Investigation of vortex-induced vibration characteristics around the NACA0009 hydrofoil with a focus on the lock-in phenomenon

The objective of this paper is to investigate the vortex-induced vibration (VIV) characteristics around NACA0009 hydrofoil, with a special emphasis on the lock-in phenomena. A synchronized experimental measurement system, comprising a high-speed camera and a laser Doppler vibrometer, was utilized to capture the global wake vortex structures and vibrational velocities. Meanwhile, an integrated fluid-structure interaction numerical method combining OpenFOAM and DEAL.II was employed to further investigate the coupling effects and lock-in mechanisms during the Vortex-Induced Vibration (VIV) process. The pressure distribution in the wake region shows periodic changes due to the alternating shedding of wake vortices, which in turn leads to hydrofoil vibration. With increasing free-stream velocity, both the vortex shedding frequency and the first-order frequency of vibration velocity trend upward, with the former rising more quickly. When the first-order frequency of the vortex shedding frequency and hydrofoil vibrational velocity approaches the hydrofoil's second-order wet natural frequency, lock-in occurs. This phenomenon accentuating the asymmetric distribution of velocity fluctuations, shortening the vortex formation length, and increase the wake thickness. Additionally, lock-in also reduces the three-dimensionality in the span of the wake vortex structure. Regarding vibration characteristics, lock-in dampens pulsation in the evolution of vibrational velocity but results in a significant increase in vibration with stronger periodicity. The occurrence of lock-in is related to the intensity of kinetic energy exchange. During lock-in, the synchronization of vortex shedding frequency with vibrational velocity results in more kinetic energy interactions between the fluid and the hydrofoil. Near the equilibrium position, more of hydrofoil's vibrational energy is converted into fluid energy. When the hydrofoil vibrates to its highest (or lowest) position, the efficiency of energy conversion from fluid kinetic energy to structural kinetic energy peaks, coinciding with the moment of trailing edge vortex shedding.