Vortex induced vibrations of a rotating circular cylinder at low Reynolds number

Vortex-induced vibration (VIV) of a rotating circular cylinder at a low Reynolds number of 150 and a low mass ratio of 2 is studied numerically. Simulations are conducted at three rotation rates of α = 0, 0.5, and 1 and reduced velocities in the range of 1–13 with an interval of 0.2. The numerical results show that the rotation of the cylinder increases the response amplitude and widens the lock-in regime for the one-degree-of-freedom (1-dof) VIV in the cross-flow direction. The two-degree-offreedom (2-dof) responses of the cylinder at α = 0.5 and 1 are significantly different from that at α = 0. For the 2-dof VIV, the response amplitude in the inline direction, which is much smaller than that in the cross-flow direction at α = 0, is increased significantly at α = 0.5 and 1. One initial branch is found at α = 0.5 and two initial branches are found at α =1. In the initial branches, the response frequency locks onto a frequency that is smaller than the natural frequency of the cylinder and the response amplitude increases with the reduced velocity. The vortex shedding is found to be in the P+S mode for reduced velocities near the higher boundary of the initial branches and 2S mode in all other reduced velocity ranges for the 2-dof VIV. Simulations are conducted under both the increasing and decreasing reduced velocity conditions. A hysteresis region is found near the higher boundary of the lower branch for α =0, 0.5, and 1 in the 1-dof of VIV and for α =0 in the 2-dof VIV. The hysteresis region occurs near the higher boundary of the initial branches for α = 0.5 and 1 in the 2-dof VIV. By analysing the component of the force coefficient that is in phase with the velocity of the cylinder, it is found that pressure force excites the vibration and the viscous force damps the vibration in both the inline and the cross-flow directions in the 2-dof VIV. The magnitude of the time averaged pressure and viscous force coefficients that are in phase with the velocities of the cylinder in the lock-in regime are found to be much greater than their counterparts outside the lock-in regime.