Effects of varied roughness coverage area on drag in a turbulent boundary layer using numerical simulations

Turbulent boundary layer (TBL) over various area coverages of rough surfaces have been studied via computational fluid dynamics using the steady Reynolds Averaged Navier–Stokes (RANS) technique. The rough surfaces are modelled by randomly distributed hemispheres with a 1 mm radius, covering 5%, 10%, 20%, 30%, 40%, and 50% of the wall surface area designed to represent a typical three-dimensional roughness and also replicate the biofouling growth of a ship's hull. The results of this study show the relationships between the roughness area coverage and the skin friction drag within a fully rough regime. The flow experiences maximum drag and the highest equivalent sand grain roughness height at 30% roughness area coverage. However, beyond this area coverage value, the drag gradually decreases. Further analysis indicates that the 30% roughness area coverage corresponds to a roughness frontal density of λ_f=0.15. Recent reports indicate that when λ_f≲0.15, the pressure drag to total drag ratio increases with increased roughness frontal density.