**Tiezhi Sun 1,2, Qingmo Xie 1, Li Zou 1,2,3,\*, Hao Wang <sup>4</sup> and Chang Xu <sup>5</sup>**


Received: 21 April 2020; Accepted: 8 May 2020; Published: 11 May 2020

**Abstract:** Cavitation is a typical and unavoidable phenomenon for small waterline ships and high-speed vehicles. It creates a highly complex multiphase flow near the free surface and is primarily represented by the free surface-cavitation interaction. In this paper, the large-eddy method and Schnerr-Sauer cavitation model are combined to address the effects of a free surface on the cavitation dynamics of a NACA66 hydrofoil. The numerical method is validated by comparing the cavitation morphology and pressure with available experimental data. The results show that the presence of a free surface affects the cavitation evolution and hydrodynamic load characteristics. Compared with the non-free surface case for the same cavitation number, the free surface suppresses the cavitation intensity and increases the frequency of cavitation shedding. Furthermore, an improved dynamic mode decomposition method is applied to investigate the unsteady cavitation flow features. The results show a correlation between the characteristic mode and the flow state. Meanwhile, the presence of a free surface is found to reduce the energy content in each order mode and results in smaller scale of the coherent structure in higher-order modes. Moreover, with increasing distance from the hydrofoil to the free surface, the cavitation intensity increases, as well as the average lift and drag coefficients. In particular, significant free-surface unsteady fluctuations are observed in the wake region.

**Keywords:** near free surface; unsteady cavitation dynamics; NACA66 hydrofoil; dynamic mode decomposition
