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Equilibrium and near-equilibrium turbulent boundary layers

Published online by Cambridge University Press:  29 March 2006

M. R. Head
M. R. Head
Affiliation:
Engineering Department, University of Cambridge
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Abstract

A well-tested integral method has been used to calculate turbulent boundary-layer development for the distribution of external velocity given by U ∝ x−0.255. The results suggest that different values of the initial momentum thickness, so long as this is below some critical value, produce a range of equilibrium layers having widely different values of the form parameter G. For values of the initial momentum thickness greater than the critical value, layers are produced which proceed more or less rapidly to separation. These results provide a plausible explanation for conflicting experimental observations made in the past.

Additional calculations for the flows U ∝ x−0.15 and U ∝ x−0.35 suggest that, in the first case, a unique equilibrium condition is approached whatever the initial momentum thickness unless this exceeds some critical value; in the second case no equilibrium condition appears possible.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 73 , Issue 1 , 13 January 1976 , pp. 1 - 8
Copyright
© 1976 Cambridge University Press

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References

Bradshaw, P. 1966 The turbulence structure of equilibrium boundary layers. Nat. Phys. Lab. Aero. Rep. no. 1184. (See also (shortened version) J. Fluid Mech. 29 (1967, 625.)Google Scholar
Bradshaw, P. 1967 The response of a constant-pressure turbulent boundary layer to the sudden application of an adverse pressure gradient. Aero. Res. Counc. R. & M. no. 3575.Google Scholar
Bradshaw, P., Ferriss, D. H. & Atwell, N. P. 1967 Calculation of boundary-layer development using the turbulent energy equation J. Fluid Mech. 28, 593.Google Scholar
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients J. Aero. Sci. 21, 98.Google Scholar
Felsch, K. O. 1965 Beitrag zur Berecknung Turbulenter Grenzschichten in zwei-dimensionaler incompressible Stromung. Doktor – ingenieur dissertation, Technische Hochschule Karlsruhe.
Head, M. R. & Patel, V. C. 1970 An improved entrainment method for the calculation of turbulent boundary layers. Aero. Res. Counc. R. & M. no. 3643.Google Scholar
Launder, B. E. & Jones, W. P. 1969 Sink flow turbulent boundary layers J. Fluid Mech. 38, 817.Google Scholar
Mellor, G. L. 1966 Pressure gradients and turbulent flow near a smooth wall J. Fluid Mech. 24, 255.Google Scholar
Mellor, G. L. & Gibson, D. M. 1963 Equilibrium turbulent boundary layers. Princeton University Mech. Engng Rep. FLD 13.Google Scholar
Mellor, G. L. & Gibson, D. M. 1966 Equilibrium turbulent boundary layers J. Fluid Mech. 24, 225.Google Scholar
Nash, J. F. 1965 Turbulent boundary layer behaviour and the auxiliary equation AGARDograph, 97, 245.Google Scholar
Stratford, B. S. 1959 An experimental flow with zero skin friction throughout its region of pressure rise J. Fluid Mech. 5, 17.Google Scholar
Townsend, A. A. 1961 Equilibrium layers and wall turbulence J. Fluid Mech. 11, 97.Google Scholar