Review of Aerofoil Parameterisation Methods for Aerodynamic Shape Optimisation

Abstract

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.

Impact of Shape Parameterisation on Aerodynamic Optimisation of Benchmark Problem

“…as used by Wu [27] and Masters [21,28] and thickness parameters will be set to t i = 1. Due to the symmetry of the problem being investigated the upper and lower surface design variables were again taken to be equal.…”

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

“…Within an optimisation procedure the choice of shape parameterisation controls the relationship between the optimisation design variables and the aerodynamic surface itself. Consequently the choice of shape parameterisation method can have a significant impact on the effectiveness and efficiency of the overall procedure 3 . Many different methods have been used within an aerodynamic optimisation framework, from standard geometric curve definitions such as B-splines 4 or NURBS 5 to aerospace-specific methods such as CST 6,7 , HicksHenne bump functions 8,9 or PARSEC 9,10 to Free-Form Deformation [11][12][13][14] , proper orthogonal decomposition 2,15,16 or the discrete method 17 .…”

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

“…Within an optimisation procedure the choice of shape parameterisation controls the relationship between the optimisation design variables and the aerodynamic surface itself. Consequently the choice of shape parameterisation method can have a significant impact on the effectiveness and efficiency of the overall procedure [3]. Many different methods have been used within an aerodynamic optimisation framework, from standard geometric curve definitions such as B-Splines [4] or NURBS [5] to aerospace-specific methods such as CST [6,7], Hicks-Henne bump functions [8,9] or PARSEC [9,10] to Free-Form Deformation [11,12,13,14], proper orthogonal decomposition [2,15,16] or the discrete method [17].…”