Mode-based energy transfer analysis of flow-induced vibration of two rigidly coupled tandem cylinders

Two rigidly coupled cylinders are commonly available in engineering practices, which are always subjected to flow-induced vibration (FIV) with large oscillating amplitude due to the complex gap flow. However, their FIV features and the underlying mechanism have not been clearly understanded. In this study, the FIV of two rigidly coupled square cylinders in a tandem arrangement was numerically investigated for Reynolds numbers 100 and 200 and gap L/D = 2.0 and 6.0 in a two-dimensional framework. The dynamic response and flow structures are first studied. Mode-based energy transfer analysis was developed based on proper orthogonal decomposition. The energy transfer between the cylinders and the coherence modes was then analyzed to uncover the underlying mechanism of the FIV. The results reveal that the soft lock-in phenomenon was observed for all cases. When the gap L/D = 2.0, the dynamic response is always smaller than a stationary cylinder and all the wake structures show "2S" modes, which results from the stabilized effects of the upstream cylinder. At L/D = 6.0, the oscillating amplitude is much higher than that of a single square cylinder, due to the vigorous interaction between gap flow and the cylinders. As Reynolds number increased from 100 to 200, both vortex-induced vibration (VIV) and galloping co-exist, while the VIV response was reduced. Concerning the energy transfer, for L/D = 2.0, the first mode pair induced by Karman vortex shedding dominated the wake flow. The primary mode governed by UC stabilized the vibration, while the second mode tended to excite the FIV. For L/D = 6.0 in the galloping branch, the first two modes belonged to the vortex-induced modes, and the third mode represented the galloping mode. The galloping mode tended to excite the flow-induced vibration, while it was contrary for the vortex-induced modes.