A Geometric Comparison of Aerofoil Shape Parameterisation Methods

A comprehensive review of aerofoil shape parameterisation methods that can be used for aerodynamic shape optimisation is presented. Seven parameterisation methods are considered for a range of design variables: class function/shape function transformations (CST); B-Splines; Hicks-Henne bump functions; a domain element approach using Radial Basis functions (RBF); B`ezier surfaces; a singular value decomposition modal extraction method (SVD); and the PARSEC method. Due to the large range of variables involved the most effective way to implement each method is first investigated. Their performance is then analysed 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 SVD method doing this most efficiently. A more detailed study is presented for three aerofoils, RAE2822, ONERA M6 (D section) and NACA4412 with geometric error and convergence of the resulting aerodynamic properties explored. The case study results give insight into the rate at which the aerodynamic properties converge relative to the geometric design variables and suggests that the geometric tolerance may not always be a sufficient condition to guarantee convergence of these properties.