CFD and machine-learning-assisted multi-objective optimization of trailing-edge serrations and vortex generators for flow-separation control on a NACA 0012 Airfoil

The aerodynamic performance of a three-dimensional NACA 0012 wing equipped with trailing-edge serrations (TES) and vortex generators (VGs) was investigated using steady Reynolds-averaged Navier–Stokes simulations with the SST k –ω turbulence model at Re = 6.8 × 10 5 , together with a machine-learning-assisted bounded multi-objective optimization framework. Baseline, TES-only, and combined TES–VG configurations with VGs positioned at 0.5 c and 0.7 c were evaluated over angles of attack from 0° to 20°. The TES-only configuration exhibited approximately 6% higher drag than the baseline over the angle-of-attack range of 12°–18°, while providing only modest lift improvements. At α = 18°, the TES–VG configurations with VGs positioned at 0.5c and 0.7c achieved predicted lift coefficients of 0.8818 and 0.8795, respectively. The 0.7c arrangement exhibited slightly lower drag, while the TES–VG configurations provided approximately 2–3% higher lift-to-drag ratios than TES alone over the 12°–18° range in the present steady-RANS simulations. After dataset auditing and duplicate removal, the CFD–ML dataset contained 121 unique paired C L – C D observations across 11 configurations and 11 angle-of-attack levels. Four capacity-controlled regression models were evaluated using complete held-out angles of 4°, 10°, and 16°. Configuration-specific cubic Ridge regression achieved the strongest performance, with RMSE values of 0.03294 for C L and 0.00531 for C D , and corresponding R 2 values of 0.9832 and 0.9846. Grouped-bootstrap uncertainty intervals at the 90% level achieved empirical coverages of 93.94% for C L and 87.88% for C D . Mission-dependent analysis identified the rounded-serration configuration as the highest-efficiency cruise solution, with C L ‾ / C D ‾ = 9.302, while the TES–VG arrangement at 0.5 c favored maximum high-lift performance and the 0.7 c arrangement provided the more balanced lift–drag response. Comparison with independent wind-tunnel measurements reproduced the angular trends, with Pearson correlations of 0.9400 for C L and 0.9809 for C D , although systematic CFD-to-experiment offsets remained. Because a VG-only configuration was not included, the present results do not permit a formal separation of additive and interaction effects between TES and VGs. The results support a bounded, mission-dependent comparison among the investigated CFD-supported configurations without implying a formal decomposition of TES–VG interaction effects.