Simulation of the flow around a circular cylinder at Re=3900 with Partially-Averaged Navier-Stokes equations

This study employs Partially-Averaged Navier-Stokes (PANS) equations to simulate the flow around a smooth circular cylinder at Reynolds number 3900. It intends to evaluate the importance of discretization and modelling errors on the accuracy of this mathematical model. Furthermore, the study addresses the effect of the physical resolution, or fraction of turbulence kinetic energy being modelled fk, on the predictions accuracy. To this end, Validation exercises are carried out using five different values of fk which range from typical values for well-resolved Scale-Resolving Simulations (fk ≤ 0.25) to Reynolds-Averaged Navier-Stokes equations (fk=1.00). Naturally, these exercises require the evaluation of numerical errors, i.e. Verification studies. Consequently, and taking advantage of the ability of PANS to enable the distinction between discretization and modelling errors, spatial and temporal grid refinement studies are carried out to assess the magnitude of the discretization error, as well as its dependence on fk. The outcome confirms the ability of PANS, in combination with fk < 0.50, to substantially decrease the modelling error when compared to fk=1.00. However, the reduction of fk tends to increase the model dependence on the spatial and temporal resolution. It is demonstrated that similarly to the effect of the spatial and temporal grid resolution on the magnitude of the numerical error, the modelling error diminishes with the physical resolution (fk → 0). The convergence of the predictions with fk is also illustrated.