Turbulent boundary layers around wing sections up to Rec=1,000,000

Reynolds-number effects in the adverse-pressure-gradient (APG) turbulent boundary layer (TBL) developing on the suction side of a NACA4412 wing section are assessed in the present work. To this end, we analyze four cases at Reynolds numbers based on freestream velocity and chord length ranging from Rec=100,000 to 1,000,000, all of them with 5° angle of attack. The results of four well-resolved large-eddy simulations (LESs) are used to characterize the effect of Reynolds number on APG TBLs subjected to approximately the same pressure-gradient distribution (defined by the Clauser pressure-gradient parameter β). Comparisons of the wing profiles with zero-pressure-gradient (ZPG) data at matched friction Reynolds numbers reveal that, for approximately the same β distribution, the lower-Reynolds-number boundary layers are more sensitive to pressure-gradient effects. This is reflected in the values of the inner-scaled edge velocity Ue+, the shape factor H, the components of the Reynolds-stress tensor in the outer region and the outer-region production of turbulent kinetic energy. This conclusion is supported by the larger wall-normal velocities and outer-scaled fluctuations observed in the lower-Rec cases. Thus, our results suggest that two complementing mechanisms contribute to the development of the outer region in TBLs and the formation of large-scale energetic structures: one mechanism associated with the increase in Reynolds number, and another one connected to the APG. Future extensions of the present work will be aimed at studying the differences in the outer-region energizing mechanisms due to APGs and increasing Reynolds number.