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Analysis of turbulent pipe and channel flows at moderately large Reynolds number

Published online by Cambridge University Press:  29 March 2006

Noor Afzal  and
Kirit Yajnik
Noor Afzal
Affiliation:
Department of Aeronautical Engineering, Indian Institute of Technology, Kanpur, India
Kirit Yajnik
Affiliation:
Aerodynamics Division, National Aeronautical Laboratory, Bangalore, India
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Abstract

Effects of moderately large Reynolds numbers R are studied by considering higher order terms in the expansions for turbulent pipe and channel flows for R → ∞. Matched asymptotic expansions using two length scales are employed to emphasize the two-layer structure of turbulent shear flows near solid walls. The effects appear as additional terms in extended forms of the law of the wall, the logarithmic velocity law, the velocity defect law and the logarithmic skinfriction law. These generalizations are critically compared with experimental results for pipe flows of Patel & Head and extremely good agreement is obtained. Also, possible applications are discussed for extending the range of skin-friction and heat-transfer devices which are based on wall similarity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 61 , Issue 1 , 23 October 1973 , pp. 23 - 31
Copyright
© 1973 Cambridge University Press

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References

Afzal, N. 1971 Compressible turbulent boundary layer at moderately large Reynolds number. Dept. of Aeron. Engng, Ind. Inst. Tech., Kanpur, Tech. Rep. no. 16/1971.Google Scholar
Afzal, N. 1973 J. Fluid Mech. 57, 1.
Afzal, N. & Yajnik, K. S. 1971 Z. angew. Math. Phys. 22, 899.
Beavers, G. S., Sparrow, E. M. & Lloyd, J. R. 1971 J. Basic Engng. 93, 296.
Chawla, T. C. & Tennekes, H. 1973 Int. J. Engng Sci. 11, 45.
Clark, J. A. 1968 J. Basic Engng, 90, 445.
Coles, D. 1956 J. Fluid Mech. 1, 191.
Coles, D. 1968 Proc. 1968 AFOSR-IFP-Stanford Conf. on Computation of Turbulent Boundary-layers, vol. 2, pp. 1–45.
Gill, A. E. 1968 J. Math. Phys. 47, 437.
Goldstein, S. 1965 Modern Developments in Fluid Dynamics, p. 366. Dover.
Head, M. R. & Ram, V. V. 1971 Aero. Quart. 22, 295.
Hinze, J. O. 1959 Turbulence, p. 515. McGraw-Hill.
Hinze, J. O. 1964 In Mechanics of Turbulence (ed. A. Favre), Gordon & Breach.
Huffmann, G. D. & Bradshaw, P. 1972 J. Fluid Mech. 53, 45.
Mellor, G. L. 1972 Int. J. Engng Sci. 10, 851.
Millikan, C. B. 1938 Proc. 5th Int. Congr. Appl. Mech., pp. 386–392.
Patel, V. C. & Head, M. R. 1969 J. Fluid Mech. 38, 181.
Rotta, J. C. 1962 In Progress in Aeronautical Sciences, vol. 2. Pergamon.
Schlichting, H. 1968 Boundary-Layer Theory, 6th edn. McGraw-Hill.
Tennekes, H. 1966 Appl. Sci. Res. 15, 232.
Tennekes, H. 1968 A.I.A.A.J. 6, 1735.
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.
Yajnik, K. S. 1970 J. Fluid Mech. 42, 411.