Robust Design of 3D Shock Control Bumps to Transport Aircraft under Realistic Uncertainties

With the continuous increase in the number of commercial flights, environmental and economic concerns are key drivers towards the reduction of operational cost and emission of greenhouse gasses. The use of aerodynamic shape optimization plays a key role in reducing aerodynamic drag and the overall carbon footprint of aircraft. It has been regularly carried out in a deterministic fashion, neglecting uncertainty. However, the sensitivity of the optimal shape to operational and environmental uncertainties can affect the real aircraft performance. A possible solution to increase the robustness of existing aircraft is the development of retrofits that are tailored to the current airliner's operations. Shock control bumps are attractive retrofit for aircraft flying in routes at considerably higher speeds than the design point. The objective of this paper is the robust design of a 3D array of shock control bumps that can be retrofitted to the XRF1 transport aircraft configuration. Realistic uncertainties in Mach number, lift coefficient and altitude are extracted following aircraft surveillance data using the OpenSky Network for a selected air route. A tailored Gradient-Based Robust Design methodology that combines the adjoint method with Gaussian Processes is used for the optimization under these uncertainties. The robust optimum array of bumps is able to mitigate the normal shock wave over the upper surface of the wing, reducing the average drag by 3.2% compared to the clean wing. More importantly, its performance is superior compared to the configurations obtained at single-point and multi-point optimization, showcasing the benefits of a probabilistic formulation for the retrofit of 3D shock control bumps