Damping effects on vortex-induced vibration of a circular cylinder and implications for power extraction

The effect of damping on vortex-induced vibration (VIV) of a circular cylinder with a fixed mass ratio (m∗=3.0) was studied through water-channel experiments. An eddy-current-based damping mechanism was constructed to provide controlled and adjustable damping values. It consisted of a permanent magnet connected to the cylinder that moves parallel to a copper plate at some predetermined gap, which determines the damping in the system. Increased damping was found to reduce the reduced-velocity range of the upper and lower branches, thus reducing the synchronization region. As the damping is increased, the lower branch remains easy to identify from the amplitude response curves, but the boundary between the initial and upper branch becomes less clear. However, the frequency response under higher damping shows similarities to that at the lowest damping and these similarities, for the first time, were used to delimit the different response branches. The existence of the upper branch was found to continue down to A∗≈0.2D. The experimental data was assembled to plot the peak amplitude response as a function of the mass-damping parameter in a “Griffin plot”. Due to a restricted variation in Reynolds number in the experiments, the measured data shows negligible scatter compared to the assembled literature data. Three sets of experiments using different sets of springs were conducted to quantify the Reynolds number effect previously established by Govardhan and Williamson (2006). An exponential fitting function was then used to successfully fit the data on the Griffin plot. Under higher damping, it was found that the total and vortex phases are no longer at either 0°or 180°, and take intermediate values throughout the response branches. The power extracted by the damping mechanism was also calculated. Maximum power extraction occurs for a combination of optimal damping and reduced velocity. The power was also found to increase with Reynolds number, correlated with the increase in vibration amplitude. At the highest Reynolds number examined, the dimensionless energy conversion ratio is 0.2, indicating that approximately 20% of the flow energy approaching the cylinder frontal cross-section can be converted to useful electrical energy. This factor increased substantially with Reynolds number from approximately 15 to 20% over the Reynolds number range considered (Re∼1700-5900). The fit devised for the peak vibration amplitude was extended for expressing the average extracted power as a function of mass-damping and Reynolds number.