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An Improved Version of the Cebeci-Smith Eddy-Viscosity Model

Published online by Cambridge University Press:  07 June 2016

M.J. Nituch
Affiliation:
(Cambridge University Engineering Department)
S. Sjolander
Affiliation:
(Cambridge University Engineering Department)
M.R. Head
Affiliation:
(Cambridge University Engineering Department)
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Summary

Although the Cebeci-Smith method of calculating turbulent boundary layers is widely used and generally gives acceptably accurate results, highly inaccurate skin-friction values are obtained for relaxing flows and equilibrium layers in strong adverse pressure gradient. In the present paper, these anomalies are removed by suitable modifications to the basic eddy-viscosity model.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1978

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References

1 Galbraith, R.A. McD. and Head, M.R. Eddy viscosity and mixing length from measured boundary layer developments. Aevonautical Quarterly, Vol. XXVI, pp. 133154, May 1975.Google Scholar
2 Cebeci, T., and Smith, A.M.O. The Analysis of Turbulent Boundary Layers. Academic Press, 1974.Google Scholar
3 Glowacki, W.J. and Chi, S.W. Effect of pressure gradient on mixing-length for equilibrium turbulent boundary layers. AIAA Paper 72-213, 1972.Google Scholar
4 Reeves, B.L. Two-layer model of turbulent boundary layers. AIAA Journal, Vol. 12, pp. 932939, 1974.Google Scholar
5 Cebeci, T. and Smith, A.M.O. A finite-difference solution of the incompressible boundary-layer equations by an eddyviscosity concept. Proceedings of the Stanford Conference on Turbulent Boundary Layer Prediction, Vol. 1, pp. 346355, AFOSR-IFP, University Press, Stanford, California, 1968.Google Scholar
6 Galbraith, R.A. McD., Sjolander, S., and Head, M.R. Mixing length in the wall region of turbulent boundary layers. Aeronautical Quarterly, Vol. XXVIII, pp. 97110, May 1977.Google Scholar
7 Townsend, A.A. Equilibrium layers and wall turbulence. Journal of Fluid Mechanics, Vol. 11, pp. 97120, 1961.Google Scholar
8 Mellor, G.L. and Gibson, D.M. Equilibrium turbulent boundary layers. Journal of Fluid Mechanics, Vol. 24, pp. 225253, 1966.Google Scholar
9 Clauser, F.H. The turbulent boundary layer. Advances in Applied Mechanics, Vol. 4, pp. 151, 1956.Google Scholar
10 Head, M.R. and Galbraith, R.A. McD. Eddy viscosity and entrainment in equilibrium boundary layers. Aeronautical Quarterly, Vol. XXVI, pp. 229242, Nov. 1975.Google Scholar
11 Head, M.R. and Patel, V.C. Improved entrainment method for calculation turbulent boundary layer development. ARC R & M 3643, 1970.Google Scholar
12 Wippermann, H.W. Ph.D. dissertation. Technische Hochschule, Karlsruhr. (as referenced by White, F.M. in Viscous Fluid Flow, McGraw-Hill, New York, 1974).Google Scholar
13 Thompson, B.G.J. A new two-parameter family of mean velocity profiles for incompressible turbulent boundary layers on smooth walls. ARC R & M 3463, 1967.Google Scholar
14 Coles, D.E., and Hirst, E.A. (editors) Proceedings of the Stanford Conference on Turbulent Boundary Layer Prediction, Vol. 2, AFOSR-IFP, University Press, Stanford, California, 1968.Google Scholar
15 Mellor, G.L. and Herring, H.J. Two methods of calculating turbulent boundary layer behaviour based on numerical solution of the equations of motion. Proceedings of the Stanford Conference on Turbulent Boundary Layer Prediction, Vol. 1, pp. 331345, AFOSR-IFP, University Press, Stanford, California, 1968.Google Scholar
16 Bradshaw, P., Ferriss, D.H. and Atwell, N.P. Calculation of boundary layer development using the turbulent energy equation. Journal of Fluid Mechanics, Vol. 28, pp. 593616, 1967.Google Scholar
17 Patankar, S.V. and Spalding, D.B. Heat and Mass Transfer in Boundary Layers. Intertext Books, London, 2nd edition, 1970.Google Scholar
18 Patel, V.C. and Head, M.R. A simplified version of Bradshaw’s method for calculating two-dimensional turbulent boundary layers. Aeronautical Quarterly, Vol. XXI, pp. 243262, 1970.Google Scholar