Model of Low-Reynolds-Number Wall Turbulence for Equilibrium Layers

  • P. Orlandi


A one-equation turbulence model simulating the wall region is applied to study the equilibrium boundary layers. In these layers a universal mixing-length distribution can be assumed, as shown in the experiments of East and Sawyer. Particular emphasis is placed on representing accurately the turbulence-energy balance in the viscous and buffer regions, where an explicit model of the pressure-work term is shown to be necessary. Comparisons with experimental results of the mean quantities in the near-wall region are presented. Analysis of the turbulence-energy balance shows a behavior in qualitative agreement with that described by Shubauer. The same initial conditions have been assumed for the whole range of favorable and adverse pressure gradients considered. The free-stream pressure gradient influences the mean quantities and the turbulence-energy balance in a manner that is in agreement with experiment.


Boundary Layer Reynolds Stress Turbulent Boundary Layer Turbulent Diffusion Turbulent Energy 
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  1. 1.
    J. Rotta, On the Theory of the Turbulent Boundary Layer, NACA TM 1344 (1950).Google Scholar
  2. 2.
    F. H. Clauser, Turbulent boundary layers in adverse pressure gradients, J. Aero. Sci. 21, 91–108 (1954).Google Scholar
  3. 3.
    A. A. Townsend, Equilibrium layers and wall turbulence, J. Fluid Mech. 11, 97–120 (1961).MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    G. L. Mellor, The effects of pressure gradients on turbulent flow near a smooth wall, J. Fluid Mech. 24, 255–274 (1966).CrossRefGoogle Scholar
  5. 5.
    P. Bradshaw, The turbulent structure of equilibrium layers, J. Fluid Mech. 29, 625–645 (1967).CrossRefGoogle Scholar
  6. 6.
    M. R. Head, Equilibrium and near-equilibrium turbulent boundary layers, J. Fluid Mech. 73, 1–8 (1976).CrossRefGoogle Scholar
  7. 7.
    P. Bradshaw, Inactive motion and pressure fluctuations in turbulent boundary layers, J. Fluid Mech. 30, 241–258 (1967).CrossRefGoogle Scholar
  8. 8.
    L. F. East and W. G. Sawyer, An Investigation of the Structure of Equilibrium Turbulent Boundary Layers, AGARD CP 271 (1979).Google Scholar
  9. 9.
    P. S. Klebanoff, Characteristics of Turbulence in a Boundary Layer with Zero Pressure Gradient, NACA Report 1247 (1955).Google Scholar
  10. 10.
    J. Laufer, The Structure of Turbulence in Fully-Developed Pipe Flow, NACA TN 2954 (1953).Google Scholar
  11. 11.
    P. Moin, W. C. Reynolds, and J. H. Ferziger, Large Eddy Simulation of Incompressible Channel Flow, Report No. TF-12, Mechanical Engineering Department, Stanford University (1978).Google Scholar
  12. 12.
    T. H. Kim, S. J. Kline, and W. C. Reynolds, The production of turbulence near a smooth wall in a turbulent boundary layer, J. Fluid Mech. 50, 133–160 (1971).CrossRefGoogle Scholar
  13. 13.
    R. F. Blackwelder and R. E. Kaplan, On the wall structure of the turbulent boundary layer, J. Fluid Mech. 76, 89–112 (1976).CrossRefGoogle Scholar
  14. 14.
    H. L. Norris and W. C. Reynolds, Turbulent Channel Flow with a Moving Wavy Boundary, Report No. TF-7, Mechanical Engineering Department, Stanford University (1975).Google Scholar
  15. 15.
    H. Ueda and J. O. Hinze, Fine-structure turbulence in the wall region of a turbulent boundary layer, J. Fluid Mech. 67, 125–143 (1975).CrossRefGoogle Scholar
  16. 16.
    G. B. Shubauer, Turbulent processes as observed in boundary layer and pipe, J. Appl. Phys. 25, 188–196 (1954).CrossRefGoogle Scholar
  17. 17.
    G. M. Lilley, A review of pressure fluctuations in turbulent boundary layers at subsonic and supersonic speeds, Arch. Mech. Stos. 16, 301–330 (1964).Google Scholar
  18. 18.
    B. E. Launder, G. J. Reece, and W. Rodi, Progress in the development of a Reynoldsstress turbulence closure, J. Fluid Mech. 68, 537–566 (1975).MATHCrossRefGoogle Scholar
  19. 19.
    P. Orlandi and W. C. Reynolds, A provisional model for unsteady turbulent boundary layers (in press).Google Scholar
  20. 20.
    K. Wieghardt, in: Proceedings of the Conference on Computation of Turbulent Boundary Layers (D. E. Coles and E. A. Hirst, eds.), Vol. 2, pp. 98-124, AFOSR-IFP-Stanford Conference (1968).Google Scholar
  21. 21.
    P. Orlandi and J. H. Ferziger, Implicit non-iterative schemes for unsteady boundary layers (in press).Google Scholar
  22. 22.
    W. P. Jones and B. E. Launder, The calculation of low-Reynolds-number phenomena with a two-equation model of turbulence, Int. J. Heat Mass Transfer 16, 1119–1130 (1973).CrossRefGoogle Scholar
  23. 23.
    G. L. Mellor and H. J. Herring, A survey of mean turbulent field closure models, AIAA J. 5, 590–599 (1973).CrossRefGoogle Scholar
  24. 24.
    B. A. Kader and A. M. Yaglom, Similarity treatment of moving-equilibrium turbulent boundary layers in adverse pressure gradients, J. Fluid Mech. 89, 305–342 (1978).MathSciNetCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • P. Orlandi
    • 1
  1. 1.Scuola di Ingegegneria Aerospaziale, Istituto di AerodinamicaUniversità degli Studi di RomaRomeItaly

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