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TECHNICAL PAPERS

Skin Friction Correlation for Smooth and Rough Wall Turbulent Boundary Layers

[+] Author and Article Information
D. J. Bergstrom, O. G. Akinlade

Department of Mechanical Engineering,  University of Saskatchewan, 57 Campus Drive, Saskatoon, SK, Canada, S7N 5A9

M. F. Tachie

Department of Mechanical and Industrial Engineering, University of Manitoba, Winnipeg, MB, Canada, R3T 2N2

J. Fluids Eng 127(6), 1146-1153 (Apr 28, 2005) (8 pages) doi:10.1115/1.2073288 History: Received August 12, 2004; Revised April 28, 2005

In this paper, we propose a novel skin friction correlation for a zero pressure gradient turbulent boundary layer over surfaces with different roughness characteristics. The experimental data sets were obtained on a hydraulically smooth and ten different rough surfaces created from sand paper, perforated sheet, and woven wire mesh. The physical size and geometry of the roughness elements and freestream velocity were chosen to encompass both transitionally rough and fully rough flow regimes. The flow Reynolds number based on momentum thickness ranged from 3730 to 13,550. We propose a correlation that relates the skin friction, Cf, to the ratio of the displacement and boundary layer thicknesses, δ*δ, which is valid for both smooth and rough wall flows. The results indicate that the ratio Cf12(δ*δ) is approximately constant, irrespective of the Reynolds number and surface condition.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 3

Mean velocity defect profiles using inner coordinates: (a) smooth and transitionally rough; (b) smooth and fully rough

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Figure 2

Mean velocity profiles using inner coordinates: (a) smooth and transitionally rough and (b) smooth and fully rough

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Figure 1

Mean velocity profiles using outer coordinates: (a) smooth and transitionally rough and (b) smooth and fully rough

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Figure 4

Variation of skin friction coefficient for a smooth surface with Reynolds number

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Figure 5

Relation of shape factor to skin friction coefficient

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Figure 6

Variation of skin friction coefficient with Reynolds number: (a) smooth and transitionally rough and (b) smooth and fully rough

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Figure 8

Variation of skin friction coefficient for smooth and rough surfaces with length scale ratio [solid line represents Eq. 9]

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Figure 7

Variation of mixed skin friction coefficient for smooth and rough surfaces with Reynolds number (DE and AK denote DeGraaf and Eaton (37) and Antonia and Krogstad (39), respectively)

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