An intuitive parameterization method with inherently high-order differentiability for compressor blade sections based on ellipse hierarchical deformation

Shape parameterization has a crucial influence on the optimal solution of aerodynamic optimization. This paper proposes a novel parameterization method for compressor blade sections based on the three-level deformation of the ellipse, which simultaneously satisfies the requirements of flexibility, smoothness, intuitiveness, and compactness. In proposed method, the first-level deformation directly controls nine key geometric parameters to construct the blade section profile, and then the second- and third-level deformations are performed respectively to coarsely and finely modify the profile while keeping the key geometric parameters unchanged. These three levels of deformation effectively decompose the design space without destroying the ellipse’s infinite differentiability, allowing designers to work only with intuitive shape-related parameters to design blade sections with inherently high-order continuity. To verify the effectiveness, six existing blade sections are first fitted and then one of them is selected for a three-level optimization. The results show that the geometry and aerodynamic performance of the fitted and the original blade sections are in good agreement, and the loss coefficient of the optimized blade section is reduced by a total of 36.41%, with 27.34%, 8.45%, and 0.62% reductions for the first to the third level, respectively. Therefore, the proposed parameterization method facilitates the design of lower-loss and higher-load compressor blade sections.