Turbulence modeling applied to flow over a sphere

Numerical simulations of the subcritical flow over a sphere 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). URANS predictions are obtained using two-layer κ-ε, κ-ω, ν^̄2-f, and the Spalart-Allmaras model. The dynamic eddy viscosity model is used in the LES. DES is a hybrid technique in which the closure is a modification to the Spalart-Allmaras model, reducing to RANS near solid boundaries and LES in the wake. The techniques are assessed by evaluating simulation results against experimental measurements, as well as through their ability to resolve time-dependent features of the flow related to vortex shedding. Simulation are performed at a Reynolds number of 10⁴, where laminar boundary-layer separation occurs at approximately 83 deg. With the exception of two-layer κ-ε, RANS predictions of the streamwise drag are in reasonable agreement with measurements. The pressure and skin-friction coefficients along the sphere are adequately predicted by the RANS models, with DES and LES results in better agreement with measurements in the aft region. Profiles of the mean velocity and turbulent kinetic energy in the near wake from all of the techniques are similar. The nearly axisymmetric URANS solutions predict the value of the main shedding frequency, albeit at substantially reduced amplitude compared to the LES and DES. 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 high frequency in the flow.