Turbulent separation delay via tuned wall-impedance on a NACA 4412 airfoil in pre-stalled conditions.

We have performed large-eddy simulations of turbulent separation control via imposed wall-impedance on a NACA-4412 airfoil in near-stalled conditions (Mach, $M_\infty = 0.3$, and chord-Reynolds numbers, $Re_c = 1.5\times 10^6$ and angle of attack, $\alpha = 14^{\circ{}}$), inspired by the experimental setup of Coles \& Woodcock (1979). We impose complex impedance boundary conditions (IBCs) using the implementation developed by Scalo, Bodart and Lele, \emph{Phys. Fluids} {\bf 27}, 035107 (2015), representing an array of sub-surface-mounted tunable Helmholtz cavities with resonant frequency, $f_\textrm{res}$, covered by a porous sheet with permeability inversely proportional to the impedance resistance. Generation of spanwise-oriented Kelvin-Helmholtz (KH) rollers of size $l_{KH,0} \simeq U_\infty / f_\textrm{res}$is observed in areas of sustained mean shear, which are convectively amplified along the shear-layer and reenergizing the separated flow via vortical-induced mixing and entrainment of irrotational fluid. Their characteristic initial size $l_{KH,0}$ is determined by the periodic wall-transpiration pattern induced, in turn, by acoustic resonance in the cavities. Several resonant frequencies and impedance have been tested, bracketing optimal conditions for control.