Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-20T05:27:34.487Z Has data issue: false hasContentIssue false
  • English
  • Français

Structural similarity in radial correlations and spectra of longitudinal velocity fluctuations in pipe flow

Published online by Cambridge University Press:  19 April 2006

K. J. Bullock ,
R. E. Cooper  and
F. H. Abernathy
K. J. Bullock
Affiliation:
Department of Mechanical Engineering, University of Queensland, St Lucia, Queensland 4067
R. E. Cooper
Affiliation:
Department of Mechanical Engineering, University of Queensland, St Lucia, Queensland 4067
F. H. Abernathy
Affiliation:
Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper describes correlation measurements in both broad and narrow frequency bands of the longitudinal velocity fluctuations in fully developed pipe flow at four positions for a reference probe whilst a second probe was traversed radially from deep in the sublayer to a position near the axis with both longitudinal and transverse separations zero (Δx = Δz = 0). Such measurements require that both the Covariant (Co) and Quadrature (Quad) correlations be determined for each of the 15 frequencies used to constrain the wave component λx.

The new data demonstrate that low frequency, large scale turbulence fluctuations extend over the majority of the radial region and that these components are highly correlated. By using a similarity variable kxy, along with a normalized wall distance y/y REF, both correlation functions, i.e. the Co and the Quad components, are shown to collapse. The physical significance of this is discussed.

The broad-band data do not collapse because of the large range of wave sizes. However, the present experiment does show that strong radial correlations exist even when one probe is at y+ = 1. This conflicts with the earlier data of Favre, but agrees with the more recent work of Comte-Bellot. There is a significant amount of turbulent energy in frequencies less than 16 Hz (ω+ = 0·008) for turbulent flows of about 105 Reynolds number.

The spectral function ωΦ(ω) is also presented for a range of y+ values. Using this form for the power spectral density, along with the stochastic wave modelling and similarity arguments of this paper, it is shown how a consistent explanation for the behaviour of these spectra is obtained. In addition some preliminary results from cross-spectral analyses are presented and suggestions made as to their physical significance.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 88 , Issue 3 , 13 October 1978 , pp. 585 - 608
Copyright
© 1978 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abernathy, F. H. 1969 Fundamentals of Boundary Layers. National Science Foundation Film.Google Scholar
Bertschy, J. R. & Abernathy, F. H. 1977 Modifications to laminar and turbulent boundary layers due to the addition of dilute polymer solutions. 2nd International Conference on Drag Reduction, 31 August to 2 September 1977, BHRA Fluid Engineering.Google Scholar
Bradshaw, P. 1971 An Introduction to Turbulence and Its Measurement. Pergamon.Google Scholar
Bremhorst, K. & Walker, T. B. 1973 J. Fluid Mech. 61, 173.Google Scholar
Comte-Bellot, G. 1969 Aero. Res. Counc. Rep. no. 31, 609.Google Scholar
Elliot, J. A. 1972 J. Fluid Mech. 53, 351–383.Google Scholar
Favre, A. J., Gaviglio, J. J. & Dumas, R. 1957 J. Fluid Mech. 2, 313.Google Scholar
Favre, A. J., Gaviglio, J. J. & Dumas, R. 1958 J. Fluid Mech. 3, 344.Google Scholar
Favre, A. J., Gaviglio, J. J. & Dumas, R. 1967 Phys. Fluids Suppl. 10, S138.Google Scholar
Grant, H. L. 1958 J. Fluid Mech. 4, 149.Google Scholar
Grass, A. J. 1971 J. Fluid Mech. 50, 233.Google Scholar
Leslie, D. C. 1973 Developments in the Theory of Turbulence. Oxford University Press.Google Scholar
Lumley, J. L. 1970 Stochastic Tools in Turbulence. Academic Press.Google Scholar
Mcconachie, P. J. 1975 The structure of turbulence in shear flows. Ph.D. thesis, Department of Mechanical Engineering, University of Queensland, Australia.Google Scholar
Mcconachie, P. J. & Bullock, K. J. 1976 J. Phys. E 9, 862–868.Google Scholar
Mcconachie, P. J., Bullock, K. J. & Kronauer, R. E. 1977 Distribution of convection velocities in turbulent pipe flow. Res. Rep. Univ. Queensland no. 2/77.Google Scholar
Morrison, W. R. B. 1968 Measurement of spectrum of turbulence in the wall region of pipe flow. 3rd Australian Conf. Hydraulics and Fluid Mechanics, paper 2622. I.E. Aust.Google Scholar
Morrison, W. B. B. 1969 Two-dimensional frequency-wave number spectra and narrow band shear stress correlations in turbulent pipe flow. Ph.D. thesis, Dept. of Mechanical Engineering, University of Queensland.Google Scholar
Morrison, W. R. B., Bullock, K. J. & Kronauer, R. E. 1971 J. Fluid Mech. 47, 639.Google Scholar
Morrison, W. R. B. & Kronauer, R. E. 1969 J. Fluid Mech. 39, 117.Google Scholar
Paterson, B. W. & Abernathy, F. H. 1972 J. Fluid Mech. 51, 177.Google Scholar
Perry, A. E. & Abell, C. J. 1975 J. Fluid Mech. 67, 257.Google Scholar
Sabot, J. & Comte-Bellot, G. 1972 C. R. hebd. Séanc. Acad. Sci., Paris 275.Google Scholar
Tritton, D. J. 1967 J. Fluid Mech. 28, 439.Google Scholar
Walker, T. B. 1971 Analogue computation of broad-band spectra. Rep. Dept. Mech. Engng Univ. Queensland no. C/71.Google Scholar