Geometric Comparison of Aerofoil Shape Parameterization Methods

A comprehensive review of aerofoil shape parameterization methods that can be used for aerodynamic shape optimization is presented. Seven parameterization methods are considered for a range of design variables: class–shape transformations; B-splines; Hicks–Henne bump functions; a radial basis function domain element approach; Bèzier surfaces; a singular-value decomposition modal extraction method; and the parameterized sections method. Because of the large range of variables involved, the most effective way to implement each method is first investigated. Their performances are then analyzed by considering the geometric shape recovery of over 2000 aerofoils using a range of design variables, testing the efficiency of design space coverage with respect to a given tolerance. It is shown that, for all the methods, between 20 and 25 design variables are needed to cover the full design space to within a geometric tolerance, with the singular-value decomposition method doing this most efficiently. A set of transonic aerofoil case studies are also presented, with geometric error and convergence of the resulting aerodynamic properties explored. These results show a strong relationship between geometric error and aerodynamic convergence and demonstrate that between 38 and 66 design variables may be needed to ensure aerodynamic convergence to within one drag and one lift count.