Flow-induced vibration of a flexible cantilever in tandem configuration

Abstract

The present work investigates the fluid-structure interaction (FSI) of a flexible cylindrical cantilever in a tandem configuration. A fully coupled fluid-structure solver based on the three-dimensional incompressible Navier-Stokes equations and Euler-Bernoulli beam equation is employed to numerically examine the coupled dynamics of the cantilever. We assess the extent to which such a flexible structure could sustain oscillations in both subcritical and post-critical regimes of Reynolds number ($Re$). Spatio-temporal power transfer patterns, response amplitudes, and vorticity dynamics are quantified and compared between isolated and tandem configurations. Results of our analysis indicate that the cantilever in tandem configuration is prone to sustained oscillations dependent on $Re$ and the reduced velocity parameter ($U^*$). In the subcritical $Re$ regime, the cantilever exhibits sustained oscillations with peak transverse oscillation amplitudes occurring within a specific range of $U^*$. Within this range, the transverse oscillations demonstrate lock-in behavior and synchronization with the vortex shedding frequency. The vorticity dynamics in the subcritical $Re$ regime reveal that in the tandem configuration, the presence of the upstream cylinder significantly modifies the wake structure, delaying vortex formation and extending the near wake. In the post-critical $Re$ regime, the cantilever shows a broader range of sustained oscillations in terms of $U^*$, with single- and multi-frequency dynamics driven by vortex-body interactions. The power transfer analysis shows cyclic energy exchange patterns between the fluid and flexible structure, with significant variations in the hydrodynamic loading along the cantilever. The findings of this work help broaden the understanding of sustained oscillations in flexible cantilevers and are relevant to the design of cantilever flow sensors.