Self-sustaining turbulent wake characteristics in fluid–structure interaction of a square cylinder

Abstract

We present a numerical study on the fluid–structure interaction of a square cylinder at subcritical Reynolds numbers 1400≤Re≤10,000. Variation in spatial and temporal structures during the self-sustaining regeneration cycle are investigated via a three-dimensional Navier–Stokes flow coupled with a freely vibrating square cylinder at relatively low mass ratio. We employ a variational fluid–structure interaction formulation based on the recently developed partitioned iterative scheme and the dynamic subgrid-scale turbulence model. To begin, we assess the response amplitudes, the synchronization regimes and the vortex shedding patterns against the experimental measurements for the flow-induced vibration of a square cylinder at zero incidence angle. Of particular interest is to predict and analyze the synchronization regimes and the associated wake structures for a range of reduced velocity. The vibration of the cylinder provides an avenue for the merging of smaller eddies in the vicinity of the cylinder and there are relatively more clustered spanwise rollers and streamwise ribs as compared to the stationary counterpart. We provide a comparative assessment of Reynolds stress distributions in the near-wake region between the VIV lock-in case and its stationary counterpart. We find that the spatial symmetry of the shearing process in the wake shifts to the temporal symmetry of Reynolds stress when the cylinder is free to vibrate. Consequently, in the vibrating case, the competition between the mean shear growth and damping results in a relatively lower frequency shearing as compared to the stationary cylinder. We introduce a representative control volume in the near-wake region to assess the kinetic energy and enstrophy evolution for the stationary and vibrating configurations. We examine the core reason of the matching of periodic wake frequency with the vibrating cylinder frequency through the development of near-wake flow structures and the kinetic energy evolution. By combining these results with the self-sustained process of coherent vortex structure development, we finally explain the formation of intermediate hairpin-like structures in close proximity to the vibrating cylinder and the absence of them in the stationary cylinder.