Spanwise correlation of unsteady force on a free vibrating square cylinder and perspectives from a time-frequency analysis

Spanwise correlation of the unsteady force is particularly relevant to vortex induced vibration (known as VIV) and VIV-galloping interaction. In this study, pressure measurements were carried out on a free vibrating square cylinder, undergoing the VIV-galloping interaction and the separated VIV and galloping at two different Scruton numbers, respectively. Results show that whether the cylinder undergoes VIV or VIV-galloping can result in appreciable difference in the unsteady lift as well as its spanwise correlation. At the same reduced velocity, the unsteady lift magnitude in VIV-galloping interaction can be 30% higher, while the cylinder’s oscillating amplitude is only ∼3% different. This high sensitivity is also reflected in the spanwise correlation. For instance, at the same reduced velocity the correlation coefficient in the VIV-galloping case can reach 0.9 for a separation distance of 15 times the cylinder’s depth, while this is only 0.75 in the VIV case. In general, better correlation is observed in the VIV-galloping case. Hilbert transform and wavelet transform as time-frequency tools were applied to the unsteady lift. The extracted instantaneous frequency is found to fluctuate randomly in real time about cylinder’s oscillation frequency, no matter in VIV or VIV-galloping cases. Thus, from the real time point of view the vortex shedding frequency is not completely “locked” by cylinder’s oscillation. Anyway, the instantaneous frequency now fluctuates weaker compared to the stationary cylinder, and spectra analysis indicates a loss of the low-frequency energy. This loss is confirmed responsible for the largely increased spanwise correlation of unsteady lift on oscillating cylinder, supported by the extracted instantaneous frequencies capable to reconstruct the spanwise correlation of unsteady lift in either VIV-galloping or VIV cases. Finally, possible dependence of the spanwise correlation on the ways the cylinder vibrates (free or forced) is highlighted.