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The structure of turbulent boundary layers along mildly curved surfaces

Published online by Cambridge University Press:  12 April 2006

B. R. Ramaprian  and
B. G. Shivaprasad
B. R. Ramaprian
Affiliation:
Institute of Hydraulic Research, University of Iowa, Iowa City
B. G. Shivaprasad
Affiliation:
Aeronautical Engineering Department, Indian Institute of Science, Bangalore
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Abstract

This paper describes a detailed study of the structure of turbulence in boundary layers along mildly curved convex and concave surfaces. The surface curvature studied corresponds to δ/Rw = ± 0·01, δ being the boundary-layer thickness and Rw the radius of curvature of the wall, taken as positive for convex and negative for concave curvature. Measurements of turbulent energy balance, autocorrelations, auto- and cross-power spectra, amplitude probability distributions and conditional correlations are reported. It is observed that even mild curvature has very strong effects on the various aspects of the turbulent structure. For example, convex curvature suppresses the diffusion of turbulent energy away from the wall, reduces drastically the integral time scales and shifts the spectral distributions of turbulent energy and Reynolds shear stress towards high wavenumbers. Exactly opposite effects, though generally of a smaller magnitude, are produced by concave wall curvature. It is also found that curvature of either sign affects the v fluctuations more strongly than the u fluctuations and that curvature effects are more significant in the outer region of the boundary layer than in the region close to the wall. The data on the conditional correlations are used to study, in detail, the mechanism of turbulent transport in curved boundary layers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 85 , Issue 2 , 21 March 1978 , pp. 273 - 303
Copyright
© 1978 Cambridge University Press

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References

Badri Narayanan, M. A., Rajagopalan, S. & Narasimha, R. 1974 Some experimental investigations of the fine scale structure of turbulence. Dept. of Aero. Engng, Indian Inst. Sci., Bangalore, Rep. no. 74 FM 15.Google Scholar
Bradshaw, P. 1967 The turbulence structure of equilibrium boundary layers. J. Fluid Mech. 29, 625.Google Scholar
Bradshaw, P. 1969 The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36, 177.Google Scholar
Bradshaw, P. 1973 Effects of streamline curvature on turbulent flow. AGARDograph no. 169.
Castro, I. P. & Bradshaw, P. 1976 The turbulence structure of a highly curved mixing layer. J. Fluid Mech. 73, 267.Google Scholar
Ellis, L. B. & Joubert, P. N. 1974 Turbulent shear flow in a curved duct. J. Fluid Mech. 62, 65.Google Scholar
Eskinazi, S. & Yeh, H. 1956 An investigation on fully developed turbulent flows in a curved channel. J. Aero. Sci. 23, 23.Google Scholar
Hinze, J. O. 1959 Turbulence. McGraw-Hill.
Irwin, H. P. A. H. & Smith, P. A. 1975 Prediction of the effect of streamline curvature on turbulence. Phys. Fluids 18, 624.Google Scholar
Johnston, J. P. & Eide, S. A. 1976 Turbulent boundary layers on centrifugal compressor blades: prediction of the effects of surface curvature and rotation. A.S.M.E. 21st Ann. Int. Gas Turbines Con., New Orleans, paper 76-FE-10.
Klebanoff, P. S. 1954 Characteristics of turbulence in a boundary layer with zero pressure gradient. N.A.C.A. Tech. Note no. 3178.Google Scholar
Laufer, J. 1954 The structure of turbulence in a fully developed pipe flow. N.A.C.A. Tech. Note no. 2954.Google Scholar
Lu, S. S. & Willmarth, W. W. 1973 Measurements of the structure of Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60, 481.Google Scholar
Magrab, E. B. & Blomquist, D. S. 1971 The Measurement of Time-Varying Phenomena. Interscience.
Meroney, R. N. & Bradshaw, P. 1975 Turbulent boundary layer growth over a longitudinally curved surface. A.I.A.A. J. 13, 1448.Google Scholar
Papailiou, K. D., Nurzia, F. & Satta, A. 1970 The inclusion of surface curvature effects in the calculation of the turbulent boundary layer with integral methods. Von Kármán Inst. Fluid Dyn. Internal Note no. 37.Google Scholar
Patel, V. C. 1968 The effects of curvature on the turbulent boundary layer. Aero. Res. Counc. R. & M. no. 3599.Google Scholar
Rajagopalan, S. 1974 Some experimental investigations of the fine scale structure of turbulence. Ph.D. thesis, Dept. Aeronautical Engineering, Indian Institute of Science Bangalore.
Ramaprian, B. R. & Shivaprasad, B. G. 1977 Mean flow measurements in turbulent boundary layers along mildly curved surfaces. A.I.A.A. J. 15, 189.Google Scholar
Rastogi, A. K. & Whitelaw, J. H. 1971 Procedure for predicting the influence of longitudinal curvature of boundary-layer flows. A.S.M.E. Winter Ann. Meeting, Washington, D.C., paper 71-WA/FE-37.Google Scholar
Schmidbauer, H. 1936 Behaviour of turbulent boundary layers on curved convex wall. N.A.C.A. Tech. Memo. no. 791.Google Scholar
Shivaprasad, B. G. 1976 An experimental study of the effect of mild longitudinal curvature on the turbulent boundary layer. Ph.D. thesis, Dept. Aeronautical Engineering, Indian Institute of Science, Bangalore.
Shivaprasad, B. G. & Ramaprian, B. R. 1977 Turbulence measurements in boundary layers along mildly curved surfaces. A.S.M.E. Winter Ann. Meeting, Atlanta, paper 77-WA/FE-6 (to appear in J. Fluids Engng).Google Scholar
So, R. M. C. 1975 A turbulence velocity scale for curved shear flows. J. Fluid Mech. 70, 37.Google Scholar
So, R. M. C. & Mellor, G. L. 1972 An experimental investigation of turbulent boundary layers along curved surfaces. N.A.S.A. Contractor Rep. no. 1940.Google Scholar
So, R. M. C. & Mellor, G. L. 1973 Experiment on convex curvature effects in turbulent boundary layers. J. Fluid Mech. 60, 43.Google Scholar
So, R. M. C. & Mellor, G. L. 1975 Experiment on turbulent boundary layers on a concave wall. Aero. Quart. 26, 25.Google Scholar
Tani, I. 1962 Production of longitudinal vortices in the boundary layer along a concave wall. J. Geophys. Res. 67, 3075.Google Scholar
Wallace, J. M., Eckelmann, H. & Brodkey, R. S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 54, 39.Google Scholar
Wattendorf, F. L. 1935 A study of the effect of curvature on fully developed turbulent flow. Proc. Roy. Soc. A 148, 565.Google Scholar
Willmarth, W. W. & Lu, S. S. 1972 Structure of Reynolds stress near the wall. J. Fluid Mech. 55, 65.Google Scholar