Optimization under Uncertainty of Shock Control Bumps for Transonic Wings

Shock control bumps are retrofit devices that increase the performance of transonic wings by decreasing wave drag. They are highly sensitive to the shock wave location and random fluctuations in flight. The objective of this paper is to optimize a 3D shock control bump for a transonic wing under stochastic flight conditions such as freestream Mach number and lift coefficient. An efficient robust gradient-based optimization framework that relies on the adjoint formulation is used. The mean and standard deviation of the drag coefficient and its gradients are efficiently obtained using Gaussian Processes. The optimum is obtained at a reduced number of iterations that is independent to the number of design parameters. The robust configuration outperforms the traditional single-point and multi-point optimum in terms of average drag reduction. A pareto front of robust optimum configurations in terms of variability and expectation of the drag is provided, enabling the designer to choose the desired configuration based on their individual needs. By taking uncertainty into account, shock control bumps extend their operating range and are able to efficiently mitigate shock waves for a range of flight condition