Bézier–PARSEC parameterization for airfoil optimization

A new parameterization method is developed for airfoils. The method combines the best characteristics of two previous polynomial methods: the Bézier parameterization and the PARSEC parameterization. The new Bézier–PARSEC (BP) parameterization is a second-order continuous combination of four Bézier curves, two each for the camber and thickness distributions. Twelve parameters control the geometry. These are all based on the aerodynamics of the shape, such as leading edge radius and angle, rather than on the Bézier control points themselves. The intent of the new parameterization is to improve the characteristics of the design space in an aerodynamic optimization problem by reducing the nonlinear interactions between design parameters. It is demonstrated that the new method is able to parameterize a broad range of airfoils, and that it has potential for accelerating convergence of evolutionary aerodynamic optimization.