Skip to main content

A transformation for compressible turbulent boundary layers with air injection

  • L. O. F. Jeromin (a1)

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.

Hide All
Baronti, P. O. & Libby, P. A. 1966 Velocity profiles in turbulent compressible boundary layers AIAA J. 4, 193202.
Black, T. J. & Sarnecki, A. J. 1958 The turbulent boundary layer with suction or injection. British ARC R. & M. no. 3387.
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.
Crocco, L. 1963 Transformations of the compressible turbulent boundary layer with heat exchange AIAA J. 1, 27232731.
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.
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.
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.
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, 404410.
Dutton, R. A. 1957 The velocity distribution of a turbulent boundary layer along a flat plate. ARC C.P. no. 453.
Dutton, R. A. 1958 The effect of distributed suction on the development of turbulent boundary layers. ARC no. 20,036.
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.
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.
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.
Ludwieg, H. & Tillmann, W. 1950 Investigations of the wall shearing stress in turbulent boundary layers. NACA TM no. 1285.
Mager, A. 1962 Transformation of the compressible turbulent boundary layer. J. Aero/Space Sci. 25, 305311.
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.
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.
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, 727738.
Rosenbaum, H. 1966 Turbulent compressible boundary layer on a flat plate with heat transfer and mass diffusion AIAA J. 4, 15481556.
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.
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.
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.
Scherrer, R. 1951 Comparison of theoretical and experimental heat transfer characteristics of bodies of revolution at supersonic speeds. NACA, Rept. 1055.
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.
Smith, D. W. & Walker, J. H. 1958 Skin friction measurements in incompresible flow. NACA TN no. 4231.
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. 211276. 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, 368387.
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.
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.
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.
Van Driest, E. R. & Boison, J. C. 1955 Boundary layer stabilization by surface cooling in supersonic flow. J. Aero/Space Sci. 22, 70.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed