High-fidelity aerodynamic shape optimization using efficient orthogonal modal design variables with a constrained global optimizer

Aerodynamic shape optimization of aerofoils using efficient orthogonal design variables is considered using a global search algorithm. A novel approach is presented for deriving shape design variables, using a proper orthogonal decomposition of a set of training aerofoils to obtain an optimally efficient set of aerofoil 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. A global search algorithm with an efficient constraint handling method has been developed and used here to optimize a suite of inviscid and viscous compressible aerofoil test cases using varying numbers of modal parameters. Often, an artefact of inviscid optimizations is an oscillatory pressure distribution, so to alleviate this drag minimization with a modulus of curvature penalty is also considered for the inviscid optimizations, where the penalty is used to force smoother pressure distributions; this is not necessary in the viscous optimizations. Results indicate that often fewer than 10 design parameters are required to obtain shock free solutions even from highly-loaded aerofoils with significant shocks.