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Experiments on the structure of turbulence in fully developed pipe flow: interpretation of the measurements by a wave model

Published online by Cambridge University Press:  12 April 2006

T. R. Heidrick ,
S. Banerjee  and
R. S. Azad
T. R. Heidrick
Affiliation:
Atomic Energy of Canada Limited, Whiteshell Nuclear Research Establishment, Pinawa, Manitoba, Canada
S. Banerjee
Affiliation:
Atomic Energy of Canada Limited, Whiteshell Nuclear Research Establishment, Pinawa, Manitoba, Canada
R. S. Azad
Affiliation:
Department of Mechanical Engineering, University of Manitoba, Winnipeg, Manitoba, Canada
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Abstract

This paper is the first of a pair that describe two-point velocity measurements made at various radial positions in water in fully developed pipe flow. Axial velocity fluctuations were measured with hot-film anemometers at two points sufficiently close together that the turbulence structure remained essentially unchanged while passing between them. Phases of the cross-spectra of these velocities were then determined and interpreted in terms of a wave model of the turbulence structure. The model assigns an axial velocity and streamwise inclination to the lines of equal phase of each frequency component of the spectra.

In general, the lines of equal phase for each frequency component are inclined to the wall in the flow direction, the lower frequencies being more inclined than the higher frequencies, though all lines of equal phase at points in the central region of the pipe tend towards the perpendicular. For points near the wall the inclinations are very pronounced.

In the central region, phase velocities of lower frequency components are lower than those for higher frequencies. All phase velocities could be normalized with respect to position by the local mean velocity. The group velocity of small-scale (large wavenumber) disturbances in the core region appears to be approximately constant and of the order of the local mean velocity. This leads to a modified form of Taylor's hypothesis.

The variance in all the measurements increases rapidly in the region y+ < 26. This may be due to the intermittent nature of the flow near the wall (which is discussed in part 2) or to a rotation of the ‘frozen’ pattern by the mean shear field between the two sensors. The magnitude of the latter effect is estimated in this paper and is significant very near the wall. The results in the central region are not affected.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 81 , Issue 1 , 9 June 1977 , pp. 137 - 154
Copyright
© 1977 Cambridge University Press

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References

Bakewell, H. P. & Lumley, J. L. 1967 Phys. Fluids 10, 1880.
Brillouin, L. 1960 Wave Propagation and Group Velocity. Academic Press.
Clauser, F. A. 1956 Turbulent boundary layer. Adv. in Appl. Mech. 4, 2.Google Scholar
Cooley, J. W. & Tukey, J. W. 1965 An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19, 297.Google Scholar
Favre, A. J. 1965 J. Appl. Mech. 22, 241.
Grant, H. L. 1958 J. Fluid Mech. 4, 149.
Heidrick, T. R. 1974 Ph.D. dissertation, University of Manitoba.
Heidrick, T. R., Azad, R. S. & Banerjee, S. 1972 In Turbulence in Liquids (ed. J. L. Zakin & G. K. Patterson), p. 143. University of Missouri-Rolla Press.
Kármán, Th. Von 1931 Collected Works, vol. 11, p. 337 (as referred to in Schlichting 1968).
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1968 Stanford Univ. Rep. MD–20.
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 J. Fluid Mech. 50, 133.
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 J. Fluid Mech. 12, 1.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 J. Fluid Mech. 30, 741.
Kovasznay, L. S. G., Komoda, H. & Vasudeva, B. R. 1962 Proc. Heat Transfer Fluid Mech. Inst., p. 1. Stanford University Press.
Lahey, R. T. & Kline, S. J. 1971 Stanford Univ. Rep. MD-26.
Landahl, M. T. 1976 J. Fluid Mech. 29, 441.
Laufer, J. 1954 N.A.C.A. Rep. no. 1174.
Martin, G. O. & Johanson, L. N. 1965 A.1.Ch.E. J. 11, 29.
Morrison, W. R. B. 1969 Ph.D. thesis, Dept. Mech. Engng, University of Queensland.
Phillips, O. M. 1967 J. Fluid Mech. 27, 131.
Prandtl, L. 1926 Z. angew. Math. Mech. 15, 136. (See also Collected Works, vol. 11, p. 736.)
Roshko, A. 1953 N.A.C.A. Tech. Note no. 2913.
Schlichting, H. 1968 Boundary Layer Theory. McGraw-Hill.
Shih, C. S. 1968 Stat. Res. Service, Can. Dept. Agric., Prog. 5011.
Stegen, G. R. & Van Atta, C. W. 1970 J. Fluid Mech. 42, 689.
Sternberg, J. 1967 Phys. Fluids Suppl. 10, S146.
Taylor, G. I. 1938 Proc. Roy. Soc. A 164, 476.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Townsend, A. A. 1958 IUTAM Boundary Layer Res. Symp. Springer.
Townsend, A. A. 1961 J. Fluid Mech. 11, 97–120.