On the contribution of roughness effects to the scaling of ship resistance

Abstract

Roughness effects are one of the main challenges of the prediction of ship resistance using traditional model tests and extrapolation procedures. Computational Fluid Dynamics (CFD) can play an important role in the improvement of empirical correlations. Nowadays, most CFD RANS solvers use an equivalent sand-grain roughness height to model roughness effects. Therefore, the simulation of roughness effects includes two main challenges: estimate the equivalent sand-grain roughness height that corresponds to a given average roughness height typically used to characterize the roughness of ships; include sand-grain roughness effects in the most accurate RANS turbulence models for the simulation of ship flows, as for example the $k-\omega$ SST eddy-viscosity model. In this work, the flows around different geometries (flat plate, submarine and two ships) at full scale Reynolds numbers ($10^8$ to $10^9$) are simulated with RANS solvers using the $k-\omega$ SST eddy-viscosity model. Roughness effects are included in the k and $\omega$ boundary conditions for values of the sand-grain roughness height covering hydraulically smooth and fully rough surfaces. It is shown that with the proper scaling, the increase of the friction resistance coefficient with the sand-grain roughness height is equivalent for the four geometries tested. Conversion of average roughness height to sand-grain roughness is assessed by comparing CFD results with Bowden and Davison and Townsin et al. empirical correlations. Results of the simulations show the best agreement with the Townsin et al. correlation with a small variation of the ratio between average roughness and sand-grain roughness heights.