Multi-point aerodynamic optimization of airfoils under stall conditions based on the unsteady discrete adjoint method

Stall is a critical unsteady aerodynamic phenomenon that leads to abrupt lift loss, drag surges, and potential flight instability. To address the challenge of designing airfoils with robust post-stall performance, this study proposes an enhanced hybrid aerodynamic optimization framework based on the discrete adjoint method. The method applies windowing techniques for weighted averaging to handle unsteady problems and reduce computational costs. A single-point post-stall optimization of the National Advisory Committee for Aeronautics 1410 airfoil achieves a 21.25% increase in the time-averaged lift and an 11.00% drag reduction. Subsequently, multi-point optimizations are performed to balance cruise efficiency with high-angle-of-attack regimes. The two-point case includes a cruise condition and a fully post-stall condition, while the three-point case incorporates two cruise conditions along with a near-stall point. Specifically, for the three-point optimization, additional free-form deformation control-point constraints are applied to prevent non-physical designs caused by saturation of the control-point movement range. Although the comprehensive drag coefficient reduction decreases to 4.24% and 7.47%, respectively, due to the inherent trade-offs between cruise and stall requirements, these results demonstrate significantly improved aerodynamic robustness across the flight envelope.