A new extension for k– [formula omitted] turbulence models to account for wall roughness

Abstract

This paper presents a new extension for k– ω turbulence models to account for surface roughness for transitionally and fully rough surfaces. It is based on the equivalent sand grain approach and accounts for theoretical considerations on the log-layer solution for fully rough surfaces. An appropriate behaviour for transitional roughness is achieved by means of wall values for k and ω which depend on the roughness Reynolds number. In the limit of vanishing roughness, the smooth wall boundary condition is recovered. For the full range of roughness Reynolds numbers the new roughness modification gives very successful predictions for a variety of flat plate turbulent boundary layer flows and for the pipe flow experiments by Nikuradse. The new method allows for the simulation of flows over rough surfaces at the same grid resolution requirements as for smooth walls. Thereby the extremely fine near-wall mesh resolution required by the Wilcox roughness modification is avoided. Secondly the new roughness modification gives significantly improved predictions in skin friction for transitional roughness Reynolds numbers compared to the roughness extension by Wilcox. Thirdly, the new roughness extension does not require a modification of the SST k– ω model, whereas a modification is necessary if the roughness extension by Wilcox is used. Finally the new method is applied successfully to predict the aerodynamic effects of surface roughness on the flow past an airfoil in highlift conditions.