Hydrofoil sections operating near the free surface are highly prone to marine cavitation, which is the appearance of vapor cavities inside an initially homogeneous liquid medium. Advances in computational and experimental research have led to a better understanding of this multiphase phenomenon, thus enabling researchers to predict and alleviate its adverse effects on hydrofoil performance. In this work, a new BEM-based adjoint optimization prediction method, where the attached cavity is modeled as a free-streamline, is proposed for the analysis of partially cavitating hydrofoils that move with a constant speed beneath the free surface. Following an inverse problem approach, this potential method poses an alternative to higher-fidelity multiphase flow models for sheet cavitation with free surface effects for hydrofoils at moderate submergence depths and angles of attack. The proposed numerical scheme predicts well the cavity shape and cavitation number, under the given cavity length assumption, when compared against experimental data and other methods. The developed numerical tool could facilitate the preliminary design of partially cavitating lifting surfaces with, or without, free surface effects.

在自由表面附近运行的水翼部分非常容易发生海洋空化，这是在最初均质的液体介质中出现蒸汽空腔。计算和实验研究的进步使人们更好地理解了这种多相现象，从而使研究人员能够预测和减轻其对水翼性能的不利影响。在这项工作中，提出了一种新的基于边界元法的伴随优化预测方法，其中附着腔被建模为自由流线，用于分析在自由表面下以恒定速度移动的部分空化水翼。遵循逆问题的方法，这种潜在的方法为具有中等浸没深度和攻角的水翼的自由表面效应的片状空化提供了一种更高保真度的多相流模型的替代方案。所提出的数值方案很好地预测了空腔形状和空化数，在给定腔长假设，与实验数据和其他方法进行比较时。开发的数值工具可以促进具有或不具有自由表面效应的部分空化提升表面的初步设计。