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The structure of a separating turbulent boundary layer. Part 1. Mean flow and Reynolds stresses

Published online by Cambridge University Press:  20 April 2006

Roger L. Simpson ,
Y.-T. Chew  and
B. G. Shivaprasad
Roger L. Simpson
Affiliation:
Southern Methodist University, Dallas, Texas 75275
Y.-T. Chew
Affiliation:
Southern Methodist University, Dallas, Texas 75275 Present address: Department of Mechanical and Production Engineering, University of Singapore.
B. G. Shivaprasad
Affiliation:
Southern Methodist University, Dallas, Texas 75275
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Abstract

The problem of turbulent-boundary-layer separation due to an adverse pressure gradient is an old but still important problem in many fluid flow devices. Until recent years little quantitative experimental information was available on the flow structure downstream of separation because of the lack of proper instrumentation. The directionally sensitive laser anemometer provides the ability to measure the instantaneous flow direction and magnitude accurately.

The experimental results described here are concerned with a nominally two-dimensional, separating turbulent boundary layer for an airfoil-type flow in which the flow was accelerated and then decelerated until separation. Upstream of separation single and cross-wire hot-wire anemometer measurements are also presented. Measurements in the separated zone with a directionally sensitive laser-anemometer system were obtained for U, V, $\overline{u^2}, \overline{v^2}, - \overline{uv}$, the fraction of time that the flow moves downstream, and the fraction of time that the flow moves away from the wall.

In addition to confirming the earlier conclusions of Simpson, Strickland & Barr (1977) regarding a separating airfoil-type turbulent boundary layer, much new information about the separated region has been gathered. (1) The backflow mean velocity profile scales on the maximum negative mean velocity UN and its distance from the wall N. A U+vs. y+ law-of-the-wall velocity profile is not consistent with this result. (2) The turbulent velocities are comparable with the mean velocity in the backflow, although low turbulent shearing stresses are present. (3) Mixing length and eddy viscosity models are physically meaningless in the backflow and have reduced values in the outer region of the separated flow.

Downstream of fully developed separation, the mean backflow appears to be divided into three layers: a viscous layer nearest the wall that is dominated by the turbulent flow unsteadiness but with little Reynolds shearing stress effects; a rather flat intermediate layer that seems to act as an overlap region between the viscous wall and outer regions; and the outer backflow region that is really part of the large-scaled outer region flow. The Reynolds shearing stress must be modelled by relating it to the turbulence structure and not to local mean velocity gradients. The mean velocities in the backflow are the results of time averaging the large turbulent fluctuations and are not related to the source of the turbulence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 113 , December 1981 , pp. 23 - 51
Copyright
© 1981 Cambridge University Press

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References

Bradshaw, P. 1967 J. Fluid Mech. 29, 625–645.
Bradshaw, P., Ferriss, D. H. & Atwell, N. P. 1967 J. Fluid Mech. 28, 593–616.
Bragg, G. M. 1974 Principles of Experimentation and Measurement. Prentice-Hall.
Cebeci, T., Khalid, E. E. & Whitelaw, J. H. 1979 A.I.A.A. J. 17, 1291–1292.
Cebeci, T. & Smith, A. M. O. 1974 Momentum Transfer in Boundary Layers. Hemisphere.
Coles, D. & Hirst, E. 1969 Computation of Turbulent Boundary Layers – 1968 AFOSR — IFP Stanford Conf. Vol. II, Data Compilation. Dept Mechanical Engng, Stanford Univ.
Coles, D. & Wadcock, A. 1979 A.I.A.A. J. 17, 321–329.
Collins, M. A. & Simpson, R. L. 1978 A.I.A.A. J. 16, 291–292.
Durão, D. F. G. & Whitelaw, J. H. 1975 Proceedings of LDA Symposium Copenhagen, pp. 138–149. P.O. Box 70, DK — 2740 Skovlunde, Denmark.
East, L. F. & Sawyer, W. G. 1979 Proc. NATO-AGARD Fluid Dynamics Symp.
Gartshore, I. S. 1967 J. Fluid Mech. 30, 547–560.
Higuchi, H. & Peake, D. J. 1978 N.A.S.A. Tech. Memo 78531.
Klebanoff, P. 1954 N.A.C.A. Rep. 1247.
Kline, S. J. & McClintock, F. A. 1953 Mech. Engng 75, 3–8.
Mclaughlin, K. D. & Tiederman, W. G. 1973 Phys. Fluids 16, 2082–2088.
Miller, J. A. 1976 Trans. A.S.M.E. I, J. Fluids Engng 98, 550–557.
Murthy, V. W. & Rose, W. C. 1978 A.I.A.A. J. 16, 667–672.
Oka, S. & Kostić, Z. 1972 DISA Information, no. 13, pp. 29–33.
Perry, A. E. & Schofield, W. H. 1973 Phys. Fluids 16, 2068–2074.
Fletcher, R. H. 1978 Trans. A.S.M.E. I, J. Fluids Engng 100, 427–433.
Rubesin, M. W., Okuno, A. F., Mateer, G. G. & Brosh, A. 1975 N.A.S.A. Tech. Memo. X-62, 465.
Sandborn, V. A. & Kline, S. J. 1961 Trans. A.S.M.E. D, J. Basic Engng 83, 317–327.
Sandborn, V. A. & Liu, C. Y. 1968 J. Fluid Mech. 32, 293–304.
Schubauer, G. B. & Klebanoff, P. S. 1951 N.A.C.A. Rep. 1030.
Shiloh, K., Shivaprasad, B. G. & Simpson, R. L. 1981 J. Fluid Mech. 113, 75–90.
Shivaprasad, B. G. & Simpson, R. L. 1981 Trans. A.S.M.E. I, J. Fluids Engng (accepted).
Simpson, R. L. 1976 A.I.A.A. J. 14, 124–126.
Simpson, R. L. 1979 Trans. A.S.M.E. I, J. Fluids Engng (to appear). (Also Project SQUID Rep. SMU-3-PU.)Google Scholar
Simpson, R. L. & Barr, P. W. 1975 Rev. Sci. Instrum. 46, 835–837.
Simpson, R. L. & Chew, Y.-T. 1979 Proceedings of Third Int. Workshop on Laser Velocimetry, pp. 179–196. Hemisphere.
Simpson, R. L., Chew, Y.-T. & Shivaprasad, B. G. 1980 Project SQUID Rep. SMU-4-PU. (To appear as DTIC or NTIS Report.)
Simpson, R. L., Chew, Y.-T. & Shivaprasad, B. G. 1981 J. Fluid Mech. 113, 53–73.
Simpson, R. L. & Collins, M. A. 1978 A.I.A.A. J. 16, 289–290.
Simpson, R. L., Heizer, K. W. & Nasburg, R. E. 1979 Trans. A.S.M.E. I, J. Fluids Engng 101, 381–382.
Simpson, R. L., Strickland, J. H. & Barr, P. W. 1974 Thermal and Fluid Sciences Center, Southern Methodist Univ., Rep. WT-3; also AD-A001115.
Simpson, R. L., Strickland, J. H. & Barr, P. W. 1977 J. Fluid Mech. 79, 553–594.
Spangenberg, W. G., Rowland, W. R. & Mease, N. E. 1967 Fluid Mechanics of Internal Flow (ed. G. Sovran), pp. 110–151. Elsevier.
Strickland, J. H. & Simpson, R. L. 1973 Thermal and Fluid Sciences Center, Southern Methodist Univ., Rep. WT-2; also AD-771170/8GA.
Wood, N. B. 1975 J. Fluid Mech. 67, 769–786.