A Unified Approach for Airfoil Parameterization Using Bezier Curves

Abstract

Introduction: Parametrization is at the core of optimization, as it defines the design space that the optimizing algorithm explores. The success of any shape optimization methodology depends extensively on the type of parameterization technique employed [10]. One straightforward route which results in the most flexible parametrization strategy is to use the nodes of the computational mesh as the design variables. One major drawback for this parameterization strategy is that, as all surface mesh nodes can move independently, the implementation of a smoothing algorithm is required to prevent the appearance of non-smooth shapes during the optimization process. In this regard, the Free-form deformation (FFD) techniques have been successfully implemented for aerodynamic shape optimization problems [Ref]. The benefit of this approach is that it imparts smooth deformations to the analysis mesh and enables the parameterization to alter the thickness, sweep, twist, etc. for the design of an aerospace system. However, in either of these parameterization strategies it is only the mesh which reaches the optimum, and must be translated into a CAD model before it can be used for further analysis or manufacturing assessments. Thus, to align with the industrial ambition of having a more integrated design workflow, the compatibility of design parameterization with Computer-Aided Design (CAD) software has become very important. In the recent past, some authors have attempted to develop optimization processes based on parameterization developed with CAD systems. These include, parameterization based on nonuniform rational B-splines (NURBS) [8], B-Splines in the Open-Cascade Technology [6], parameters defining CAD features [3] and Bezier curves [4] within CATIA V5. But there has been no standard approach which can be followed to parameterize different airfoil geometries and can also be used within CAD systems. In this research, a unified approach is presented to obtain the Bezier parameterizations for different airfoil geometries obtained from the UIUC Airfoil Data Site [2].