Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-01T11:12:45.242Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence in plane channel flows

Published online by Cambridge University Press:  20 April 2006

M. M. M. El Telbany  and
A. J. Reynolds
M. M. M. El Telbany
Affiliation:
Department of Mechanical Engineering, Brunel University, Uxbridge, Middlesex, England
A. J. Reynolds
Affiliation:
Department of Mechanical Engineering, Brunel University, Uxbridge, Middlesex, England
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper complements an earlier study of the mean velocities in turbulent flows in a flat channel, one of whose walls can move relative to the other, so that the role of the stress gradient within the wall layers can be varied widely and in a controlled manner.

Measurements of longitudinal, normal and lateral velocity fluctuation intensities (u′,v′,w′) and of shear stresses have been made in essentially fully developed flows established by various combinations of pressure gradient and wall velocity The channel aspect ratio (breadth/height) has been varied between 12 and 28 and the development ratio (development length/height) between 20 and 45. The introduction of a turbulence-generating grid at the entrance to the duct increases the effective development length.

The study has considered twenty-six flows that are two-dimensional in the mean, which have been established by blowing and relative motion either in the same direction or directly opposed. Empirical descriptions, based on similarity laws incorporating either the wall stress or the local stress, are developed for the turbulence near the walls and in the core. The profiles of u′, v′ and w′ coalesce, to a reasonable approximation, when normalized with appropriate length and velocity scales. Extensive ‘plateau’ regions are identified, in which the scaled intensities are sensibly constant.

A number of quantities characteristic of the structure of the turbulence are considered, in order to elucidate the effect of the stress gradient on the wall layer, and stages in the erosion of the constant-stress layer are identified.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 111 , October 1981 , pp. 283 - 318
Copyright
© 1981 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

Acrivlellis, M. 1977 Hot-wire measurements in flows of low and high turbulence intensity. DISA Information no. 22.Google Scholar
Alcaraz, E., Charnay, G. & Mathieu, J. 1975 Turbulent energy balance in a two-dimensional wall jet developing over a convex surface. C.R. Acad. Sci. Paris 280, 613–616.Google Scholar
Badri Narayanan, M. A. & Ramjee, V. 1969 On the criteria for reverse transition in a two-dimensional boundary-layer flow. J. Fluid Mech. 35, 225–241.Google Scholar
Bradshaw, P. 1969 A note on reverse transition. J. Fluid Mech. 35, 387–390.Google Scholar
Bradshaw, P., Ferris, D. H. & Atwell, H. P. 1967 Calculation of boundary-layer development using the turbulent energy equation. J. Fluid Mech. 28, 593.Google Scholar
Champagne, F. H. & Sleicher, C. A. 1967 Turbulence measurements with inclined hot-wires. II. Hot-wire response equations. J. Fluid Mech. 28, 177–182.Google Scholar
Champagne, F. H., Sleicher, C. A. & Wehrmann, O. H. 1967 Turbulence measurements with inclined hot-wires. I. Heat transfer measurements with inclined hot-wires. J. Fluid Mech. 28, 153–175.Google Scholar
Comte-Bellot, G. 1965 Ecoulement turbulent entre deux parois parallèles. Publications Scientifiques et Techniques du Ministère de l'air no. 419.Google Scholar
El Telbany, M. M. M. & Reynolds, A. J. 1980 Velocity distributions in plane turbulent channel flows. J. Fluid Mech. 100, 1–29.Google Scholar
El Telbany, M. M. M. & Reynolds, A. J. 1981a The structure of plane Couette flow. Trans. A.S.M.E. I, J. Fluids Engng (submitted).
El Telbany, M. M. M. & Reynolds, A. J. 1981b The empirical description of turbulent channel flows. Int. J. Heat Mass Transfer (in the press).
Hanjalić, K. 1970 Two-dimensional asymmetric turbulent flow in ducts. Ph.D. thesis, University of London.
Hanjalić, K. & Launder, B. E. 1972 Fully developed asymmetric flow in a plane channel. J. Fluid Mech. 51, 301–335.Google Scholar
Hatziavramidis, D. T. & Hanratty, T. J. 1979 The representation of the viscous wall region by a regular eddy pattern. J. Fluid Mech. 95, 655–679.Google Scholar
Hinze, J. O. 1975 Turbulence. New York: McGraw-Hill.
Hussain, A. K. M. F. & Reynolds, W. C. 1975 Measurements in fully developed turbulent channel flow. Trans. A.S.M.E. I, J. Fluid Engng 97, 568–578.Google Scholar
Kanevce, G. & Oka, S. 1973 Correcting hot wire readings for influence of fluid temperature variations. DISA Information no. 15.Google Scholar
Klebanoff, P. S. 1955 Characteristic of turbulence in a boundary layer with zero pressure gradient. N.A.C.A. Tech. Note, 1247.
Laufer, J. 1951 Investigation of turbulent flow in a two-dimensional channel. N.A.C.A. Rep. 1053.Google Scholar
Laufer, J. 1954 The structure of turbulence in fully developed pipe flow. N.A.C.A. Rep. 1174.Google Scholar
Launder, B. E. & Stinchcombe, H. S. 1967 Non-normal similar turbulent boundary layers. Mech. Engng Dept. Imperial College, Rep. TWF/TN/21.Google Scholar
Lawn, C. J. 1969 Turbulence measurements with hot wires at B.N.L. CEGB, Research and Development Dept., Rep. RD/B/M1277.Google Scholar
Morrison, W. R. B. & Kronauer, R. E. 1969 Structural similarity for fully developed turbulence in smooth tubes. J. Fluid Mech. 39, 117–141.Google Scholar
Pavel, V. C. & Head, M. R. 1968 Reversion of turbulent to laminar flow. J. Fluid Mech. 34, 371–392.Google Scholar
Perry, A. E. & Abell, C. J. 1977 Asymptotic similarity of turbulence structures in smooth and rough-walled pipes. J. Fluid Mech. 79, 785–799.Google Scholar
Robertson, J. M. & Johnson, H. F. 1970 Turbulence structure in plane Couette flow. J. Engng Mech., A.S.C.E. 96, 1171–1182.Google Scholar
Spettel, F., Mathieu, J. & Brison, J. F. 1972 Tensions de Reynolds et production d’énergie cinétique turbulente dans les jets pariéteux sur parois planes et concaves. J. Méc. 11, 403–425.Google Scholar
Tailland, A. & Mathieu, J. 1967 Jet pariétal. J. Méc. 6, 103–131.Google Scholar
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97–120.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn, pp. 150–158. Cambridge University Press.
Webster, C. A. 1962 A note on the sensitivity to yaw of a hot wire anemometer. J. Fluid Mech. 13, 307–312.Google Scholar