流体拓扑优化方法及其在叶轮机械中的应用

相比于结构拓扑优化，流体拓扑优化的发展较为滞后。为了促进流体拓扑优化在叶轮机械领域的应用，根据公开资料中的研究成果，首先介绍了该方法的理论基础，包括优化问题数学模型、流动控制方程及求解方法、灵敏度分析技术、优化不稳定问题的预防措施及几何重构方法。然后总结归纳了流体拓扑优化在叶轮机械气动热力学领域的研究现状，通过对涡轮叶片内部冷却结构、涡轮叶片叶顶结构以及离心压气机弯道设计的描述，指出该方法的技术优势。研究表明，相比于传统形状和尺寸优化方法，拓扑优化具有更高的设计自由度，且突破了结构参数化的限制，有助于挖掘具有优良性能的新型结构。最后，对流体拓扑优化方法在未来叶轮机械设计中的发展进行了展望。

Fluid Topology Optimization Method and Its Application in Turbomachinery

Relative to structural topology optimization, fluid topology optimization method is inadequately developed. In order to promote the application of fluid topology optimization in turbomachinery field, theoretical basis of this method is introduced according to research achievements in the open literature. It includes mathematical formulations for the optimization, fluid governing equations and their solution method, sensitivity analysis techniques, preventive measures of unstable problems and geometrical reconstruction approaches. Then, literature review on current studies of fluid topology optimization about aero-thermal problems in turbomachinery field is summarized. In order to pinpoint the technological superiority of this method, relevant designs of turbine blade internal cooling structure, turbine blade tip geometry and centrifugal compressor bend are described. These studies indicate that compared to traditional shape and size optimization methods, the topology optimization has higher degrees of design freedom and can overcome the limitation of structure parameterization. This can aid to excavate novel structures with good performance. Finally, future prospects of the development of fluid topology optimization in turbomachinery field are forecasted.