D-optimal polynomial chaos expansion for adjoint-based aerodynamic robust optimization in transonic flows

Robust design optimization (RDO) is of significant importance for the development of engineering-viable aircrafts with practical utility. However, computational expense in CFD-based aerodynamic design optimization can severely constrain the overall fidelity of uncertainty treatment. This paper establishes a novel and efficient adjoint-based aerodynamic robust optimization framework integrating the latest gradient-enhanced polynomial chaos uncertainty quantification method coupled with D-optimal design. The proposed framework accommodates operational and geometric stochastic variables, with the latter dimensionally reduced through a Karhunen-Loève expansion (KLE) to enhance computational tractability. Validation studies demonstrate that compared to previous approaches, the proposed uncertainty quantification method maintains comparable and more stable quantification in transonic flows while reducing sample computational complexity from O(m^p) to O(m^p−1), and exhibits favorable compatibility with hyperbolic truncation. Subsequently, the framework is applied to robust optimization case studies in transonic flows involving the RAE2822 airfoil and ONERA M6 wing, subjected to 8 and 11 stochastic variables respectively. Through robust optimization, the optimized designs for both configurations exhibit reduced expectation values and standard deviations considering stochastic perturbations, showing superior performance stability compared to their deterministic optimization counterparts. The results also reveal that the Mach number and treatment of shock waves constitute critical factors for RDO in the transonic regime.