Large-eddy simulation (LES) is used to simulate flow over a three-dimensional elliptical hydrofoil at 12 degrees angle of attack and Reynolds numbers () of and based on root chord length and freestream velocity. The simulations are performed at the cavitation number () of 2.1 and are based on the experiments of Boulon et al. (1999), who studied the tip vortex cavitation behavior under the confinement of side and bottom walls. The present simulations correspond to their case where the confinement due to the bottom wall is negligible. The computational model of Brandao and Mahesh (2022) that treats vapor as a passive scalar in an incompressible liquid is extended to account for multiple groups of bubbles of different sizes, effectively making it a polydisperse model. This allows us to investigate the effects of water quality on inception. The simulations include two different freestream nuclei distributions that are taken from the water tunnel data of Khoo et al. (2020c). It was found that inception is strongly dependent on the amounts of nuclei in the freestream. When the flow is depleted of nuclei, inception is an intermittent event confined to a location very close to the hydrofoil tip. However, when the flow is rich in nuclei, a larger portion of the tip vortex cavitates, as well as part of the suction side very close to the leading edge of the hydrofoil. Probability density functions revealed that cavitation occurs in any region experiencing a pressure field lower than vapor pressure when the flow is rich in nuclei, while extremely low values of pressure (usually kPa of tension) are required to make a flow depleted of nuclei cavitate. The topology of a flow poor in nuclei was investigated and inception was found to occur in regions dominated by irrotational straining with high stretching rates. Lagrangian statistics showed that as is increased, nuclei have higher likelihood of experiencing very low pressure fields. However, the amount of time they are subject to very low pressures is also shorter with increasing .

中文翻译：

---

初始条件下椭圆水翼尖端涡空化的大涡模拟

大涡模拟 (LES) 用于模拟 12 度攻角下三维椭圆水翼上的流动，雷诺数 () 为 和 基于根弦长度和自由流速度。模拟是在空化数 () 为 2.1 时进行的，并且基于 Boulon 等人的实验。 (1999)，他研究了侧壁和底壁约束下的尖端涡空化行为。当前的模拟对应于底壁的限制可以忽略不计的情况。 Brandao 和 Mahesh（2022）的计算模型将蒸汽视为不可压缩液体中的被动标量，该模型被扩展为考虑多组不同尺寸的气泡，有效地使其成为多分散模型。这使我们能够研究水质对初始的影响。模拟包括两种不同的自由流核分布，这些分布取自 Khoo 等人的水洞数据。 （2020c）。研究发现，起始强烈依赖于自由流中的原子核数量。当流耗尽核时，起始是一个间歇性事件，仅限于非常靠近水翼尖端的位置。然而，当流动富含核时，尖端涡流的较大部分以及非常靠近水翼前缘的吸力侧的部分会形成空穴。概率密度函数表明，当流富含核时，空化发生在任何压力场低于蒸气压的区域，而需要极低的压力值（通常是kPa张力）才能使核流耗尽空化。研究了核中贫乏流动的拓扑结构，发现起始发生在以高拉伸率的无旋应变为主的区域。拉格朗日统计表明，随着压力的增加，原子核经历非常低压场的可能性就更大。然而，随着压力的增加，它们承受极低压力的时间也会缩短。