Opposition control applied to turbulent wings

We conducted high-resolution large-eddy simulations (LESs) to explore the effects of opposition control (OC) on turbulent boundary layers (TBLs) over a wing at a chord-based Reynolds number (${Re}_c$) of 200,000. Two scenarios were studied: flow over the suction sides of the NACA0012 wing section at a $0^{\circ}$ angle of attack, and the NACA4412 wing section at a $5^{\circ}$ angle of attack, representing TBLs under mild and strong nonuniform adverse pressure gradients (APGs), respectively. Our results show that the effectiveness of OC in reducing friction drag decreases significantly with increasing APG intensity. This reduction is linked to intensified wall-normal convection caused by the stronger APG. OC, designed to reduce near-wall fluctuations, attenuates the outer peak of streamwise velocity fluctuations and the production term of the turbulent kinetic energy budget. We also confirmed the formation of a "virtual wall," where the balance between viscous diffusion and dissipation at the virtual wall plane mirrors that at the physical wall. Spectral analyses reveal that the wall-normal transport of small-scale structures to the outer region due to the APG negatively impacts OC performance. We also examined uniform blowing and body-force damping as control strategies. Uniform blowing mimics the effects of a stronger APG, while body-force damping shares similarities with OC in the streamwise development of the TBL, despite differences in turbulent statistics. This study is the first detailed analysis of OC applied to TBLs under nonuniform APGs with complex geometries.