Evolution of the vibration amplitude Figure 0 1 Frequency spectrum of vibration amplitude 5. Conclusions In this paper, the unsteady cavitating flow around a modified NACA66 hydrofoil and corresponding flow-induced vibration characteristics are studied. The primary findings include: 1) With the decreasing of the cavitation number, the cavitating flows display incipient cavitation, sheet cavitation, cloud cavitation and supercavitation. The corresponding vibration magnitude changes with different cavitation regimes: maximum vibration amplitude keeps relative small for the inception cavition and sheet cavitation, and increases dramatically for the cloud cavitation because of the increasing unsteadiness of cavity structures around the hydrofoil. The mean cavity lengths decrease with the increase of the cavitation number. The increase of the maximum vibration amplitude for the cloud cavitation is due to the unsteady cavity shedding and a sharp decline of the vibration amplitude for the supercavitation is mainly because of the relative steady characteristics in that stage. 2) For the cloud cavitation regime, the partial sheet cavity is formed at initial time of a period and develops along with the formation of the re-entrant jet. As the re-entrant jet reaches the vicinity of the leading edge, the cloud cavity with high vapor fraction sheds downstream, with the interaction between counter-rotating vortices, which result to the final shedding of the whole cavities as well as the vortex structures. 3) The cavitation development strongly affects the vibration response, which is corresponding to the periodically developing and shedding of the large-scale cloud cavity, with the main frequency is accordance with the cavity shedding frequency and other two vibration frequencies are corresponding to the bending and twisting frequency. Acknowledgments The authors gratefully acknowledge the support by the National Natural Science Foundation of China (Grant Nos.: 51306020 and 11172040), the Natural Science Foundation of Beijing (Grant No. 3144034), the Excellent Young Scholars Research Fund of Beijing Institute of Technology and the China Scholarship Council (No.201506030091). References [1] Joseph D D 1995 Cavitation in a flowing liquid Phys. Rev. E 51 1649-1650 [2] Paik B G, Kim K S, Kim K Y, Ahn J W, Kim T G, Kim K R, Jang Y H, Lee S U 2011 Test method of cavitation erosion for marine coatings with low hardness Ocean Eng. 38(13) 1495- 1502 [3] Ji B, Luo, X W, Arndt R E A, Peng X X, Wu Y L 2015 Large eddy simulation and theoretical investigation of the transient cavitating vortical flow structure around a NACA66 hydrofoil Int. J. Multiph. Flow 68 121-134