In this paper, the cavitating flow over a flexible NACA66 hydrofoil is studied numerically by a modified fluid-structure interaction strategy with particular emphasis on understanding the flow-induced vibration and the cavitating vortical flow structures. The modified coupling approaches include (1) the hydrodynamic solution obtained by the large eddy simulation (LES) together with a homogenous cavitation model, (2) the structural deformation solved with a cantilever beam equation, (3) fluid-structural interpolation and volume mesh motion based on the radial basis functions and greedy algorithm. For the flexible hydrofoil, the dominant flow-induced vibration frequency is twice of the cavity shedding frequency. The cavity shedding frequency is same for the rigid and flexible hydrofoils, demonstrating that the structure vibration is not large enough to affect the cavitation evolution. The predicted cavitating behaviors are strongly three-dimensional, that is, the cavity is (a) of a triangular shape near the hydrofoil tip, (b) of a rectangular shape near the hydrofoil root, and (c) with a strong unsteadiness in the middle of the span, including the attached cavity growth, oscillation and shrinkage, break-off and collapse downstream. The unsteady hydroelastic response would strongly affect the cavitation shedding process with small-scale fragments at the cavity rear part. Furthermore, three vortex identification methods (i.e., the vorticity, the Q- criteria and the Ω method) are adopted to investigate the cavitating vortex structures around the flexible hydrofoil. It is indicated that the cavity variation trend is consistent with the vortex evolution. The vortex structures are distributed near the foil trailing edge and in the cavitation region, especially at the cavity-liquid interface. With the transporting downstream the shedding cavities, the vortices gradually increase in the wake flows.

在本文中，通过改进的流固耦合策略对挠性NACA66水翼上的空化流进行了数值研究，尤其着重于了解流动引起的振动和空化涡流结构。改进的耦合方法包括（1）通过大涡模拟（LES）获得的流体动力解以及同质的空化模型；（2）通过悬臂梁方程求解的结构变形；（3）流体-结构插值和体积网格基于径向基函数和贪婪算法的运动。对于柔性水翼，主要的流动引起的振动频率是空腔脱落频率的两倍。刚性和柔性水翼的空腔脱落频率相同，表明结构振动不足以影响空化的发展。预测的空化行为具有很强的三维性，即（a）在水翼形尖端附近为三角形，（b）在水翼根部附近为矩形，并且（c）在空腔中具有很强的不稳定性。跨度的中部，包括附着的腔体生长，振荡和收缩，下游的破裂和塌陷。不稳定的水弹性响应会强烈影响空化后的过程，在空洞后部会出现小规模的碎片。此外，三种涡旋识别方法（即涡度，（b）在水翼根部附近呈矩形，并且（c）在跨度的中部具有强烈的不稳定性，包括附着的空洞生长，振荡和收缩，下游折断和塌陷。不稳定的水弹性响应会强烈影响空化后的过程，在空洞后部会出现小规模的碎片。此外，三种涡旋识别方法（即涡度，（b）在水翼根部附近呈矩形，并且（c）在跨度的中部具有强烈的不稳定性，包括附着的空洞生长，振荡和收缩，下游折断和塌陷。不稳定的水弹性响应会强烈影响空化后的过程，在空洞后部会出现小规模的碎片。此外，三种涡旋识别方法（即涡度，采用Q-准则和Ω方法研究柔性水翼周围的空化涡结构。结果表明，空洞的变化趋势与涡旋演化是一致的。涡流结构分布在箔片后缘附近和空化区域中，尤其是在腔-液界面处。随着流向下游的脱落腔，涡流在尾流中逐渐增加。