Numerical evaluation of the two-degree-of-freedom vortex-induced vibration prediction using forced vibration

This study employs direct numerical simulation to investigate the two-degree-of-freedom vortex-induced vibration (VIV) of a circular cylinder via the immersed boundary method. The wake structure characteristics and hydrodynamic coefficients of VIV are compared with those of forced vibration under the identical cross-flow and in-line amplitudes as well as the same phase difference between the cross-flow and inline vibrations, to validate the similarity between the forced vibration and VIV. The results demonstrate that the characteristics of forced vibration align closely with those of VIV at the same Reynolds number when the amplitudes and phase difference are consistent. In addition, the effect of phase difference is further examined in the forced vibration. When the dimensionless cross-flow amplitude exceeds 0.59, varying the phase difference leads to the alteration of vortex shedding mode. Four vortex shedding modes are identified: 2S (two single vortices are released per shedding cycle), 2P (two pairs of counter-rotating vortices are released from the upper and lower sides of the cylinder per shedding cycle), PþS (a single vortex and a pair of counter-rotating vortices are released from the cylinder per shedding cycle), and PþS^- (two pairs of counter-rotating vortices are released from the upper and lower sides of the cylinder per shedding cycle, and the secondary vortex on one side is weaker than the other side and dissipates within the subsequent 1–2 cycles, which is a newly observed mode). The existence of PþS^- mode is further verified using dynamic mode decomposition method. The curve of the mean energy transfer coefficient of VIV coincides with that of forced vibration, providing further evidence that the forced vibration can be effectively used to predict VIV.