Hostname: page-component-7c8c6479df-7qhmt Total loading time: 0 Render date: 2024-03-28T22:26:50.224Z Has data issue: false hasContentIssue false

Low-Reynolds-number turbulent boundary layers

Published online by Cambridge University Press:  26 April 2006

Lincoln P. Erm
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria 3052, Australia Present address: Aeronautical Research Laboratory, 506 Lorimer Street, Port Melbourne, Victoria, 3207, Australia.
Peter N. Joubert
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria 3052, Australia

Abstract

An investigation was undertaken to improve our understanding of low-Reynolds-number turbulent boundary layers flowing over a smooth flat surface in nominally zero pressure gradients. In practice, such flows generally occur in close proximity to a tripping device and, though it was known that the flows are affected by the actual low value of the Reynolds number, it was realized that they may also be affected by the type of tripping device used and variations in free-stream velocity for a given device. Consequently, the experimental programme was devised to investigate systematically the effects of each of these three factors independently. Three different types of device were chosen: a wire, distributed grit and cylindrical pins. Mean-flow, broadband-turbulence and spectral measurements were taken, mostly for values of Rθ varying between about 715 and about 2810. It was found that the mean-flow and broadband-turbulence data showed variations with Rθ, as expected. Spectra were plotted using scaling given by Perry, Henbest & Chong (1986) and were compared with their models which were developed for high-Reynolds-number flows. For the turbulent wall region, spectra showed reasonably good agreement with their model. For the fully turbulent region, spectra did show some appreciable deviations from their model, owing to low-Reynolds-number effects. Mean-flow profiles, broadband-turbulence profiles and spectra were found to be affected very little by the type of device used for Rθ ≈ 1020 and above, indicating an absence of dependence on flow history for this Rθ range. These types of measurements were also compared at both Rθ ≈ 1020 and Rθ ≈ 2175 to see if they were dependent on how Rθ was formed (i.e. the combination of velocity and momentum thickness used to determine Rθ). There were noticeable differences for Rθ ≈ 1020, but these differences were only convincing for the pins, and there was a general overall improvement in agreement for Rθ ≈ 2175.

Type
Research Article
Copyright
© 1991 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

Barlow, R. S. & Johnston, J. P. 1988 Structure of a turbulent boundary layer on a concave surface. J. Fluid Mech. 191, 137.Google Scholar
Brederrode, V. De & Bradshaw, P. 1974 A note on the empirical constants appearing in the logarithmic law for turbulent wall flows. Imperial College Aero. Rep. 74–03. Dept. Aeronautics, IC, London.Google Scholar
Coles, D. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191.Google Scholar
Coles, D. E. 1962 The turbulent boundary layer in a compressible fluid. Appendix A: A manual of experimental boundary-layer practice for low-speed flow. Rand Rep. R-403-PR.Google Scholar
Coles, D. E. 1968 The young persons guide to the data. In Proc. Computation of Turbulent Boundary Layers, 1968, AFOSR-IFP-Stanford Conf., Vol. II (ed. D. E. Coles & E. A. Hirst).
Erm, L. P. 1988 Low-Reynolds-number turbulent boundary layers. Ph.D. thesis, University of Melbourne.
Erm, L. P., Smits, A. J. & Joubert, P. N. 1987 Low Reynolds number turbulent boundary layers on a smooth flat surface in a zero pressure gradient. In Turbulent Shear Flows 5 (ed. F. Durst, B. E. Launder, J. L. Lumley, F. W. Schmidt & J. H. Whitelaw). Springer. See also Proc. Fifth Symp. on Turbulent Shear Flows, Cornell University, Ithaca, New York, Aug. 7–9, 1985.
Banville, P. S. 1977 Drag and turbulent boundary layer of flat plates at low Reynolds numbers. J. Ship Res. 21, 30.Google Scholar
Huffman, G. D. & Bbadshaw, P. 1972 A note on von KaArmaAn's constant in low Reynolds number turbulent flows. J. Fluid Mech. 53, 45.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. CR Acad. Sci. URS8 30, 301.Google Scholar
Kovasznay, L. S. G. 1948 Spectrum of locally isotropic turbulence. J. Aero. Sci. 15, 745.Google Scholar
LigranI, P. M. & Bbadshaw, P. 1987 Spatial resolution and measurement of turbulence in the viscous sublayer using subminiature hot-wire probes. Exps. Fluids 5, 407.Google Scholar
Macmillan, F. A. 1956 Experiments on Pitot-tubes in shear flow. Aero. Res. Counc. R. & M. 3028.Google Scholar
Murlis, J. 1975 The structure of a turbulent boundary layer at low Reynolds number. Ph.D. thesis, Imperial College, London
Murlis, J., Tsai, H. M. & Bbadshaw, P. 1982 The structure of turbulent boundary layers at low Reynolds numbers. J. Fluid Mech. 122, 13.Google Scholar
Patel, V. C. 1965 Calibration of the Preston tube and limitations on its use in pressure gradients. J. Fluid Mech. 23, 185.Google Scholar
Pery, A. E. 1982 Hot-Wire. Anemometry. Oxford University Press.
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163.Google Scholar
Perry, A. E. & Li, J. D. 1990 Experimental support for the attached-eddy hypothesis in zero-pressure-gradient turbulent boundary layers. J. Fluid Mech. 218, 405.Google Scholar
Perry, A. E., Lim, K. L. & Henbest, S. M. 1985 A spectral analysis of smooth flat-plate boundary layers. In Proc. Fifth Symp. on Turbulent Shear Flows, Cornell University, Ithaca, New York, Aug. 7–9, 1985.
Perry, A. E., Lim, K. L. & Henbest, S. M. 1987 An experimental study of the turbulence structure in smooth- and rough-wall boundary layers. J. Fluid Mech. 177, 437.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. 1978 The turbulent boundary layer at low Reynolds number. Ph.D. thesis, University of Maryland.
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Turbulent boundary layer at low Reynolds number. Phys. Fluids 24, 802.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
Smits, A. J., Matheson, N. & JOubert, P. N. 1983 Low-Reynolds-number turbulent boundary layers in zero and favourable pressure gradients. J. Ship Res. 27, 147.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to RtH = 1410. J. Fluid Mech. 187, 61.Google Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164, 476.Google Scholar
Witt, H. T., Watmuff, J. H. & Joubert, P. N. 1983 Some effects of rotation on turbulent boundary layers. In Proc. Fourth Symp. on Turbulent Shear Flows, Karlsruhe, F. R. Germany, Sep. 12–14, 1983.