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The representation of the viscous wall region by a regular eddy pattern

Published online by Cambridge University Press:  19 April 2006

Dimitrios T. Hatziavramidis  and
Thomas J. Hanratty
Dimitrios T. Hatziavramidis
Affiliation:
Department of Chemical Engineering, University of Illinois, Urbana
Thomas J. Hanratty
Affiliation:
Department of Chemical Engineering, University of Illinois, Urbana
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Abstract

A model for the kinematics of a turbulent flow close to a solid boundary is explored. The field is assumed to be homogeneous in the direction of mean flow. The equations of motion are solved numerically for a flow which is periodic in time and in a direction transverse to the direction of mean flow. The period is taken to be the time interval between ‘bursts’ and the wavelength, the spacing of the streaky structure close to the wall observed by a number of investigators. Good agreement is obtained between the calculated flow field and experimental results, especially for y+ < 15. This agreement suggests that the flow oriented eddies in the viscous wall region can be represented by a model which views the flow in this region to be coherent and to be associated with spanwise flow deviations in a well-mixed outer region. The model allows for the periodic movement of low momentum fluid from the wall, which, because of the assumption of a well mixed outer region, gives rise to a shear layer. This seems to correspond to the observed ‘bursting’ phenomenon. The calculations confirm the suggestion by Fortuna and Hanratty (Fortuna 1970; Hanratty, Chorn & Hatziavramidis 1977) that the secondary flow in the viscous wall region generated by these spanwise flow deviations gives rise to the development of large velocity fluctuations in the direction of mean flow and accounts for the experimentally observed maximum in the velocity fluctuations close to the wall. Also, the comparison of calculations with measurements of the average velocity and with an experimental quadrant analysis of the Reynolds stress suggests that the secondary flow is making a major contribution to the Reynolds stress.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 95 , Issue 4 , 27 December 1979 , pp. 655 - 679
Copyright
© 1979 Cambridge University Press

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References

Aziz, K. & Hellums, J. C. 1967 Phys. Fluids 10, 314.
Bakewell, H. P. & Lumley, J. L. 1967 Phys. Fluids 10, 1800.
Blackwelder, R. F. & Kaplan, R. E. 1972 12th Symp. IUTAM.
Brodkey, R. S., Wallace, J. M. & Eckelmann, H. 1974 J. Fluid Mech. 63, 209.
Corino, E. R. & Brodkey, R. S. 1969 J. Fluid Mech. 37, 1.
Corrsin, S. 1956 Symp. on Naval Hydrodyn.
Eckelman, L. D. 1971 The Structure of Wall Turbulence and its Relation to Eddy Transport. Ph.D. thesis, Department of Chemical Engineering, University of Illinois, Urbana.
Eckelmann, H. 1974 J. Fluid Mech. 65, 439.
Fage, F. A. & Townsend, H. C. H. 1932 Proc. Roy. Soc. A 135, 656.
Fortuna, G. 1970 Effect of Drag Reducing Polymers on Flow Near a Wall. Ph.D. thesis, Department of Chemical Engineering, University of Illinois, Urbana.
Fortuna, G., Gilead & Hanratty, T. J. 1972 J. Fluid Mech. 53, 575.
Frankel, S. P. 1950 Math Tables and Other Aids to Computation 4, 65.
Grass, A. J. 1971 J. Fluid Mech. 50, 233.
Gurkham, A. A. & Kader, B. A. 1970 Paris Heat Transfer Conf., FC 2, p. 5.
Hanratty, T. J., Chorn, L. G. & Hatziavramidis, D. T. 1977 Phys. Fluids Suppl.
Hatziavramidis, D. T. 1978 Interpretation of the Flow in the Viscous Wall Region as a Driven Flow. Ph.D. thesis, Department of Chemical Engineering, University of Illinois, Urbana.
Hinze, J. O. 1975 Turbulence, 2nd ed.
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 J. Fluid Mech. 50, 133.
Kline, S. J. & Runstadler, P. W. 1959 J. Appl. Mech. 2, 166.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 J. Fluid Mech. 30, 741.
Landahl, M. T. 1972 J. Fluid Mech. 56, 775.
Ladfer, J. 1954 N.A.C.A. Rep. 1174.
Laufer, J. & Narayanan, M. A. B. 1971 Phys. Fluids 14, 182.
Lee, M. K., Eckelman, L. D. & Hanratty, T. J. 1974 J. Fluid Mech. 66, 17.
Mitchell, J. E. & Hanratty, T. J. 1966 J. Fluid Mech. 26, 199.
Mollo-Christensen, E. 1971 A.I.A.A. J. 9, 1217.
Nychas, S. G., Hershey, H. C. & Brodkey, R. S. 1973 J. Fluid Mech. 61, 513.
Offen, G. R. & Kline, S. J. 1975 J. Fluid Mech. 70, 209.
Peaceman, D. W. & Rachford, H. H. 1955 J. Soc. Ind. Appl. Math. 3, 28.
Pearson, C. A. 1965 J. Fluid Mech. 21, 611.
Schraub, F. A. & Kline, S. J. 1965 Thermosci. Div., Mech. Eng. Dept. Rep. No. MD-12. Stanford University.
Schubert, G. & Corcos, G. M. 1967 J. Fluid Mech. 29, 113.
Sternberg, J. 1962 J. Fluid Mech. 13, 241.
Sternberg, J. 1965 AGARD 97.
Taylor, G. I. 1932 Proc. Roy. Soc. A 135, 678.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow.
Ueda, H. & Hinze, J. O. 1975 J. Fluid Mech. 67, 125.
Ueda, H. & Mitzushina, T. 1977 Proc. Symp. on Turbulence in Liquids 41.
Wallace, J. M., Eckelmann, J. & Brodkey, R. S. 1972 J. Fluid Mech. 54, 39.
Willmarth, W. W. & Lu, S. S. 1971 J. Fluid Mech. 55, 481.
Zaric, Z. 1972 4th All Union Heat Mass Transfer Conf.