A Verification and Validation Study of RANS Based Roughness Models at Model and Full Scale Reynolds Numbers

Most flows that occur in naval applications exhibit large Reynolds numbers (Re > 10⁷), which means that roughness elements need to be extremely small to have hydraulically smooth conditions, i.e. friction and pressure forces that are not affected by the surface roughness. Therefore, modeling accurately roughness effects remains one of the biggest challenges of Computational Fluid Dynamics (CFD). There are two main difficulties in the simulation of roughness effects in turbulent flows: the characterization of the surface roughness and the inclusion of the roughness effects in the mathematical model. This work focuses on the latter problem assuming that it is possible to define an equivalent sand-grain roughness height that characterizes the desired surface roughness.
For high Reynolds number wall bounded flows, the most common mathematical model are the Reynoldsaveraged Navier-Stokes (RANS) equations that require the use of turbulence models. Roughness effects are accounted for using the equivalent sand-grain roughness height and its effect can be included in two different ways: modification of the boundary conditions of the turbulence quantities transport equations keeping the shearstress at the wall determined from its definition; or using wall-functions to determine the shear-stress and the turbulence quantities at the wall. In this paper, we explore the first technique in three eddy-viscosity models (k−ω SST, k−√kL and Spalart & Allmaras). The use of wallfunctions is only investigated for the k−ω SST model. The roughness model that is based only on the change of the ω boundary condition at the wall is also combined with an Explicit Algebraic Reynolds-Stress model and with the SSG/LRR-ω Reynolds-stress model.
The goal of this study is twofold: assess the performance of the turbulence and roughness models combinations; and compare the discrepancies between different turbulence and roughness models combinations at model and full-scale Reynolds numbers. The selected test cases are two two-dimensional geometries for which reference empirical data is available in the literature, i.e. flat plate