Free-form aerodynamic wing optimization using mathematically-derived design variables

Aerodynamic shape optimizations of aerofoils and wings using mathematically-derived design variables are presented. A novel approach is used for deriving design variables using a proper orthogonal decomposition of a set of training aerofoils to obtain an efficient, reduced set of deformation ‘modes’ that represent typical design parameters such as thickness and camber. A major advantage of this extraction method is the production of orthogonal design variables, and this is particularly important in aerodynamic shape optimization. These design parameters have previously been tested on geometric shape recovery problems and been shown to be efficient at covering a large portion of the design space, hence the work is extended here to consider their use in aerodynamic shape optimization in two and three dimensions. Using these mathematically-extracted design variables allows the use of global search algorithms for the optimization process in two dimensions, since a small number of parameters are required and these are also orthogonal. In three dimensions a parallel gradient-based optimiser is used. It is shown for two-dimensional inviscid compressible test cases, fewer than 10 aerofoil modes are required to obtain shock free solutions from initial strong shock, highly-loaded aerofoils. In three dimensions, a small number of local and global deformation modes are compared to a section-based application of these modes and to a previously-used section-based domain element approach to defor- mations, and applied to a transonic wing optimisation. The modal approach is shown to be particularly efficient with, again, fewer than 10 design variables required to achieve an effective optimisation.