Validation exercises for the calculation of the flow around a squared column with rounded corners at high Reynolds numbers with the rans equations

This paper presents Validation studies, i.e. evaluation of the modelling error, for the ensemble averaged Navier-Stokes (RANS) equations supplemented by eddy-viscosity models (SST k-ω and Spalart & Allmaras). The selected test case is the flow around a squared column with rounded corners at Reynolds number ranging from 10⁵ to 10⁷. Selected flow quantities include time-averaged quantities of drag and lift coefficients, base pressure coefficient, Strouhal number and the standard deviation of the lift coefficient. For this latter quantity, ensemble (phase) averaging must also be applied to the experimental data to obtain quantities with the same physical meaning, as illustrated in this work.Even for the simple assumption of two-dimensional flow of the present simulations, the level of grid refinement and iterative convergence criteria required to obtain acceptable numerical uncertainties is more demanding than those typically observed in the open literature. However, the most important result obtained in this study is that the use of turbulence models developed for statistically steady flows may lead to flow fields that physically are at least questionable. From the three Reynolds numbers tested using three eddy-viscosity models, statistically periodic solutions with zero lift were only obtained with the SST k-ω at Re = 10⁵. However, in that case, it is possible to numerically (including statistical, iterative and discretization errors) converge two different flow fields for the same space boundary conditions, but different solution strategies (start up of the vortex shedding).