A Surface Parameterization Method for Airfoil Optimization and High Lift 2D Geometries Utilizing the CST Methodology

For aerodynamic modeling and optimization, it is desirable to limit the number of design variables to reduce model complexity and the requirements of the applied optimization scheme. The Class/Shape Transformation (CST) surface parameterization method presented by Kulfan has proven to be particularly useful for this while maintaining a wide range of applications. These include everything from smooth airfoils to 3D axi-symmetric bodies and wings. However, the CST method is confined to smooth geometries. This limits the CST method in applications incorporating discontinuous surfaces such as high lift aerodynamics with circulation control (CC) slots and flaps. The trailing edge slot on a circulation control wing (CCW) airfoil is not well modeled by the CST method. A parameterization of a CCW airfoil will result in the trailing edge slot being smoothed over. Therefore, a modified CST method must be utilized. For the case of parameterizing a known CCW airfoil, this is accomplished by detecting drastic changes in curvature and beginning a new parameterization in a "multi-surface parameterization" method. For creating a new CCW airfoil, this is achieved by modifying the 2D CST equations to incorporate a slot thickness term that also includes the horizontal location. These two methods can then be extended into 3D to model a circulation control wing (CCW) or even a blended wing body (BWB) aircraft incorporating CCW. The multi-surface parameterization modification can also be used to model other complex geometries to further enhance the robust nature of the CST method, thus creating a valuable design tool.