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The effects of curvature on sheared turbulence

Published online by Cambridge University Press:  26 April 2006

A. G. L. Holloway  and
S. Tavoularis
A. G. L. Holloway
Affiliation:
Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada K1N 6N5 Present address: Department of Mechanical engineering, University of New brunswick, Fredericton, Canada E3B 5A3.
S. Tavoularis
Affiliation:
Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada K1N 6N5
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Abstract

The present experiments are an extension of previous studies on nearly homogeneous, parallel, shear flows and represent an attempt to study the effects of curvature on sheared turbulence in relative isolation from wall and entrainment effects. Uniformly sheared turbulence was allowed to reach a state of transverse statistical homogeneity in a straight rectangular duct: it was then passed into a curved duct, also of rectangular cross-section. The near homogeneity of the turbulence and the near uniformity of the shear were preserved. In the present experiments, the parameter S = (Uc/Rc)(dU/dn) spanned a wide range, from approximately -0.50 to over 1.0 (Uc is the centreline velocity, dU/dn the mean shear and Rc the radius of curvature on the centreline of the duct). Variation of S was achieved by using two curved tunnel sections as well as by adjusting the shear. Measurements indicate that the growth of the turbulent stresses and lengthscales was enhanced for S < 0 and suppressed for S > 0. For S > 0.05, the stresses decayed. In cases where sufficiently large total strain was achieved, the stresses seemed to grow or decay roughly exponentially and to develop in a quasi-self-preserving manner. The magnitude of the dimensionless shear stress decreased monotonically with increasing S, while, for sufficiently large positive values of S, this quantity reversed sign, to achieve the same sense as the mean shear. Measurements of the integral lengthscales and the Taylor microscales are presented and their dependence upon curvature discussed. The results in ‘mildly curved’ flows are used to derive approximate expressions for the dependence upon S of the various terms in the Reynolds stress equations, including the pressure-strain rate covariance tensor.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 237 , April 1992 , pp. 569 - 603
Copyright
© 1992 Cambridge University Press

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References

Barlow, R. S. & Johnston, J. P. 1988a Structure of a turbulent boundary layer on a concave surface. J. Fluid Mech. 191, 191–137.Google Scholar
Barlow, R. S. & Johnston, J. P. 1988b Local effects of large-scale eddies on bursting in a concave boundary layer. J. Fluid Mech. 191, 191–177.Google Scholar
Bradshaw, P. 1973 Effects of Streamline Curvature on Turbulent Flow. AGARDograph No. 169. NATO.Google Scholar
Castro, I. P. & Bradshaw, P. 1976 The turbulence structure of a highly curved mixing layer. J. Fluid Mech. 73, 265–304.Google Scholar
Champagne, F. H., Harris, V. G. & Corrsin, S. 1970 Experiments on nearly homogeneous turbulent shear flow. J. Fluid Mech. 41, 81–139.Google Scholar
Corrsin, S. 1963 Turbulence: Experimental Methods. Handbuch der Physik, Vol. 8, Part 2 (ed. S. FluUgge & C. Truesdell), pp. 523–590. Springer.
Dean, W. R. 1928 Fluid motion in a curved channel. Proc. R. Soc. Lond. A 121, 402–420.Google Scholar
Eskinazi, S. & Erian, F. F. 1969 Energy reversal in turbulent flows. Phys. Fluids 12, 1988–1998.Google Scholar
Eskinazi, S. & Yeh, H. 1956 Fully developed turbulent flow in a curved channel. J. Aeronaut. Sci. 23, 23–35.Google Scholar
Gibson, M. M. & Verriopoulos, C. A. 1984 Turbulent boundary layer on a mildly curved convex surface: Part 2, Temperature field measurements. Exp. Fluids 2, 73–80.Google Scholar
Gibson, M. M., Verriopoulos, C. A. & Vlachos, K. S. 1984 Turbulent boundary layer on a mildly curved convex surface: Part 1, Mean flow and turbulence measurements. Exp. Fluids 2, 17–24.Google Scholar
Gillis, J. C. & Johnston, J. P. 1983 Turbulent boundary layer and structure on a convex wall and its redevelopment on a flat wall. J. Fluid Mech. 135, 123–153.Google Scholar
GoUrtler, H. 1940 uUber eine dreidimensionale InstabilitaUt laminarer Grenzschichten an konkaven WaUnden. Nachr. Ges. GoUttingen, Math.-Phys. K1, 2.Google Scholar
Harris, V. G., Graham, J. A. H. & Corrsin, S. 1977 Further experiments in nearly homogeneous turbulent shear flow. J. Fluid Mech. 81, 657–687.Google Scholar
Hinze, J. O. 1975 Turbulence, 2nd edn. McGraw Hill.
Hoffman, P. H., Muck, K. C. & Bradshaw, P. 1985 The effect of concave surface curvature on turbulent boundary layers. J. Fluid Mech. 161, 371–403.Google Scholar
Holloway, A. G. L. 1989 The effects of curvature on sheared turbulence. Ph.D. dissertation, University of Ottawa.
Hunt, I. A. & Joubert, P. N. 1979 Effects of small streamline curvature section turbulent duct flow. J. Fluid Mech. 91, 633–659.Google Scholar
Karnik, U. & Tavoularis, S. 1987 Generation and manipulation of uniform shear with the use of screens. Exp. Fluids 5, 247–254 (referred to herein as KT).Google Scholar
Komori, S., Ueda, H., Ogino, F. & Mizushina, T. 1983 Turbulence structure in stably stratified open-channel flow. J. Fluid Mech. 130, 13–26.Google Scholar
Koyama, H. S. 1981 Turbulent shear flows behind cylinder and sphere in curved channels. In Proc. 3rd Symp. Turbulent Shear Flows, Davis, USA, pp. 4.12–4.16.
Margolis, D. P. & Lumley, J. L. 1965 Curved turbulent mixing layer. Phys. Fluids 8, 1775–1785.Google Scholar
Meroney, R. N. & Bradshaw, P. 1975 Turbulent boundary layer growth over a longitudinally curved surface. AIAA J. 13, 1448–1453.Google Scholar
Moser, R. D. & Moin, P. 1987 The effects of curvature in wall bounded turbulent flows. J. Fluid Mech. 175, 479–510.Google Scholar
Muck, K. C., Hoffman, P. H. & Bradshaw, P. 1985 The effect on convex surface curvature on turbulent boundary layers. J. Fluid Mech. 161, 347–369.Google Scholar
Kakano, S., Takahashi, A., Shizawa, T. & Honomi, S. 1981 Effects of stable and unstable free streams on a turbulent flow over a concave surface. In Proc. 3rd Symp. Turbulent Shear Flows, Davis, USA, pp. 4.18–4.23.
Ramaprian, B. R. & Shivaprasad, B. G. 1978a Turbulence measurements in boundary layers along mildly curved surfaces. Trans. ASME I: J. Fluids Engng 100, 37–46Google Scholar
Ramaprian, B. R. & Shivaprasad, B. G. 1978b The structure of turbulent boundary layers along mildly curved surfaces. J. Fluid Mech. 85, 85–272.Google Scholar
Ramaprian, B. R. & Shivaprasad, B. G. 1982 The instantaneous structure of mildly curved turbulent boundary layers. J. Fluid Mech. 115, 39–58.Google Scholar
Rayleigh, Lord 1916 On the dynamics of revolving fluids. Scientific Papers, Vol. 6, 447–453.
Savill, A. M. 1983 The turbulence structure of a highly curved two-dimensional wake. In Structure of Complex Turbulent Shear Flow, IUTAM Symp., Marseille (ed. R. Dumas & L. Fulachier). Springer.
Shizawa, T. & Honami, S. 1985 Experiments on turbulent boundary layers over a concave surface - Response of turbulence to curvature. In Proc. 5th Symp. Turbulent Shear Flows, Ithaca, USA, pp. 21.1–21.6.
Smits, A. J., Young, S. T. P. & Bradshaw, P. 1979 The effect of short regions of hish surface curvature on turbulent boundary layers. J. Fluid Mech. 94, 209–242.Google Scholar
So, R. M. C. & Mellor, G. L. 1973 Experiment on convex curvature effects in turbulent boundary layers. J. Fluid Mech. 60, 43–62.Google Scholar
So, R. M. C. & Mellor, G. L. 1975 Experiment on turbulent boundary layers on a concave wall. Aeronaut. Q., February, 25–40.Google Scholar
Synge, J. L. 1933 The stability of heterogeneous liquids. Trans. R. Soc. Canada 27, Series 3, Section 3, 1–18.Google Scholar
Synge, J. L. 1938 On the stability of a viscous liquid between rotating coaxial cylinders. Proc. R. Soc. Lond. 167, 250–256.Google Scholar
Tavoularis, S. 1985 Asymptotic laws for transversely homogeneous turbulent shear flow. Phys. Fluids 28, 999–1001.Google Scholar
Tavoularis, S. & Corrsin, S. 1981 Experiments in a nearly homogeneous shear flow with a uniform mean temperature gradient. Part 1. J. Fluid Mech. 104, 311–347.Google Scholar
Tavoularis, S. & Karnik, U. 1989 Further experiments on the evolution of turbulent stresses and scales in uniformly sheared turbulence. J. Fluid Mech. 204, 457–478 (referred to herein as TK).Google Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. Roy. Soc. Lond. A 223, 289–343.Google Scholar
Wyngaard, J. C., Tennekes, H., Lumley, J. L. & Margolis, D. P. 1968 Structure of turbulence in a curved mixing layer. Phys. Fluids 11, 1251–1253.Google Scholar