Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T21:01:53.308Z Has data issue: false hasContentIssue false
  • English
  • Français

The Departure from Equilibrium of Turbulent Boundary Layers

Published online by Cambridge University Press:  07 June 2016

H. McDonald
H. McDonald*
Affiliation:
United Aircraft Research Laboratories, Connecticut
Get access

Summary

Recently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

Type
Research Article
Information
Aeronautical Quarterly , Volume 19 , Issue 1 , February 1968 , pp. 1 - 19
Copyright
Copyright © Royal Aeronautical Society. 1968

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

1. Moses, H. L. The behavior of turbulent boundary layers in adverse pressure gradients. Massachusetts Institute of Technology, Gas Turbine Laboratory Report No. 73, May 1966.Google Scholar
2. Escudier, M. P. and Spalding, D. B. A note on the turbulent uniform property hydrodynamic boundary layer on a smooth impermeable wall; comparisons of theory with experiment. ARC 27 302, FM 3642, August 1965.Google Scholar
3. Zwarts, F. J. The development of an incompressible turbulent boundary layer in an arbitrary pressure gradient. McGill University MERL Report No. 65-7, October 1965.Google Scholar
4. Mellor, G. L. Turbulent boundary layers with arbitrary pressure gradients and divergent or convergent cross flows. Princeton University, Gas Dynamics Laboratory Report 775, March 1966.Google Scholar
5. Mueller, T. J. and Robertson, J. M. A study of the mean motion and turbulence downstream of a roughness element. Modern Developments in Theoretical and Applied Mechanics, Vol. 1. Plenum Press, 1963.Google Scholar
6. Bradshaw, P. and Ferriss, D. H. The response of a retarded equilibrium turbulent boundary layer to the sudden removal of pressure gradient. National Physical Laboratory, Aero Report 1145, March 1965.Google Scholar
7. Bradshaw, P. The turbulence structure of equilibrium boundary layers. National Physical Laboratory, Aero Report 1184, January 1966.Google Scholar
8. Goldberg, P. Upstream history and apparent stress in turbulent boundary layers. Massachusetts Institute of Technology, Gas Turbine Laboratory Report No. 85, May 1966.Google Scholar
9. Rotta, J. C. Critical review of existing methods for calculating the development of turbulent boundary layers. Paper presented at the symposium on “The Fluid Mechanics of Internal Flow”, General Motors Research Laboratories, Detroit, September 1965.Google Scholar
10. Nash, J. F. Turbulent boundary layer behaviour and the auxiliary equation. National Physical Laboratory, Aero Report 1137, February 1965. (See also AGARDograph 97, May 1965.)Google Scholar
11. Nash, J. F. and Macdonald, A. G. J. A calculation method for the incompressible turbulent boundary layer, including the effect of upstream history on the turbulent shear stress. National Physical Laboratory, Aero Report 1234, ARC 29088, December 1966.Google Scholar
12. McDonald, H. and Stoddart, J. A. P. On the development of the incompressible turbulent boundary layer. British Aircraft Corporation (Warton) Ltd., Ae 225, March 1965. R & M 3484, 1967.Google Scholar
13. Bradshaw, P., Ferriss, D. H. and Atwell, N. P. Calculation of boundary layer development using the turbulent energy equation. National Physical Laboratory, Aero Report 1182, January 1966.Google Scholar
14. McDonald, H. On incompressible two-dimensional turbulent boundary layers. United Aircraft Research Laboratories Report El 10339-2, November 1966.Google Scholar
15. Mellor, G. L. and Gibson, D. M. Equilibrium turbulent boundary layers. Journal of Fluid Mechanics, Vol. 24, Part 2, p. 225, 1966.CrossRefGoogle Scholar
16. Clauser, F. H. Turbulent boundary layers in adverse pressure gradients. Journal of the Aeronautical Sciences, Vol. 21, p. 91, 1954.CrossRefGoogle Scholar
17. Townsend, A. A. The structure of turbulent shear flow. Cambridge University Press, 1956.Google Scholar
18. Rotta, J. C. On the theory of the turbulent boundary layer. NACA TM 1344, February 1953. (Translation of “Uber die Theorie der turbulenten Grenzschichten”, Mitteilungen aus dem Max-planck-Institut für Stromungsforschung, Göttingen, No. 1, 1950.)Google Scholar
19. Townsend, A. A. Equilibrium layers and wall turbulence. Journal of Fluid Mechanics, Vol. 11, p. 97, 1961.CrossRefGoogle Scholar
20. Stoddart, J. A. P. Some analyses of the constant velocity defect turbulent boundary layer. British Aircraft Corporation (Warton), Aerodynamics Tech. Note Ae 260, May 1966.Google Scholar
21. Stoddart, J. A. P. Some calculated properties of the two-dimensional turbulent boundary layer shear stress distribution. British Aircraft Corporation (Warton), Aerodynamics Tech. Note Ae 264, July 1966.Google Scholar
22. Coles, D. E. The law of the wake in the turbulent boundary layer. Journal of Fluid Mechanics, Vol. 1, Part 2, p. 191, July 1956.CrossRefGoogle Scholar
23. Sandborn, V. A. and Slogar, R. J. Study of the momentum distribution of turbulent boundary layers in adverse pressure gradients. NACA TN 3264, 1955.Google Scholar
24. Newman, B. G. Some contributions to the study of the turbulent boundary layer. Australian Department of Supply Report No. ACA-53, 1951.Google Scholar
25. Schubauer, G. B. and Klebanoff, P. S. Investigation of separation of the turbulent boundary layer. NACA Report 1030, 1951.Google Scholar
26. Schubauer, G. B. and Spanoenberg, W. G. Forced mixing in boundary layers. Journal of Fluid Mechanics, Vol. 8, Part 1, p. 10, May 1960.CrossRefGoogle Scholar
27. Taulbee, D. B. Separation of a turbulent shear flow ahead of a normal step. PhD Dissertation, Department of Theoretical and Applied Mechanics, University of Illinois, 1964.Google Scholar
28. Tillmann, W. Untersuchungen über Besonderheiten bei turbulenten Reibungsschichten an Platten. Zentralstelle Wissenschaftliche Berichte, Kaiser-Wilhelm Institut, Göttingen, U & M 6627, 1945.Google Scholar
29. McCullough, G. B. and Gault, D. E. Examples of three representative types of airfoil section stall at low speeds. NACA TN 2502, September 1951.Google Scholar
30. Head, M. R. Entrainment in the turbulent boundary layer. ARC R & M 3152, September 1958.Google Scholar