Parameterizing Airfoil Shape Using Aerodynamic Performance Parameters

A novel shape parameterization for airfoils (named as PAERO) is proposed to provide design variables related to the aerodynamic characteristics based on the linearized aerodynamic theory. The idea is inspired by the classical thin airfoil theory. Instead of describing the airfoil geometry explicitly, the mean camber line of an airfoil can be implicitly defined by the vortex distribution on the chord line that is expressed by a Fourier series in the thin airfoil theory. The Fourier series is parameterized by the Fourier coefficients specified by users. Within the frame of linearized aerodynamic theory, the first three Fourier coefficients are determined by the angle of attack, lift coefficient, and pitching moment coefficient, naturally providing three aerodynamic performance parameters. Then, the airfoil shape parameterization is completed by further parameterizing the thickness distribution by either the Class-Shape-Transformation method or the B-splines, depending on the specific applications. The test results show that the proposed shape parameterization has the same ability of fitting the existing airfoils as the traditional Class-Shape-Transformation method, but providing more aerodynamic performance parameters that are proved to be highly useful in applications.