Opposition control applied to turbulent wing sections

Opposition control (OC) is a reactive flow-control approach that mitigates the near-wall fluctuations by imposing blowing and suction at the wall, being opposite to the off-wall observations. We carried out high-resolution large-eddy simulations to investigate the effects of OC on turbulent boundary layers (TBLs) over a wing at a chord-based Reynolds number ( ${Re}_c$ ) of $200 \ 000$ . Two cases were considered: flow over the suction sides of the NACA0012 wing section at an angle of attack of $0^{\circ }$ , and the NACA4412 wing section at an angle of attack of $5^{\circ }$ . These cases represent TBLs subjected to mild and strong non-uniform adverse pressure gradients (APGs), respectively. First, we assessed the control effects on the streamwise development of TBLs and the achieved drag reduction. Our findings indicate that the performance of OC in terms of friction-drag reduction significantly diminishes as the APG intensifies. Analysis of turbulence statistics subsequently reveals that this is directly linked to the intensified wall-normal convection caused by the strong APG: it energizes the control intensity to overload the limitation that guarantees drag reduction. The formation of the so-called virtual wall that reflects the mitigation of wall-normal momentum transport is also implicitly affected by the pressure gradient. Control and pressure-gradient effects are clearly apparent in the anisotropy invariant maps, which also highlight the relevance of the virtual wall. Finally, spectral analyses indicate that the wall-normal transport of small-scale structures to the outer region due to the APG has a detrimental impact on the performance of OC. Uniform blowing and body-force damping were also examined to understand the differences between the various control schemes. Despite the distinct performance of friction-drag reduction, the effects of uniform blowing are akin to those induced by a stronger APG, while the effects of body-force damping exhibit similarities to those of OC in terms of the streamwise development of the TBL although there are differences in the turbulent statistics. To authors’ best knowledge, the present study stands as the first in-depth analysis of the effects of OC applied to TBL subjected to non-uniform APGs with complex geometries.