A review of parameterization methods for airfoil design

Abstract

Airfoil parameterization, or the description of airfoil geometry by a tractable set of parameters, has been the focus of a multitude of publications for nearly a century. The present work provides an explanation of and commentary on a large portion of these methods, as well as a summary of their use in airfoil design and optimization. Recommendations for using airfoil parameterization methods is provided, taking into account the type of airfoil design problem, as well as an updated review of current parameterization techniques. Additionally, a novel parameterization technique using $G^2$-continuous composite Bézier curves is introduced. This airfoil parameterization method is compared in terms of performance against a selection of other airfoil parameterization methods from the literature in a set of airfoil fitting problems. This comparison demonstrates that higher-order parameterization methods provide better fidelity of airfoil representation than the lower-order parameterization methods, both when applied to an NACA 0012 airfoil and an RAE 2822 airfoil. The composite Bézier approach also gave excellent results used to define other well-known airfoils. A comparison of aerodynamic shape optimizations using these parameterization approaches further showed that higher-order methods like the degree-5 B-spline and degree-6 Bézier provide a more effective optimal design, when compared to lower-order methods.