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

At high Reynolds numbers, the classical von Kármán vortex shedding is accompanied by random fluctuations in the instantaneous vortex shedding frequency (IVSF). Recently, the non-synchronized IVSF fluctuations in the spanwise direction have also been recognized as critical in the spanwise loss of unsteady lift correlation. As the spanwise correlation of unsteady force is relevant to vortex-induced vibration (VIV) and VIV-galloping interaction, particular interest in IVSF arises for a cylindrical body oscillating in the frequency lock-in state. 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. Hilbert transform and wavelet transform, as time-frequency tools, were used to extract IVSF from the unsteady lift. Results first show that whether the cylinder undergoes VIV or VIV-galloping can result in significant differences in the unsteady lift as well as its spanwise correlation. At the same reduced velocity, the magnitude of the unsteady lift for the cylinder in VIV-galloping interaction can be 30% higher, while the oscillating amplitude is only ∼3% different. This high sensitivity to the oscillating amplitude is also reflected in the spanwise correlation, with the correlation coefficient at large separation differing by up to 20%. Either in VIV or VIV-galloping cases, the extracted IVSF is found to fluctuate randomly. Thus, from the real-time point of view, the vortex shedding frequency is not completely “locked” by the cylinder's oscillation. Anyway, IVSF now fluctuates more weakly compared to the stationary cylinder, and spectral analysis indicates a loss of the low-frequency energy. This loss is confirmed to be responsible for the largely increased spanwise correlation of unsteady lift on the oscillating cylinder. The present study provides new insight into spanwise force correlation from the perspective of IVSF and offers valuable references for future mathematical modeling.