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The distribution of convection velocities in turbulent pipe flow

Published online by Cambridge University Press:  20 April 2006

P. J. Mcconachie
P. J. Mcconachie
Affiliation:
Department of Mechanical Engineering, University of Queensland, Brisbane, Australia
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Abstract

The structure of fully developed turbulence in a smooth circular tube has been studied for a Reynolds number of 69000 (based on centre-line velocity and radius) and at a distance from the wall of y+ = 70. The data were taken as correlations of the longitudinal component of turbulence in narrow frequency bands, the longitudinal and transverse separations being varied simultaneously. Fourier transformation of these correlations defines power spectral density functions with frequency ω and longitudinal and transverse wavenumbers kx and kz as the independent variables. In this form the data show the distribution of convection velocity among waves of different size and inclination as well as defining the coherence lengths associated with such wave packets.

Essential features of a geometrically similar wave description of the turbulence are discussed, such a model allowing considerable simplification in the description of the turbulence both for two-point and three-point space-time correlations of the velocity field. Morrison & Kronauer (1969) predicted that the wave convection velocity should depend only on total wavenumber k in a specific manner related to the mean velocity profile. The experimentally determined convection velocities contradict this prediction. An alternative formulation for convection velocity involving an additional empirical function of frequency S(ω), fits the data for the range of experimentation. Unfortunately the results provide no information on the functional dependence (if any) of convection velocity on distance from the wall.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 103 , February 1981 , pp. 65 - 85
Copyright
© 1981 Cambridge University Press

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