Estimation and prediction of the roughness function on realistic surfaces

Abstract

Large-eddy simulations are carried out in turbulent open-channel flows to determine the roughness function and the equivalent sand-grain roughness height, k_s, over sand-grain roughness and different types of realistic roughness replicated from hydraulic turbine blades. A range of Reynolds numbers and mean roughness heights is chosen, leading to both transitionally and fully rough regimes. The start of the fully rough regime is shown to depend on the roughness type, and k_s depends strongly on the surface topography. We then examine several existing correlations that predict k_s based on the information of the surface geometry. In the cases where the surface slope is an important parameter, the moments of surface height statistics do not predict the roughness function, while the existing forms of slope-based correlations perform well. The range of applicability of various correlations is shown to vary with the roughness topography, as the critical value of the effective slope, separating the waviness and roughness regimes, is shown to be higher for a realistic surface, compared to the value for the more regular types of roughness that were previously studied.

Keywords:

• turbulent flows
• boundary layers
• large-eddy simulations
• roughness

Acknowledgements

Support from Hydro Québec, the Natural Science and Engineering Research Council of Canada (NSERC), and the High Performance Computing Virtual Laboratory (HPCVL) is acknowledged. Professor Alberto Scotti is thanked for the code generating the volume fraction for the immersed boundary method.