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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

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

## Abstract

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 $Cf1∕2∕(δ*∕δ)$ is approximately constant, irrespective of the Reynolds number and surface condition.

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## Figures

Figure 4

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

Figure 5

Relation of shape factor to skin friction coefficient

Figure 1

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

Figure 2

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

Figure 3

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

Figure 6

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

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)

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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