On The Numerical Requirements Of RANS And Hybrid Turbulence Models

The evaluation of different mathematical models for the prediction of turbulent flows depends on the ability to reduce the numerical error to negligible levels, i.e. to values clearly below the modelling error. In this work we assess the numerical requirements, i.e. grid/time refinement, iterative and statistical convergence levels, to achieve such goal for three different mathematical models: Reynolds-Averaged NavierStokes (RANS) equations supplemented by an eddy-viscosity model; Delayed Detached Eddy Simulation (DDES) and eXtra Large Eddy Simulation (XLES). To this end, numerical simulations are performed with RANS and the two hybrid models (blend of RANS and LES) for the flow around a circular cylinder at a Reynolds number of 3900. The results show that the grid/time refinement and iterative and statistical (for DDES and XLES) convergence levels required to achieve such goal are clearly more demanding than those usually found in the open literature, especially for the two models that simulate directly the large scales of turbulence, DDES and XLES. Nonetheless, the comparison of mean flow quantities with available experimental data suggests that the hybrid models reduce the modelling error when compared to RANS.