Adjoint-based robust optimization design of laminar flow airfoil under flight condition uncertainties

Due to the high sensitivity of laminar wings to uncertain factors, although there have been a lot of engineering application attempts, so far laminar flow technology has not been effectively applied to the wings of large passenger aircraft. To address this issue, we develop an adjoint-based robust optimization design framework. The framework mainly includes a Reynolds-Averaged Navier-Stokes solver coupled with the simplified eN method, coupled adjoint equations considering the transition, a gradient-enhanced polynomial chaos expansion, and a statistical moment gradient solver. The robust optimization designs of laminar airfoils subject to uncertainties in flight conditions for subsonic and transonic conditions are performed and compared with the results with deterministic optimization. The results show that the robust design can improve the ability of the laminar airfoil to resist the uncertain disturbance of flight conditions and reduce the mean and standard deviation by reasonably balancing the deterministic and uncertain performance. The mean and standard deviation of the drag coefficient can be reduced by 28%-36% and 20%-71%. Meanwhile, a longer and more stable laminar flow region can be obtained. In contrast, the deterministic design may lead to a large decrease in the robustness of performance. The successful results demonstrate the effectiveness of the established robust design method for laminar airfoils, and could be applied and extended for future laminar flow wings design. Although the present framework is verified by 2D optimization examples, it has the potential to be applied to quasi-3D and 3D laminar wings, as well as actual large passenger aircraft design.& COPY; 2023 Elsevier Masson SAS. All rights reserved.