Flow-induced vibrations of a circular cylinder positioned upstream of a fixed cylinder

The present work employs the immersed boundary method to perform direct simulations of flow-induced vibrations in a tandem cylinder at laminar flows, where only the upstream cylinder (UC) is allowed to vibrate. The primary focus is to elucidate the vibration response of the UC and the underlying hydrodynamic mechanisms when a fixed downstream cylinder (DC) is introduced. The results indicate that varying spacing ratios ( L/D) and reduced velocities ( U*) leads to both self-limiting galloping and lock-in instabilities in the UC. The resonance regions for the UC can be categorized into different regimes, such as lock-in, harmonic lock-in (HLN), upper branch, and lower branch regimes, based on various mechanisms. Notably, the vibrations in the HLN regime are distinct from the traditional lock-in observed in a bare cylinder, with the oscillation frequency locking onto the higher-order fluid force frequency and the occurrence of larger amplitudes. Regarding the interference galloping instability, we show that the self-limiting amplitude is related to the vortex shedding points on either side of the DC. The introduction of a fixed DC results in the observation of six vortex shedding modes: C(2S), 2S, P+T, 2T, 2P, and Aperiodic. Among these, weak vortices in the 2P mode are found to suppress the vibration amplitude. The asymmetrical and aperiodic evolution of the wake flow generates even-order fluid forces. Furthermore, an analysis of the energy transfer indicates that the tandem cylinders exhibit high fluid kinetic energy conversion ability over a wide range of U*-L/D.