Application-Speci¯c Class Functions for the Kulfan Transformation of Airfoils
Stephen L. Powell, András Sóbester · 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference · 2010
Choosing a geometry representation technique for multidisciplinary design optimization can be a difficult task, especially for geometries such as airfoils where a vast array of techniques exist. We require a formulation that can accurately approximate existing airfoils whilst limiting the number of variables, thereby reducing the cost of exploring the design space. In addition to this, the technique must also have the ability to consistently produce physically viable shapes when used in multidisciplinary design optimization. One such geometry technique designed to meet these requirements is the Kulfan class-shape transformation: a class function is used to describe the underlying shape of an object, with the more intricate detail approximated by a shape function generally comprised of Bernstein polynomials. Evidence indicates that, although this method can accurately approximate a subsonic airfoil with a small number of terms in the shape function, it finds it difficult to approximate NASA’s SC(2) airfoils with the same degree of accuracy. We suggest that the Kulfan transformation can perform better using a different class function for these SC(2) airfoils, which we find using a Genetic Programming(GP) search. We modify the GP search by introducing a local search to optimize the coefficients in each expression, thus rewarding (in evolutionary terms) the expression’s ability to produce an appropriate class function. We compare the performances of the evolved class functions found with the general class function, showing that the evolved class functions provide better accuracy for approximating the SC(2) family of airfoils.