Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-20T21:47:03.706Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of turbulent boundary layers at low Reynolds numbers

Published online by Cambridge University Press:  20 April 2006

J. Murlis ,
H. M. Tsai  and
P. Bradshaw
J. Murlis
Affiliation:
Department of Aeronautics, Imperial College, London SW7 2BY Present address: Centre for Overseas Pest Research, Wright's Lane, London W8.
H. M. Tsai
Affiliation:
Department of Aeronautics, Imperial College, London SW7 2BY
P. Bradshaw
Affiliation:
Department of Aeronautics, Imperial College, London SW7 2BY
Get access Rights & Permissions [Opens in a new window]

Abstract

Conditionally sampled hot-wire and ‘cold-wire’ (resistance-thermometer) measure- ments confirm the general flow picture advanced by Falco (1974, 1977, 1980; see also Smith & Abbott 1978) and by Head & Bandyopadhyay (1981; see also Smith & Abbott) on the basis of smoke observations and more limited hot-wire measurements. The probability density function of turbulent-zone lengths in the intermittent region varies rapidly with Reynolds number, supporting the above authors’ finding that the hairpin-vortex ‘typical eddies’ in the viscous superlayer scale on the viscous length ν/uτ, rather than on boundary-layer thickness. However the average turbulent-zone length, deduced as an integral moment of the probability distribution, tends to a constant fraction of the boundary-layer thickness above a momentum-thickness Reynolds number of 5000, which strongly suggests that at high Reynolds numbers the overall shape of the turbulent irrotational interface is controlled by the classical ‘large eddies’ and not by the viscosity-dependent small eddies. The intermittency profile is practically independent of Reynolds number. The second-order structural parameter $\overline{u^2}/\overline{v^2}$ increases strongly with increasing Reynolds number but the triple-product parameters, with the exception of the u-component skewness, vary only slowly with Reynolds number. This behaviour of the intermittency and velocity statistics is most simply explained by supposing that the lengthscale of the large eddies is nearly independent of Reynolds number while their intensity is somewhat lower at low Reynolds number. ‘Typical eddies’ evidently contribute to the Reynolds stresses at low Reynolds number, but it is probable that the large eddies carry most of the triple products at any Reynolds number. Our results confirm the usual finding that the mixing length and dissipation length parameter increase, while the wake component of the velocity profile decreases, as Reynolds number decreases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 122 , September 1982 , pp. 13 - 56
Copyright
© 1982 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

Andreopoulos, J. 1978 Symmetric and asymmetric near wake of a flat plate. Ph.D. thesis, Imperial College, London
Andreopoulos, J. & Bradshaw, P. 1980 Measurements of interacting turbulent shear layers in the near wake of a flat plate. J. Fluid Mech. 100, 639.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Bradshaw, P. 1971 An Introduction to Turbulence and Its Measurement. Pergamon.
Bradshaw, P. 1972 Two more low-turbulence wind tunnels driven by centrifugal blowers. Imperial College Aero. Rep. no. 72–10.Google Scholar
Bradshaw, P. 1974 The effect of mean compression or dilatation on the turbulence structure of supersonic boundary layers. J. Fluid Mech. 63, 449.Google Scholar
Bradshaw, P. & Murlis, J. 1974 On the measurement of intermittency in turbulent flows. Imperial College Aero. Rep. no. 74–04.Google Scholar
Brederode, V. & Bradshaw, P. 1978 Influence of the side walls on the turbulent centre plane boundary layer in a square duct. Trans. A.S.M.E. I: J. Fluids Engng 100, 91Google Scholar
Brown, G. L. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20, S243.Google Scholar
Bushnell, D. M., Cary, A. M. & Holley, B. B. 1975 Mixing length in low Reynolds number compressible turbulent boundary layers. A.I.A.A. J. 13, 1119.Google Scholar
Castro, I. P. 1973 A highly distorted turbulent free shear layer. Ph.D. thesis, Imperial College, London
Castro, I. P. & Bradshaw, P. 1976 The turbulence structure of a highly curved mixing layer. J. Fluid Mech. 73, 265.Google Scholar
Chen, C. H. P. & Blackwelder, R. F. 1978 Large scale motion in a boundary layer: a study using temperature contamination. J. Fluid Mech. 89, 1.Google Scholar
Chevray, R. & Tutu, N. K. 1978 Intermittency and preferential transport of heat in a round jet. J. Fluid Mech. 88, 133.Google Scholar
Coles, D. E. 1962 The turbulent boundary layer in a compressible fluid. Rand. Rep. R403–PR, ARC 24473: Appendix A: A manual of experimental boundary layer practice for low speed flow.Google Scholar
Coles, D. E. & Hirst, E. A. (Eds.) 1969 Proc. 1968 AFOSR-IFP-Stanford Conf. on computation of turbulent boundary layers. Thermosciences Division, Stanford University.
Corrsin, S. & Kistler, A. L. 1955 Free stream boundaries of turbulent flows. NACA Rep. no. 1244.Google Scholar
Dean, R. B. 1977 A single formula for the complete velocity profile in a turbulent boundary layer. Trans. A.S.M.E. I: J. Fluids Engng 98, 723Google Scholar
Dean, R. B. & Bradshaw, P. 1976 Measurements of interacting shear layers in a duct. J. Fluid Mech. 78, 641.Google Scholar
Falco, R. E. 1974 Some comments on turbulent boundary layer structure inferred from the movements of a passive contaminant. A.I.A.A. Paper no. 74–99.
Falco, R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluid Suppl. 20, S124.Google Scholar
Falco, R. E. 1980 Combined simultaneous flow visualization/hot-wire anemometry for the study of turbulent flows. Trans. A.S.M.E. I: J. Fluids Engng 102. 174.Google Scholar
Fiedler, H. (ed.) 1978 Structure and Mechanisms of Turbulence I, II. Lecture Notes in Physics, vols. 75, 76. Springer.
Fiedler, H. & Head, M. R. 1966 Intermittency measurements in the turbulent boundary layer. J. Fluid Mech. 25, 719.Google Scholar
Finley, P. J., Phoe, K. C. & Poh, C. J. 1966 Velocity measurements in a thin turbulent water layer. Houille Blanche 21, 713.Google Scholar
Grant, H. L. 1958 The large eddies of turbulent motion J. Fluid Mech. 4, 149.Google Scholar
Green, J. E. 1971 A note on the turbulent boundary layer at low Reynolds number in compressible flow at constant pressure. Personal communication.
Hancock, P. E. 1980 The effects of free stream turbulence on turbulent boundary layers. Ph.D. thesis, Imperial College, London
Head, M. B. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structures. J. Fluid Mech. 107, 297.Google Scholar
Hedley, T. B. & Keffer, J. F. 1974a Turbulent/non-turbulent decisions in an intermittent flow. J. Fluid Mech. 64, 675.Google Scholar
Hedley, T. B. & Keffer, J. F. 1974b Some turbulent/non-turbulent properties of an intermittent flow. J. Fluid Mech. 64, 645.Google Scholar
Huffman, G. D. & Bradshaw, P. 1972 A note on von Kárman's constant in low Reynolds number turbulent flows. J. Fluid Mech. 53, 45.Google Scholar
Inman, P. N. & Bradshaw, P. 1981 Mixing length in low Reynolds number, low speed turbulent boundary layers. A.I.A.A. J. 19, 653.Google Scholar
Klebanoff, P. S. 1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA Rep. no. 1247.Google Scholar
Kline, S. J. & Falco, R. E. 1980 Summary of the AFOSR/MSU Research Specialists Workshop on Coherent Structure in Turbulent Boundary Layers. AFOSR TR-80–0290.
Kovasznay, L. S. G., Kibens, V. & Blackwelder, R. F. 1970 Large scale motions in the intermittent region of a turbulent boundary layer. J. Fluid Mech. 41, 283.Google Scholar
Larue, J. C. & Libby, P. A. 1974 Temperature fluctuations in the plane turbulent wake. Phys. Fluids 17, 1956.Google Scholar
Mabey, D. G. 1977 Some observations on the wake component of the velocity profiles of turbulent boundary layers at subsonic and supersonic speeds. RAE Tech. Rep. TR 77004.Google Scholar
Mabey, D. G. 1979 Aero. Q. 30, 590.
Muck, K. C. 1980 Comparison of various schemes for the generation of the turbulent intermittency function. Imperial College Aero. Rep. no. 80–03.Google Scholar
Murlis, J. 1975 The structure of a turbulent boundary layer at low Reynolds number. Ph.D. thesis, Imperial College, London
Paizis, S. T. & Schwartz, W. H. 1974 An investigation of the topography and motion of the turbulent interface. J. Fluid Mech. 63, 315.Google Scholar
Patel, V. C. 1965 Calibration of the Preston tube and limitations on it use in pressure gradients. J. Fluid Mech. 23, 185.Google Scholar
Preston, J. H. 1958 The minimum Reynolds number for a turbulent boundary layer and the selection of a transition device. J. Fluid Mech. 3, 373.Google Scholar
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Turbulent boundary layers at low Reynolds numbers. Phys. Fluids 24, 802.Google Scholar
Sandborn, V. A. 1959 Measurements of intermittency of turbulent motion in a boundary layer. J. Fluid Mech. 6, 221.Google Scholar
Simpson, R. L. 1970 Characteristics of turbulent boundary layers at low Reynolds numbers with and without transpiration. J. Fluid Mech. 42, 769.Google Scholar
Smith, C. R. & Abbott, D. E. (eds.) 1978 Coherent Structure of Turbulent Boundary Layers: Proc. AFOSR/Lehigh University Workshop. Mech. Engng Dept. Lehigh University.
Theodorsen, T. 1952 Mechanism of turbulence. In Proc. 2nd Midwestern Conference on Fluid Mechanics, Ohio State University, p. 1.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow, Cambridge University Press.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
Weir, A. D. & Bradshaw, P. 1974 Apparatus and programs for digital analysis of fluctuating quantities in turbulent flow. Imperial College Aero. Rep. no. 74–09.Google Scholar
Weir, A. D., Wood, D. H. & Bradshaw, P. 1981 Interacting turbulent shear layers in a plane jet. J. Fluid Mech. 107, 237.Google Scholar
Wieghardt, K. 1944 Zum Reibungswiderstand rauher Platten. Kaiser-Wilhelm-Institut für Strömungsforschung, Göttingen, UM 6612.
Willmarth, W. W. 1975 Structure of turbulence in boundary layers. Adv. Appl. Mech. 15, 159.Google Scholar