Flow-induced oscillations of a clamped flexible ring

The flow-induced oscillations of a clamped flexible ring in a uniform flow were explored using the penalty immersed boundary method. Both inverted and conventional ring configurations were examined, with systematic analysis focused on the effects of bending rigidity and eccentricity. Four distinct oscillation modes were identified across parameter variations: flapping (F), deflected oscillation (DO), transverse oscillation (TO) and equilibrium (E) modes. Each mode exhibited a 2S wake pattern. The inverted ring sustained the DO mode under low bending rigidity with a deflected shape, transitioning to the TO mode at higher bending rigidity. In the TO mode, a lock-in phenomenon emerged, enabling the inverted ring to achieve a high power coefficient due to a simultaneous rise in both oscillation amplitude and frequency. By contrast, the conventional ring exhibited the F mode at low bending rigidity and transitioned to the E mode as rigidity increased, although its power coefficient remained lower because of reduced critical bending rigidity. For the inverted ring, low eccentricity enhanced oscillation intensity but limited the operational range of the TO mode. In contrast, for the conventional ring, reducing eccentricity led to an increase in oscillation amplitude. Among the investigated configurations, the inverted-clamped ring achieved the highest energy-harvesting efficiency, surpassing those of the conventional clamped ring and a buckled filament.