Flow-induced vibration of a square cylinder in low-Re flows: Excitation mechanisms at different mass ratios

Two-dimensional numerical simulations of flow-induced vibration (FIV) of a square cylinder in laminar flow with a Reynolds number Re = 170 are carried out, and the influence of the mass ratio on the FIV characteristics is studied. The results show that the mass ratio affects the vibration responses distinctly in different regimes. In the vortex-induced vibration (VIV) regime, a larger mass ratio results in a smaller amplitude. On the contrary, in the galloping regime, a larger mass ratio leads to a greater amplitude, causing the galloping starts at a lower reduced velocity. Furthermore, the VIV-galloping coupling effect, as observed in the galloping regime, becomes stronger with increasing mass ratio. To further elucidate the vibration mechanisms, the instantaneous phase lag between displacement and lift force, the work done by the vortex lift and the potential lift, and their influences on vibration responses are carefully investigated. In the VIV regime, the vortex lift contributes primarily to the vibration while the potential lift becomes significant in the galloping regime. More specifically, both forces do positive work in the initial and upper branches of VIV, leading to an increase in the vibration amplitude. However, in the lower branch, the potential lift continues to contribute positively, while the vortex lift does negative work, extracting energy from the vibration system. The counteracting vortex and potential lift cause a decrease in the vibration amplitude. With further increasing the reduced velocity, the vortex lift alternately promotes or inhibits the vibration in the galloping regime, while the potential lift consistently contributes positively to the work done, playing a leading role. As a result, the vibration amplitude increases in the galloping regime.