This article presents the development of a new inverse design algorithm capable of generating blade geometries for cavitating cascade flows. With this methodology, we demonstrate the controllability of the pressure distribution in and around the cavity and thereby provide a means to regulate the aggressiveness of blade cavitation phenomena. The solver proposed here uses the Tohoku–Ebara equation of state to model phase change, combined with bespoke preconditioning and multigrid methods designed to handle the system's ill conditioning and cope with the hypersonic flow regime of the mixture, respectively. Blade geometries and the cavitating flow field are calculated simultaneously in a robust and efficient manner, with a blade loading that matches the target distribution. In this article, the accuracy of the cavitating flow solver is first demonstrated for the NACA0015 hydrofoil case and associated experimental data. The inverse design procedure is then applied to a typical axial flow pump cascade: a new blade profile is generated with a topology that successfully reduces the gradient of the pressure jump at cavity closure.

中文翻译：

---

一种强大的逆向设计求解器，用于控制水翼叶栅上空化流的潜在侵蚀性

本文介绍了一种新的逆向设计算法的开发，该算法能够为空化叶栅流生成叶片几何形状。通过这种方法，我们证明了空腔内和空腔周围压力分布的可控性，从而提供了一种调节叶片空化现象侵袭性的方法。这里提出的求解器使用 Tohoku-Ebara 状态方程来模拟相变，结合定制的预处理和多重网格方法，分别用于处理系统的病态和处理混合物的高超声速流动状态。叶片几何形状和空化流场以稳健有效的方式同时计算，叶片载荷与目标分布相匹配。在本文中，空化流动求解器的准确性首先在 NACA0015 水翼案例和相关实验数据中得到证明。然后将逆向设计程序应用于典型的轴流泵级联：生成新的叶片轮廓，其拓扑结构成功地降低了空腔闭合时的压力跳跃梯度。