General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Department of Aerospace Engineering, University of BristolA 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: CSTs; B-Splines; Hicks-Henne bump functions; a Radial Basis function (RBF) domain element approach; Bèzier 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 set 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.

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This paper presents a review of aerofoil shape parameterisation methods that can be used for aerodynamic shape optimisation. Six parameterisation methods are considered for a range in design variables: Class function/Shape function Transformations (CST); B-splines; Hicks-Henne bump functions; a domain element approach using Radial Basis functions (RBF); Bèzier surfaces; and a singular value decomposition modal extraction method (SVD); plus the PARSEC method. The performance of each method is analysed by considering geometric shape recovery on over 1000 aerofoils using a range of design variables, testing the efficiency of design space coverage. A more in-depth analysis is then presented for three aerofoils, NACA4412, RAE2822 and ONERA M6 (D section), with geometric error and convergence of the resulting aerodynamic properties presented. In the large scale test it is shown that, for all the methods, a large number of design variables are needed to achieve significant design space coverage. For example at least 25 design variables are needed to cover 80% of the design space regardless of the method used; this is often higher than is desired for two-dimensional studies, suggesting that further work may be required to reduce the number of design variables needed.