Shock-Aware Constrained Optimization of the RAE2822 Transonic Airfoil via a Two-Channel vSDF Surrogate with Closed-Loop CFD Verification

Shock-aware aerodynamic shape optimization of transonic airfoils requires surrogate models that capture both integral aerodynamic trends and shock-relevant pressure distribution features. This study addresses drag-oriented optimization of the RAE2822 transonic airfoil under a lift-targeted condition with baseline relative thickness feasibility, rather than strict target pressure inverse design. Each airfoil is parameterized by a 16-dimensional CST vector and mapped to a two-channel vertical signed distance field representation of the upper- and lower-surface Cp curves, from which shock descriptors, including the shock location indicator xs and the pressure jump magnitude ΔCp, are extracted in a deterministic, implementation-consistent manner. To quantify the reliability of surrogate-derived shock metrics, a held-out uncertainty analysis is performed on 500 samples. The surrogate achieves MAE/RMSE values of 0.00474/0.00602 for CL and 4.66×10−4/6.33×10−4 for CD, while the recovered shock-related quantities yield 0.00201/0.01598 for xs and 0.00200/0.00336 for ΔCp. Scatter plots and error histograms show tight one-to-one trends for most samples, with limited outliers mainly associated with locally ambiguous pressure gradient patterns. Overall, the surrogate is more reliable for capturing shock intensity trends than for prescribing an exact shock location; accordingly, xs is interpreted as a trend-level descriptor, whereas ΔCp is treated as the more stable engineering indicator inside the optimization loop. The trained surrogate is embedded in a differential evolution optimizer with soft penalties on lift deviation and thickness feasibility violation, and selected designs are re-evaluated through closed-loop SU2 RANS simulations. CFD verification shows that the optimized design reduces drag from CD=0.01463 to CD=0.01229 (a 16.0% reduction) and reduces the shock jump from ΔCp=0.239 to ΔCp=0.046 (an 80.7% reduction). For the optimized design, the prediction-to-CFD differences are ΔCL=+0.0042 and ΔCD=+0.00012. These results support an engineering-oriented and auditable shock-aware closed-loop optimization workflow, with final design conclusions established by CFD verification rather than surrogate-predicted shock location alone.