Turbomachinery design is increasingly carried out by means of automated workflows based on high-fidelity physical models and optimization algorithms. The parametrization of the blade geometry is an essential aspect of such workflows because it defines the design space in which an optimal solution can be found. Currently, parametrization methods used for this purpose are often tailored to one particular type of turbomachinery blade, do not provide shape derivatives required for gradient-based optimization, or are not suited to re-parametrize a baseline blade geometry defined by a set of scattered point coordinates in a systematic way. This paper thus presents a general blade parametrization method for axial, radial, and mixed flow blades based on typical turbomachinery design variables and NURBS curves and surfaces. The shape derivatives are computed by means of the complex-step method, allowing the integration of the parametrization into gradient-based shape optimization workflows. In addition, the method enables the re-parametrization of a blade geometry defined by a cloud of points by solving a two-step optimization problem. The capabilities of the method are demonstrated by replicating eight blade geometries in two and three dimensions with an accuracy comparable to the tolerances of current manufacturing technologies.

借助基于高保真物理模型和优化算法的自动化工作流程，越来越多地进行涡轮机械设计。叶片几何形状的参数化是此类工作流程的重要方面，因为它定义了可以在其中找到最佳解决方案的设计空间。当前，用于此目的的参数化方法通常是针对一种特定类型的涡轮机械叶片量身定制的，不提供基于梯度的优化所需的形状导数，或者不适合对由一组分散点定义的基准叶片几何形状进行重新参数化有系统地进行协调。因此，本文基于典型的涡轮机械设计变量以及NURBS曲线和曲面，针对轴向，径向和混合流叶片提出了一种通用的叶片参数化方法。形状导数是通过复杂步骤方法计算的，从而可以将参数化集成到基于梯度的形状优化工作流程中。另外，该方法通过解决两步优化问题，使得能够对由点云定义的叶片几何形状进行重新参数化。该方法的功能通过复制二维和三维的八个叶片几何形状而得以证明，其精度可与当前制造技术的公差相媲美。