Shape Parameterization of Airfoil Shapes Using Bezier Curves

Abstract

Shape parameterization plays an important role in aerodynamic shape optimization process. The parameterization method used for optimization must be able to accurately model the aerodynamic body and also it should be flexible enough to take all the possible shapes in the design space. In this paper, we have studied Bezier curve approximation of airfoil using fourth-order, sixth-order and eighth-order Bezier curves. We observe that sixth-order Bezier can accurately model the airfoil shape. In order to represent an airfoil using Bezier curves we have to find control points vector $P$ and vector $t$ of nodes, where each node corresponds to one data point. An iterative process with an initial guess of vector $t$ was used to find the best possible control points vector $P$ and vector $t$. Two different airfoil geometries were modeled using Bezier curves in this paper. The results for both the airfoil problems show that sixth-order Bezier curves can model airfoil shapes accurately. Also new shapes can be produced easily from Bezier curves just by moving the control points, hence Bezier curves can be used to parameterize aerodynamic shapes for shape optimization problems.