A unified approach for airfoil parameterization using Bezier curves

Parametrization is at the core of optimization, as it defines the design space that the optimizing algorithm explores. In addition, an industrial design workflow requires the components to be represented as the computer-aided design (CAD) model and seeks an optimized geometry also in the CAD format. This research aims to develop a unified approach for parameterizing two-dimensional airfoil geometries using the mathematical definitions of Bezier curves. In this work, an efficient and robust methodology is proposed which can be used to obtain the optimum locations of the Bezier control points, that approximately represents the airfoil shape (described using a set of data points). An error metric is defined to quantify the deviation of the approximated Bezier curve from the airfoil surface. The proposed methodology is validated on six different airfoil configurations, ranging from symmetrical NACA0012 airfoil to asymmetrical seven-digit NACA airfoil NACA747A315. This work is a step in the direction to create automated parameterization methodology, that can be implemented within a CAD system to parameterize three-dimensional aircraft wing models.