A modeling framework for scale-resolving computations of turbulent flow over porous and rough walls

The present work is focused on the development of a modeling framework for scale-resolving simulations of turbulent flow over porous and rough walls. In particular, the investigations and modeling efforts are guided by technical applications involving consequential physical phenomena in the vicinity of rough surfaces. Apart from internal combustion engines, where the near-wall region has been identified as important with respect to the formation of pollutants, turbulent flow over porous or rough walls can be found in a variety of other technical systems as well as the environment. In order to enable computationally efficient scale-resolving simulations accurately capturing the modification of turbulent flow in the vicinity of rough walls, a RANS-based (RANS: Reynolds-averaged Navier Stokes) sub-scale model and a roughness closure relying on a mathematical framework originating from the field of porous media modeling is proposed. The sub-scale model, termed as eddy-resolving (ER) ζ-f model, is derived on the basis of an elliptic-relaxation RANS model, which is essentially sensitized to resolved turbulent fluctuations by introducing a newly formulated source term motivated by the scale-adaptive simulation concept. With respect to roughness modeling, findings of this study emphasize the importance to consider blockage effects associated with rough surfaces. Consequently, volume-averaged governing equations are applied and a roughness model accounting for the drag roughness elements exert on the flow through a volumetric forcing term in the momentum equation is proposed. The ER ζ-f model is successfully validated in an extensive computational study. Its high predictive accuracy and computational efficiency is demonstrated by comparison to several sub-scale models from literature. Furthermore, validation results for the proposed roughness model exhibit a high level of qualitative and quantitative agreement with reference data for flow over irregular rough surfaces, both with respect to mean flow and turbulence statistics, as well as predicted friction coefficients.