On the Numerical Prediction of the Flow Around Smooth Circular Cylinders

The numerical prediction of the flow around a smooth cylinder is one the classical test cases of Computational Fluid Dynamics (CFD). Different mathematical models have been used to address this statistically periodic flow. Namely, ensemble-averaged Navier-Stokes equations (URANS); partially-averaged Navier-Stokes equations (PANS); space filtered Navier-Stokes equations (large eddy-simulation LES or variational multi-scale VMS) and direct solution of the Navier-Stokes equation (DNS). Although all these models deal with turbulence in a very different way, all of them require a numerical solution and so they all require a careful control of the numerical uncertainty. We present an overall view of the values of the average drag coefficient (one of the most simple flow quantities that we could select) that have been published in the open literature, which shows a worrying spread of data. Therefore, it is logical to wonder if all these results are obtained with negligible numerical errors/uncertainties, especially when the scatter in the data also applies to results obtained with the same mathematical model. In this paper, we present Solution Verification exercises for the simplest model of those mentioned above: URANS. The calculations are performed at different Reynolds numbers and with different iterative convergence criteria using the ReFRESCO solver. The two-equation SST k–ω eddy-viscosity turbulence model is used in all the calculations performed in this study. The results presented show that numerical (iterative and discretization) errors may have a strong impact in the predictions and that misleading apparent convergence may be obtained with careless iterative convergence criteria. Furthermore, it is shown that grids with similar numbers of cells but different space distributions may lead to significantly different numerical uncertainties.