Role of the turbulence model in prediction of turbulent flow over a sphere

Numerical simulations of the sub-critical flow over a sphere at a Reynolds number of 10 ⁴ are presented. The primary aim is to compare prediction of some of the main physics and flow parameters from solutions of the unsteady Reynolds-averaged Navier-Stokes (URANS) equations, Large Eddy Simulation (LES), and Detached Eddy Simulation (DES). The techniques are assessed against experimental measurements and through an inter-comparison of the time-dependent features resolved using the different models. Predictions of the streamwise drag using URANS with leading closure models as well as results from LES and DES are in reasonable agreement with measurements. The pressure coefficient along the sphere is adequately predicted by the RANS models, with DES and LES results in slightly better agreement with data. The nearly axisymmetric URANS solutions predict the value of the main shedding frequency, but not its amplitude and other time-dependent features of the flow. DES compares favorably with LES in that both techniques resolve eddies down to the grid scale in the wake and are better able to capture unsteady phenomena, including formation of Kelvin-Helmholtz instabilities in the detached shear layers and the associated higher frequencies in the flow.