Modifications of class-shape transformation driven by aerodynamic concerns over leading-edge region

Geometrical representation method plays a fundamental role in aerodynamic design in that it makes preparation for design space. A good design space should be composed of design variables that are more likely to attain the solution to the problem than others. This study finds that due to the characteristics of Bernstein polynomials, a conventional class-shape transformation (CST) geometrical representation method is insufficiently focused on the leading-edge region of airfoils/wings. However, more aerodynamic attention is required there because it has strong relationship with the aerodynamic performance of whole geometry. The lack of design variables assigned to the leading-edge region is likely to compromise the effort in finding better optimization results in design space. While maintaining the convenience and accuracy of conventional CST, this study proposes two types of modifications to add more aerodynamic insights into the leading-edge region: (1) an approach of supplementary vertical CST aiming to describe the leading-edge region upon the fitting result of conventional CST; (2) an approach of globally transforming airfoil surfaces into a single-value function with respect to x-direction so that the leading-edge region avoids being split up into two separate parts. With those two modifications, the leading edge can be put to the center of geometric description by rotating the local coordinate system after tackling some other issues that come with the operation. Modification 1 is intuitive, although it requires additional attention to some parameters for the continuity between the leading-edge region and other regions of the airfoil. Modification 2 is convenient to implement, but has limitations on accuracy control because the result of shape error has to account for the introduction global transforming function. Two modifications are illustrated, and their applications are discussed in the study, showing the perspective of being utilized in aerodynamic design that involves delicate difference of aerodynamic performance brought by variations of leading-edge shape.