Efficient Modal Design Variables Applied to Aerodynamic Optimization of a Modern Transport Wing

Aerodynamic shape optimization of a transonic wing using mathematically-extracted modal design variables is 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. 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 been tested previously on geometric shape recovery problems and aerodynamic shape optimization in two dimensions, 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 three dimensions. It has been shown previously that fewer than 10 aerofoil modes are required to obtain shock free solutions from initial strong shock, highly-loaded aerofoils. Wing shape optimization in transonic flow is performed here using an upwind flow-solver and parallel gradient-based optimizer, and a small number of global deformation modes are compared to a section-based local application of these modes and to a previously-used section-based domain element approach to surface deformations. The modal approach is shown to be particularly effective, with local application of modal design variables resulting in a shock-free solution and a 30% reduction in drag.