Vortex-induced vibration and flutter of a filament behind a circular cylinder

Flow past a flexible filament, a two-dimensional splitter plate with negligible thickness, attached behind a circular cylinder is investigated. The Reynolds number based on the free-stream speed of incoming flow and diameter of the cylinder is \(\textrm{Re}=100\). At this \(\textrm{Re}\), the flow for a rigid filament is steady. However, a flexible filament undergoes flow-induced vibration for a range of reduced speed, \(U^*\), defined as inverse of the first nondimensionalized natural frequency of the filament. Over the wide range of \(U^*\) considered in this work (\(U^*\le 240\)), it exhibits both flutter and vortex-induced vibration (VIV). Lock-in with various normal modes related to bending of the filament, each in a different regime of reduced speed, is observed during VIV. Interestingly, the fluid–structure system does not lock-in with the first normal mode of bending but with higher modes. The flow is steady for an extended range of reduced speed both before and after the lock-in with second mode. Two patterns of vortex shedding are observed. The \(\textsf{2P}\) mode is associated with high-frequency vibration, while the \(\mathsf {2\,S}\) mode is observed during relatively low-frequency oscillation. A symmetry-breaking pitchfork bifurcation leads to static deflection of the filament during the first steady regime. The filament exhibits flutter response, at large reduced speed, with relatively low amplitude and frequency. No vortex shedding is observed during flutter. The fluid forces that cause flutter arise from asymmetry across the two sides of the filament in the zones of recirculation downstream of the cylinder. Comparison of the space-time patterns of energy transfer at the fluid–filament interface for flutter and vortex-induced vibration reveals that the energy transfer is much smaller during flutter compared to VIV. The point of maximum energy transfer is located close to the root of the filament in case of flutter, while it is near the tip during VIV.