A numerical analysis of the flow over stationary and transversely oscillating circular cylinders at Reynolds numbers of 3900 and 3600, respectively, is undertaken to assess various turbulence modeling techniques for the simulation of vortex shedding phenomena. Four turbulence models are considered, namely the one-equation SpalartAllmaras model [Spalart & Allmaras (1994)] and the k-τ model by Speziale et al. (1992) for URANS closure, the constant-coefficient Smagorinsky-Lilly subgrid-scale model for Large Eddy Simulations, and the adaptive k-τ model proposed by Magagnato & Gabi (2002) for Very Large Eddy Simulations. A key contribution of this work is comparison of results obtained with the same numerical procedure, discretization algorithms, and artificial dissipation but different turbulence modeling techniques in order to properly differentiate between errors due to numerical and to modeling aspects.

Through the study of the flow around the stationary cylinder, it is shown that the use of an inadequate time step has a small effect on global average quantities, but a noticeable impact on the pressure coefficient around the cylinder, as well as on the evolution of velocity along the centerline, thus showing that simulations with too large a time step are unable to properly resolve the recirculation zone and wake. Global average quantities are found to be relatively insensitive to three-dimensional resolution.

Detailed analysis ofthree-dimensional URANS simulations reveals that the SpalartAllmaras model is unable to properly predict the location of the separation point, separation being delayed significantly. This results in too small a mean recirculation zone, under-estimated back-pressure, and up to 25% over-estimation of the drag. Yet, this simple model provides an accurate value for the Strouhal number and good fluctuating velocity profiles. The k-τ Speziale turbulence model predicts all global quantities accurately, and yields good velocity profiles along the wake as well as an adequate pressure distribution on the cylinder wall.

Large and Very Large Eddy Simulations of the flow around a stationary cylinder reveal an important three-dimensionality, and the formation on the upper and lower surfaces of two secondary eddies in addition to the two large vortices. Furthermore, the LES properly captures the dynamics in the laminar boundary layer as reflected by the skin friction values even though it makes use of a constant coefficient Smagorinsky subgrid-scale model.

In the study of the transversely oscillating cylinder with two-dimensional URANS k-τ Speziale simulations, the lock-in region starts at significantly lower motion frequencies than observed in experimental results, while the phase shift was not observed. No numerical studies close to this Reynolds number are available in the literature, and further investigation is required