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Turbulent boundary-layer flow and structure on a convex wall and its redevelopment on a flat wall

Published online by Cambridge University Press:  20 April 2006

J. C. Gillis  and
J. P. Johnston
J. C. Gillis
Affiliation:
S. Levy Inc., 1999 S. Bascom Avenue, Campbell, CA 95008
J. P. Johnston
Affiliation:
Department of Mechanical Engineering, Stanford University, CA 94305
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Abstract

Two experiments (δ/R = 0.05 and 0.10) were performed to determine how boundary-layer turbulence is affected by strong convex curvature. The flow passed from a flat surface, over convex surface with 90° of turning, and then onto a flat recovery surface. The pressure gradient along the test surface was forced to be zero.

After the sudden introduction of curvature, the shear stress in the outer part of the boundary layer is sharply diminished. The wall shear also drops off quickly downstream. When the surface suddenly becomes flat again, the wall-shear and the shear-stress profiles recover very slowly towards flat-wall conditions. The shear-stress profiles in the curved region for both experiments collapse when $-\overline{uv}/u^2_{\tau}$ is plotted vs. distance from the wall normalized on wall radius, n/R. The strong-curvature data of So & Mellor also fall on the same curve. Thus suggests an asymptotic state for the shear-stress profiles of strongly curved boundary layers where R rather than boundary-layer thickness controls the active turbulence lengthscales. In this asymptotic region, the active shear-layer thickness is less than its initial value at the start of curvature. In the recovery region, the width of the active shear layer regrows slowly within the original velocity-gradient boundary layer, like a developing boundary layer under a free stream with a velocity gradient normal to the wall.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 135 , October 1983 , pp. 123 - 153
Copyright
© 1983 Cambridge University Press

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References

Adams, E. & Johnston, J. P. 1981 A mixing-length model for the prediction of convex curvature effects on turbulent boundary layers. Rep. IL-42, Thermosci. Div., Mech. Engng Dept, Stanford.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 Effect of streamline curvature on turbulent flow. AGARDograph 169.Google Scholar
Castro, I. R. & Bradshaw, P. 1976 The turbulence structure of a highly curved mixing layer J. Fluid Mech. 73, 265.Google Scholar
Cebeci, T., Hirsh, R. S. & Whitelaw, J. H. 1979 On the calculation of laminar and turbulent boundary layers on longitudinally curved surfaces AIAA J. 17, 434.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
Gibson, M. M., Jones, W. P. & Younis, B. A. 1980 Calculation of turbulent boundary layers on curved surfaces. Mech. Engng Dept, Imperial College, Rep. FS/80/6.Google Scholar
Gillis, J. C. & Johnston, J. P. 1980 Experiments on the turbulent boundary layer over convex walls, and its recovery to flat-wall conditions. In Selected Papers from the 2nd Intl Symp. on Turbulent Shear Flows. Springer.
Gillis, J. C., Johnston, J. P., Moffat, R. J. & Kays, W. M. 1980 Rep. HMT-31, Stanford University Dept Mech. Engng.
Hoffmann, P. H. & Bradshaw, P. 1978 Turbulent boundary layers on surfaces of mild longitudinal curvature. Imperial College Aero Rep. 78–04.Google Scholar
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 in centrifugal compressor blades: prediction of the effects of surface curvature and rotation. Trans. ASME I: J. Fluids Engng 98, 374.Google Scholar
Jones, W. P. & Launder, B. E. 1972 The calculation of low Reynolds number phenomena with a two-equation model of turbulence Intl J. Heat Mass Transfer. 15, 301.Google Scholar
Kármán, T. Von 1934 Some aspects of the turbulence problem. In Proc. 4th Intl Congr. Appl. Mech., Cambridge, p. 54.
Klebanoff, P. S. 1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA Rep. 1247.Google Scholar
Kline, S. J. et al. 1969 In Proc. 1968 AFOSR-IFP-Stanford Conf. on the Computation of Turbulent Boundary Layers, Stanford University.
Launder, B. E., Priddin, C. H. & Sharma, B. I. 1977 The calculation of turbulent boundary layers on spinning and curved surfaces. Trans. ASME I: J. Fluids Engng. 99, 231.Google Scholar
Launder, B. E., Reese, G. J. & Rodi, W. 1975 Progress in the development of a Reynoldsstress turbulence closure J. Fluid Mech. 68, 537.Google Scholar
Meroney, R. N. & Bradshaw, P. 1975 Turbulent boundary layer growth over a longitudinally curved surface AIAA J. 13, 1448.Google Scholar
Patel, V. C. 1968 The effects of curvature on the turbulent boundary layer. Aero. Res. Counc. ARC 30427, FM 3974.Google Scholar
Ramaprian, B. S. & Shivaprashad, B. G. 1978 The structure of turbulent boundary layers along mildly curved surfaces J. Fluid Mech. 85, 273.Google Scholar
Rastogi, A. K. & Whitelaw, J. H. 1971 Procedure for predicting the influence of longitudinal surface curvature on boundary layer flow. ASME 71-WA/FE-37.Google Scholar
Rayleigh, Lord 1917 On the dynamics of revolving fluids Proc. R. Soc. Lond. A93, 148.Google Scholar
Schmidbauer, H. 1936 Behavior of turbulent boundary layers in curved convex walls. NACA TM 791.Google Scholar
Simon, T. W. et al. 1981 Turbulent boundary layer heat transfer experiments: convex curvature effects, including introduction and recovery. Rep. HMT-31, Thermosci. Div., Dept Mech. Engng, Stanford.Google Scholar
Simon, T. W. & Honami, S. 1981 Incompressible flow entry cases having boundary layers with streamwise wall curvature (0230). Final Evaluation Report for the 1980-81 AFOSR-HTTM-Stanford Conf. on Complex Turbulent Flows: Comparison of Computation and Experiment, Thermosci. Div., Mech. Engng Dept, Stanford.
Smits, A. J., Young, S. T. B. & Bradshaw, P. 1979 The effects of short regions of high surface curvature on turbulent boundary layers J. Fluid Mech. 94, 243.Google Scholar
So, R. M. S. 1978 Turbulent boundary layers with large streamline curvature effects Z. angew. Math. Phys. 29, 55.Google Scholar
So, R. M. C. & Mellor, G. L. 1972 An experimental investigation of turbulent boundary layers along curved surfaces. NASA-CR-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
Thomann, H. 1967 Effect of streamwise wall curvature on heat transfer in a turbulent boundary layer J. Fluid Mech. 33, 283.Google Scholar
Wattendorf, F. L. 1935 A study of the effect of curvature on fully developed turbulent flow Proc. R. Soc. Lond. 148, 565.Google Scholar
Wendt, F. 1953 Turbulente Strömungen zwischen zwei rotierenden conaxialen Zylindren Ing.-Arch 4, 577.Google Scholar
Wilcken, H. 1967 Effects of curved surfaces on turbulent boundary layers. NASA TTF 11421.Google Scholar