Geometry parameterization plays a significant role in axial compressor design and optimization, and it can also be used to model geometric deviations that may occur during manufacturing or operation. In such applications, it is necessary to use the minimum possible set of variables to parameterize the geometry while still maintaining an acceptable level of accuracy. Achieving this balance between compactness and precision is essential for efficient aerodynamic analysis and design processes.



In this paper, several widely used parameterization methods in the field of aerodynamics are implemented and compared in the specific context of axial compressor blades. The investigated approaches include common curve-fitting methods, class/shape function transformation, parametric sections, Hicks–Henne functions, and singular value decomposition. In addition, the Lange method, which is a commonly used parameterization approach for compressor blade airfoils, is also presented and discussed in detail.



To assess the efficiency and effectiveness of these methods, two transonic compressor blade airfoils were parameterized and compared. Their performance was evaluated in terms of accuracy and suitability for representing blade geometry with a limited number of design variables. The results showed that the curve-fitting methods exhibit the lowest error among the methods considered. However, since the Lange method relies on explicit variables and provides reasonable accuracy, particularly at the leading and trailing edges, it can be regarded as a reliable and practical choice for turbomachinery design applications where these regions are critical.



Overall, the study indicates that there is no globally optimal parameterization method. The most suitable choice depends on several factors, including the number of parameters, the geometry of interest, and the type of problem being addressed. To facilitate decision-making in design and optimization studies, the methods were systematically compared and ranked based on key criteria. This provides guidance for selecting an appropriate parameterization strategy that meets both accuracy and efficiency requirements in specific engineering tasks.