Efficient aeroelastic wing optimization through a compact aerofoil decomposition approach

Efficient optimization of an aeroelastic wing is presented through multi-disciplinary analysis using low-dimensional modal design variables. Much work in wing optimization has concentrated on high-fidelity surface control, therefore utilising often hundreds of design variables. However, whilst fine surface control can be useful, problems can arise such as large disparities in design variable values when planform variables are introduced, slow convergence speeds, and lack of compatibility with global algorithms. Therefore, the focus of this paper is to filter the design space of this problem to reduce the dimensionality and complexity of the problem. Orthogonal geometric design variables are derived in the geometric space via singular value decomposition. Orthogonality of design variables leads to a well-conditioned design space and ensures effective optimizer convergence. These variables are applied in a sectional fashion for fixed planform drag minimization of a flexible transonic wing, using a gradient-based optimizer. Shock-free solutions are demonstrated when optimizing a rigid wing, indicating suitability of the aerofoil modes for sectional-based wing optimization. However, it is shown that these wings have poor performance when subsequently deformed under flight loads, hence optimisation including full aeroelastic performance is performed. Encouragingly, shock-free solutions are again computed. Loading is shifted outboard, leading to increased tip deflection. Monotonic improvement in the objective function (drag) with increase in dimensionality is also proven. Furthermore, applying these sectional deformation modes globally across the wing with only 10 design variable leads to a 28% drag reduction, which is within 7 drag counts of when the modes are applied locally through 82 design variables. This therefore opens the possibility of introducing global optimization algorithms to high-fidelity aeroelastic wing optimization.