Effect of surface roughness on the coefficients of a power law for the mean velocity in a turbulent boundary layer

Abstract

Mean velocity profiles in a two-dimensional zero pressure gradient turbulent boundary layer were obtained for a hydraulically smooth surface and 10 different rough surfaces created from sand paper, steel perforated sheet, and steel woven wire mesh. The physical size and geometry of the roughness elements were chosen to achieve transitionally rough and fully rough flow regimes. The measurements were made in a subsonic wind tunnel, and the Reynolds number based on the momentum thickness ranged from 3730 to 13 550. The power law formulation of George and Castillo (1997, Applied Mechanics Review, 50, 689) was used to estimate the skin friction coefficients for transitionally rough and fully rough flows, as well as hydraulically smooth flow. The values of the friction velocity obtained for the rough surfaces using the defect law and the power law profile fitting techniques were within ±3%. Values of the power law coefficient C _i and exponent γ were determined by fitting the power law formulation to the experimental data. The surface roughness was found to significantly affect the behaviour of the coefficient C _i and exponent γ in the power law relations. Based on the experimental results, correlations are proposed for the coefficient C _i and exponent γ as a function of the roughness shift Δ U ⁺ for transitionally rough flows.

Acknowledgements

Financial support in terms of a NSERC Discovery Grant to D.J.B. and a University of Saskatchewan scholarship to O.G.A. is gratefully acknowledged.