Using validation metrics to assess RANS turbulence models performance at full scale Reynolds numbers

One of the major advantages of Computational Fluid Dynamics (CFD) is the ability to simulate flows at full-scale Reynolds numbers, which for naval applications can reach values of 10⁹ . For this range of Reynolds numbers, the Reynoldsaveraged Navier-Stokes (RANS) equations are still the most common mathematical model. The averaging procedure used to derive the RANS equations generates the Reynolds-stresses that are determined by a turbulence model. In the last 50 years several turbulence models have been proposed in the open literature ranging from the initial eddy-viscosity algebraic methods to Reynolds-stress models that solve 7 additional transport equations. The assessment of the modeling error of RANS simulations requires the existence of experimental data and so most of the reported exercises of modeling error assessment are performed at model-scale Reynolds numbers. Furthermore, many of these studies rely on simple graphical comparisons without the quantification of experimental, numerical and input uncertainties.
In this paper we apply the V&V20 validation metrics to quantitatively assess the modeling error of RANS using six different turbulence models in the simulation of the flow around the KVLCC2 at model-scale Reynolds number, for which experimental data are available at six cross-sections of the stern and nearwake region including the propeller plane. It is illustrated that graphical comparisons are less conclusive than the quantitative assessment of the modeling error taking into account uncertainties of experiments and simulations.
The same validation metrics are applied to quantify the differences between simulations performed with the same models at full-scale Reynolds number. The results show quantitatively hat differences between the results obtained with the six turbulence models at full-scale Reynolds number are much smaller than those observed at model-scale Reynolds number. In the absence of experimental data at full-scale, such exercise suggests that the role of the turbulence model in full-scale flows around ships is not as important as in model-scale simulations.