On the asymmetric vortex evolution in the near wake behind polygonal cylinders in an incident flow

Asymmetric evolution of coherent vortices behind polygonal cylinders in an incident flow is studied using Proper Orthogonal Decomposition (POD) based phase averaging analysis. Flow around polygonal cylinders of side number N is an element of [5, 8] at Reynolds number 104 is simulated using three-dimensional Large Eddy Simulation for six incident angles a to cover the entire incidence spectrum. POD analysis is performed on a two-dimensional subset of the data at the mid-span of the cylinder. It is found that except heptagon at corner orientation, where extra secondary vortex shedding is observed, all the other cases resemble the classical periodic K & aacute;rm & aacute;n vortex shedding at the Strouhal frequency. The first pair of POD eigenvalues show similar and dominant energy content in all the cases, with negligible N or a dependence. Maximum circulation of primary vortices calculated using the POD-based phase averaging method displays significant asymmetry between the vortices shed on the upper and lower sides, when the cylinder is at off-principal orientations with respect to the incoming flow. This maximum circulation on each side of the wake occurs close to a properly defined vortex formation distance where vortex centroids are closest apart in the transverse direction. Correlation analysis reveals that the difference of the maximum circulations between the upper and lower sides scales weakly with the time-mean lift coefficient, and their sum scales well with the time-mean drag coefficient positively and Strouhal number inversely.