Free and forced vibrations of a wavy cylinder in cross flow at low Reynolds numbers

Kai Zhang, Dai Zhou, Hiroshi Katsuchi, Hitoshi Yamada, Zhaolong Han, Yan Bao

Published 2018-12-13Version 1

Wavy circular cylinders have been reported to be effective in suppressing the Karman vortex shedding and reducing hydrodynamic forces. However, their vibrational characteristics in cross flow have not been well understood. By means of direct numerical simulations, the current paper investigates the free and forced vibrations of a wavy cylinder at low Reynolds numbers. The wavy cylinder is optimally designed so that it annihilates the vortex shedding in the fixed configuration for $Re\geq 120$. Nevertheless, it is disclosed that by flexible-mounting the coupled fluid-structure system could still be destabilized, leading to large-amplitude vibrations. The forced vibration reveals that for a fixed amplitude, a critical forcing frequency exists, below which the oscillating wavy cylinder preserves the flow control efficacy, and above which the inherent shedding resurrects in the wake, further leading to the lock-in phenomenon. More interestingly, the developed vortex shedding could persist even without the sustained forcing, implying the existence of the bistable states in the wavy cylinder wake. The observations in the current work suggest that the application of wavy cylinder as drag/vibration-mitigation device in realistic engineering structures should not be encouraged.