skin friction of air injected into the boundary layer of a cone at M = 2.7. NACA RM A 65 D 05.Google Scholar
Thompson, B. C. J. 1964 A critical review of existing methods of calculating the turbulent boundary layer. ARC no. 26109, ARC F.M. no. 3492.Google Scholar
Van Driest, E. R. & Boison, J. C. 1955 Boundary layer stabilization by surface cooling in supersonic flow. J. Aero/Space Sci. 22, 70.Google Scholar