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A turbulent flow over a curved hill Part 1. Growth of an internal boundary layer

Published online by Cambridge University Press:  21 April 2006

V. Baskaran ,
A. J. Smits  and
P. N. Joubert
V. Baskaran
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville 3052, Australia Present address: Dept. of Aeronautics, Imperial College, London SW7 2BY, UK.
A. J. Smits
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville 3052, Australia Present address: Dept. of Mechanical & Aerospace Eng., Princeton University, NJ 08544, USA.
P. N. Joubert
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville 3052, Australia
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Abstract

Two experiments were performed to study the response of turbulent boundary layers to sudden changes in surface curvature and pressure gradient. In the first experiment, the behaviour of a boundary layer negotiating a two-dimensional curved hill was examined. Prior to separating on the leeward side of the hill, the layer experienced a short region of concave surface curvature, followed by a prolonged region of convex surface curvature. The corresponding pressure gradient changed from adverse to favourable, and back to adverse. In the second experiment, the flow over a symmetrical wing was studied. This wing had the same profile as the hill with a very similar pressure distribution. The obvious difference between the two experiments was the use of leading and trailing edge plates in the hill flow. The results show that an internal layer forms in the flow over the curved hill, and that this internal layer displays many similarities to the boundary layer observed on the free wing. The internal layer grows as an independent boundary layer beneath a turbulent free-shear layer, and as it develops it establishes its own wall (inner) and wake (outer) regions. The perturbation responsible for initiating the growth of the internal boundary layer seems to be an abrupt change in surface curvature. Once formed, the internal boundary layer dictates the skin-friction distribution and the process of separation over the hill. The effect of the perturbation in wall curvature appears to be different from that due to prolonged convex curvature in that the former affects the flow in the vicinity of the wall instantly, while the latter affects the flow far away from the wall only after the flow turns through some angle. Physical explanations are offered for the qualitative difference between the effects of mild and strong convex curvature, and for the saturated behaviour observed in strongly curved flows. Finally, the results are compared with the behaviour of wind flow over terrestrial hills. In both cases, the internal layer dominates the flow behaviour, even though the scaling laws for the flows over actual hills are not obeyed in the present case. A qualitative comparison reveals that the present internal layer is thicker than that reported in meteorological flows. This appears to be due to the effect of curvature, which perturbs the wake region of the internal layer in the present hill flow, while in meteorological studies the effect of curvature is generally small enough to be neglected.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 182 , September 1987 , pp. 47 - 83
Copyright
© 1987 Cambridge University Press

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References

Abell, C. J. 1977 Scaling laws for pipe flows. Ph.D. thesis, University of Melbourne.
Andreopoulos, J. & Bradshaw, P. 1980 J. Fluid Mech. 100, 639.
Andreopoulos, J. & Wood, D. H. 1982 J. Fluid Mech. 118, 143.
Baskaran, V. 1983 Turbulent flow over a curved hill. Ph.D. thesis, University of Melbourne.
Baskaran, V. & Joubert, P. N. 1984 Mean and turbulent flow data for a boundary layer over a two-dimensional curved hill. Rep. FM-16. Department of Mech. Eng., University of Melbourne.
Blackwelder, R. F. & Kovasznay, L. S. G. 1972 J. Fluid Mech. 53, 61.
Bradley, E. F. 1980 Q. J. R. Met. Soc. 106, 101.
Bradshaw, P. 1973 Effects of streamline curvature on turbulent flow. AGAR Dograph 169.
Bradshaw, P. & Pontikos, N. S. 1985 J. Fluid Mech. 159, 105.
Bradshaw, P. & Unsworth, K. 1974 An improved FORTRAN program for Bradshaw-Ferris-Atwell method of calculating turbulent shear layers. I.C. Aero Rep. 74–02.Google Scholar
Britter, R. E., Hunt, J. C. R. & Richards, K. J. 1981 Q. J. R. Met. Soc. 107, 91.
Castro, I. P. & Bradshaw, P. 1976 J. Fluid Mech. 73, 265.
Chandrsuda, C. & Bradshaw, P. 1981 J. Fluid Mech. 110, 171.
Coles, D. E. 1962 The turbulent boundary layer in a compressible fluid. Rep. R-403-PR. Rand Corp., Santa Monica.
De Brederode, V. & Bradshaw, P. 1974 A note on the empirical constants appearing in the logarithmic law for turbulent wall flows. I.C. Aero Rep. 74–03.Google Scholar
Dean, R. B. & Bradshaw, P. 1976 J. Fluid Mech. 78, 641.
Dumas, R. & Fulachier, L. (eds) 1982 Proc. IUTAM Symp. Structure of Complex Turbulent Shear Flows, Marseille.
Gibson, M. M., Verriopoulos, C. A. & Vlachos, N. S. 1984 Exp. Fluids 2, 17.
Gillis, J. C. & Johnston, J. P. 1983 J. Fluid Mech. 135, 123.
Hall, P. 1984 The Görtler vortex instability mechanism in three-dimensional boundary layers. NASA CR-172370.
Hoffmann, P. H., Muck, K. C. & Bradshaw, P. 1985 J. Fluid Mech. 161, 371.
Jackson, P. S. & Hunt, J. C. R. 1975 Q. J. R. Met. Soc. 101, 929.
Jones, W. P. & Launder, B. E. 1972 J. Fluid Mech. 56, 337.
Kline, S. J., Cantwell, B. J. & Lilley, G. M. (ed) 1982 Proc. 1980–81 AFOSR-HTTM Stanford Conf. on Complex Turbulent Flow, Vol. 1. Thermosciences Div., Stanford University.
Marumo, E., Suzuki, K. & Sato, T. 1978 J. Fluid Mech. 87, 121.
Muck, K. C. 1982 Turbulent boundary layers on mildly curved surfaces. Ph.D. thesis, Imperial College, London
Muck, K. C., Hoffmann, P. H. & Bradshaw, P. 1985 J. Fluid Mech. 161, 347.
Narasimha, R. & Sreenivasan, K. R. 1973 J. Fluid Mech. 61, 417.
Patel, V. C. 1965 J. Fluid Mech. 23, 185.
Perry, A. E. 1982 Hot-Wire Anemometry. Clarendon.
Prabhu, A., Narasimha, R. & Rao, B. N. S. 1982 Structure and mean flow similarity in curved turbulent boundary layers. In Proc. IUTAM Symp. Structure of Complex Turbulent Shear Flows, Marseille (ed. R. Dumas & L. Fulachier)
Prabhu, A. & Sundarasiva Rao, B. N. 1981 Turbulent boundary layers in a longitudinally curved stream. Rep. 81 FM 10. I.I.Sc., Bangalore, India.
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Phys. Fluids 24, 802.
Ramaprian, B. R. & Shivaprasad, B. G. 1978 J. Fluid Mech. 85, 273.
Simpson, R. L. 1979 Some features of strongly accelerated boundary layers. In Second Symp. on Turbulent Shear Flows, Imperial College, London.
Simpson, R. L., Chew, Y. T. & Shivaprasad, B. G. 1981 J. Fluid Mech. 113, 53.
Smits, A. J., Eaton, J. A. & Bradshaw, P. 1979a J. Fluid Mech. 94, 243.
Smits, A. J., Matheson, N. & Joubert, P. N. 1983 J. Ship Res. 27, 147.
Smits, A. J. & Wood, D. H. 1985 Ann. Rev. Fluid Mech. 17, 321.
Smits, A. J., Young, S. T. B. & Bradshaw, P. 1979b J. Fluid Mech. 94, 209.
So, R. M. C. & Mellor, G. L. 1972 An experimental investigation of turbulent boundary layers along curved surfaces. NASA CR-1940.
Spalart, P. R. & Leonard, A. 1985 Direct numerical simulation of equilibrium turbulent boundary layers. In Fifth Symp. on Turbulent Shear Flows, Cornell University, Ithaca, New York.
Tani, I. 1968 In Proc. AFOSR-IFP-Stanford Conf. on Computation of Turbulent Boundary Layers (ed. S. J. Kline, M. V. Morkovin, G. Sovran & D. J. Cockrell), pp. 483–494. Thermosciences Div., Dept. of Mechanical Engineering, Stanford University.
Taylor, P. A. 1977 Boundary-Layer Met. 11, 439.
Tsuji, Y. & Morikawa, Y. 1976 Aero. Q. 27, 15.
Wood, D. H. & Bradshaw, P. 1982 J. Fluid Mech. 122, 57.
Wood, D. H. & Bradshaw, P. 1984 J. Fluid Mech. 139, 347.