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A Unified View of the Law of the Wall Using Mixing-Length Theory

Published online by Cambridge University Press:  07 June 2016

V C Patel
V C Patel*
Affiliation:
Institute of Hydraulic Research, University of Iowa
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Summary

It is shown that, if the well-known mixing-length formula is regarded simply as a relationship between the velocity and the stress distributions in the wall region of a turbulent flow, then a truly universal distribution of mixing length is sufficient to describe the experimentally observed departures of the velocity distribution from the usual law of the wall as a result of severe pressure gradients and transverse surface curvature. Comparisons have been made with a wide variety of experimental data to demonstrate the general validity of the mixing-length model in describing the flow close to a smooth wall.

An extension of the re-laminarisation criterion of Patel and Head, and some experimental evidence, suggest that the thick axisymmetric boundary layer on a slender cylinder placed axially in a uniform stream cannot be maintained in a fully turbulent state for values of the Reynolds number, based on friction velocity and cylinder radius, below a certain critical value.

Type
Research Article
Information
Aeronautical Quarterly , Volume 24 , Issue 1 , February 1973 , pp. 55 - 70
Copyright
Copyright © Royal Aeronautical Society. 1973

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References

1 Batchelor, G K Note on free turbulent flows, with special reference to the two-dimensional wake. Journal of the Aeronautical Sciences, Vol 17, p 441, 1950.CrossRefGoogle Scholar
2 Patel, V C Head, M R Reversion of turbulent to laminar flow. Journal of Fluid Mechanics, Vol 34, p 371, 1968.CrossRefGoogle Scholar
3 Patel, V C Calibration of the Preston tube and limitations on its use in pressure gradients. Journal of Fluid Mechanics, Vol 23, p 185, 1965.CrossRefGoogle Scholar
4 Reichardt, H Vollständige Darstelling der turbulenten Geschwindigkeitsverteilung in glatten Leitungen. Zeitschrift für Angewandte Mathematik und Mechanik, Vol 31, p 208, 1951.CrossRefGoogle Scholar
5 Deissler, R G Analysis of turbulent heat transfer, mass transfer and friction in smooth tubes at high Prandtl and Schmidt numbers. NACA Technical Report 1210, 1954.Google Scholar
6 van Driest, E R On turbulent flow near a wall. Journal of the Aeronautical Sciences, Vol 23, pp 1007 and 1036, 1956.CrossRefGoogle Scholar
7 Stratford, B S The prediction of separation of the turbulent boundary layer. Journal of Fluid Mechanics, Vol 5, p 1, 1959.CrossRefGoogle Scholar
8 Townsend, A A Equilibrium layers and wall turbulence. Journal of Fluid Mechanics, Vol 11, p 97, 1961.CrossRefGoogle Scholar
9 McDonald, H The effect of pressure gradient on the law of the wall in turbulent flow. Journal of Fluid Mechanics, Vol 35, p 311, 1969.CrossRefGoogle Scholar
10 Patel, V C Contributions to the study of turbulent boundary layers. PhD Thesis, Cambridge University, England, 1965.Google Scholar
11 Mellor, G L The effects of pressure gradients on turbulent boundary layers. Journal of Fluid Mechanics, Vol 24, p 255, 1966.CrossRefGoogle Scholar
12 Newman, B G Some contributions to the study of the turbulent boundary layer. Australian Department of Supply, Report ACA-53, 1951.Google Scholar
13 Head, M R Rechenberg, I The Preston tube as a means of measuring skin friction. Journal of Fluid Mechanics, Vol 14, p 1, 1962.CrossRefGoogle Scholar
14 Patel, V C Head, M R Some observations on skin friction and velocity profiles in fully developed pipe and channel flows. Journal of Fluid Mechanics, Vol 38, p 181, 1969.CrossRefGoogle Scholar
15 Rao, G N V The law of the wall in a thick axisymmetric turbulent boundary layer. Journal of Basic Engineering, Transactions ASME, Series D, Vol 89, p 237, 1967.CrossRefGoogle Scholar
16 Rothfus, R R Monrad, C C Senecal, V E Velocity distribution and fluid friction in smooth concentric annuii. Industrial and Engineering Chemistry, Vol 42, p 2511, 1950.CrossRefGoogle Scholar
17 Owen, W M Experimental study of water flow in annular pipes. Proceedings ASCE, Vol 77, Separate No. 88, 1951.Google Scholar
18 Knudsen, J G Katz, D L Velocity profiles in annuii. Proceedings of Midwestern Conference on Fluid Mechanics, 1950.Google Scholar
19 Brighton, J A Jones, J B Fully developed turbulent flow in annuii. Journal of Basic Engineering, Transactions ASME, Series D, Vol 86, p 835, 1964.CrossRefGoogle Scholar
20 Quarmby, A An experimental study of turbulent flow through concentric annuii. International Journal of Mechanical Sciences, Vol 9, p 205, 1967.CrossRefGoogle Scholar
21 Levy, S Turbulent flow in an annulus. Journal of Heat Transfer, Transactions ASME, Vol 89, p 25, 1967.CrossRefGoogle Scholar
22 Lawn, C J Elliott, C J Fully developed turbulent flow through concentric annuii. Central Electricity Generating Board, Berkeley, England, Report RD/B/N1878, 1971.Google Scholar
23 Richmond, R L Experimental investigation of thick axially symmetric boundary layers on cylinders at subsonic and hypersonic speeds. PhD Thesis, California Institute of Technology, Pasadena, 1957.Google Scholar
24 Yu, Y S Effect of transverse curvature on turbulent boundary layer characteristics. Journal of Ship Research, Vol 3, p 33, 1958.CrossRefGoogle Scholar
25 Yasuhara, M Experiments of axisymmetric boundary layers along a cylinder in incompressible flow. Transactions, Japan Society for Aerospace Science, Vol 2, p 33, 1959.Google Scholar
26 Keshavan, N R Axisymmetric incompressible turbulent boundary layers in zero pressure gradient flow. MSc Thesis, Indian Institute of Science, Bangalore, India, 1969.Google Scholar
27 Willmarth, W W Yang, C S Wall-pressure fluctuations beneath turbulent boundary layers on a flat plate and a cylinder. Journal of Fluid Mechanics, Vol 41, p 47, 1970.CrossRefGoogle Scholar
28 Landweber, L Effect of transverse curvature on frictional resistance. David Taylor Model Basin Report 689, 1949.Google Scholar
29 Cebeci, T Laminar and turbulent incompressible boundary layers on slender bodies of revolution in axial flow. Journal of Basic Engineering, Transactions ASME Series D, Vol 92, p 545, 1970.CrossRefGoogle Scholar
30 Clauser, F H The turbulent boundary layer. Advances in Applied Mechanics, Vol 4, p 1, 1956.CrossRefGoogle Scholar
31 White, F M Written discussion of the paper of Cebeci. Journal of Basic Engineering, Transactions ASME, Vol 92, p 550, 1970.CrossRefGoogle Scholar