Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T17:35:05.484Z Has data issue: false hasContentIssue false

Eddy Viscosity and Entrainment in Equilibrium Boundary Layers

Published online by Cambridge University Press:  07 June 2016

M R Head
Affiliation:
Cambridge University, Engineering Department
R A McD Galbraith
Affiliation:
Cambridge University, Engineering Department
Get access

Summary

The properties of equilibrium turbulent boundary layers have been examined using Thompson’s family of velocity profiles along with alternative π – G relationships. The relationship which is in best agreement with measurements of equilibrium layers confirms an earlier suggestion that (νT/Uδ*)max is not a universal constant for such layers but decreases for small and negative values of π. A close relationship is established between eddy viscosity and entrainment, and it is shown that veδ/νT is effectively constant for π > 2.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1975

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 Galbraith, R A McD Head, M R Eddy viscosity and mixing length from measured boundary layer developments. Aeronautical Quarterly, Vol XXVI, pp 133153, May 1975.CrossRefGoogle Scholar
2. Clauser, F H Turbulent boundary layers. Advances in Applied Mechanics, Vol 4, Academic Press, 1956.Google Scholar
3 Townsend, A A Equilibrium layers and wall turbulence. Journal of Fluid Mechanics, Vol 11, pp 97120, 1960.Google Scholar
4 Mellor, G L Gibson, D M Equilibrium turbulent boundary layers. Journal of Fluid Mechanics, Vol 24, pp 225253, 1966.Google Scholar
5 Head, MR Equilibrium and near-equilibrium turbulent boundary layers. To be published in the Journal of Fluid Mechanics.Google Scholar
6 Thompson, B G J A new two-parameter family of mean velocity profiles for incompressible boundary layers on smooth walls. ARC R & M 3463, 1965.Google Scholar
7 Head, M R Patel, V C Improved entrainment method for calculating turbulent boundary layer development. ARC R & M 3643, 1970.Google Scholar
8 Nash, J F Turbulent boundary layer behaviour and the auxiliary equation. ARC Current Paper 835, 1965.Google Scholar
9 Bradshaw, P The turbulent structure of equilibrium turbulent boundary layers. Journal of Fluid Mechanics, Vol 29, pp 625645, 1967.CrossRefGoogle Scholar
10 Herring, H J Norbury, J F Some experiments on equilibrium turbulent boundary layers in favourable pressure gradients. Journal of Fluid Mechanics, Vol 27, pp 541549, 1967.CrossRefGoogle Scholar
11 Thwaites, B (Editor) Incompressible Aerodynamics. Clarendon Press, Oxford, p 73, 1960.Google Scholar
12 Coles, D Measurements in the boundary layer on a smooth flat plate in supersonic flow, 1: The problem of the turbulent boundary layer. Jet Propulsion Laboratory, California Institute of Technology report, 1953. (Available as Zeitschrift fur angewandte Mathematik und Physik, Part 5, 1954.)Google Scholar
13 Coles, D The law of the wake in the turbulent boundary layer. Journal of Fluid Mechanics, Vol l,p 218, 1956.Google Scholar
14 Coles, D The turbulent boundary layer in a compressible fluid. RAND report R-403-PR, 1962.Google Scholar
15 Smith, D W Walker, J H Skin friction measurements in incompressible flow. NASA TR R-26, 1959.Google Scholar
16 Wieghardt, K Proceedings of the Stanford Conference on Turbulent Boundary Layer Prediction, Vol 2, AFOSR-IFP, University Press, Stanford, California, 1968.Google Scholar
17 Clauser, F H Turbulent boundary layers in adverse pressure gradients. Journal of the Aeronautical Sciences, Vol 21, pp 91108, 1954.Google Scholar
18 Head, MR Bradshaw, P Zero and negative entrainment in turbulent shear flow. Journal of Fluid Mechanics, Vol 46, pp 385394, 1971.CrossRefGoogle Scholar
19 Spalding, D B The kinetic-energy-deficit equation of the turbulent boundary layer. AGARD-ograph 97, Part 1, pp 191244, 1965.Google Scholar
20 Michel, R Quemard, C Durant, R Hypothesis on the mixing length and application to the calculation of turbulent boundary layers. Proceedings of the Stanford Conference on Turbulent Boundary Layer Prediction, Vol 1, p 202, AFOSR-IFP, University Press, Stanford, California, 1968.Google Scholar