# Aerodynamic Efficiency Improvement on a NACA-8412 Airfoil via Active Flow Control Implementation
###### Abstract
Another advantage of SJAs is that do not require external fluid supply. When considering the implementation of SJAs, two parameters are particularly relevant: the non-dimensional frequency \(F^{+}=fC/U_{\infty}\), where \(f\) is the dimensional frequency, \(C\) the airfoil chord and \(U_{\infty}\) the free-stream velocity, and the momentum coefficient (\(C_{\mu}\)). \(C_{\mu}\) is defined as \(C_{\mu}=(h\rho_{jet}(U_{j}^{2})\sin\theta)/(C\rho_{\infty}(U_{\infty}^{2}))\), where \(h\) is the jet width, \(\rho_{jet}\) is the jet density and \(\rho_{\infty}\) is the far field one, \(U_{j}\) characterizes the jet maximum velocity, the parameter \(\theta\) defines the inclination angle of the jet versus the adjacent surface. [PERSON] et al. [22] and [PERSON] and [PERSON] [23] studied the SJA frequency, position and \(C_{\mu}\) when applied to a symmetric airfoil and observed that when locating the actuator near to the boundary layer separation point, the momentum coefficient needed to reattach the flow was smaller. Regarding the actuation frequency, they found that when it was an order of magnitude higher than the vortex shedding one (\(F^{+}\mathcal{O}(10)\)), the flow was completely reattached. SJAs on a NACA-0015 airfoil at \(Re=8.96\times 10^{5}\) were experimentally studied by [PERSON] et al. [24]. They increased the stall angle from \(12^{\circ}\) to \(18^{\circ}\) and observed that for AoA \(>10^{\circ}\), the effectiveness of the actuation considerably increased. At AoA \(>25^{\circ}\), considerably high actuation frequencies were needed to observe large flow variations. The same airfoil and Reynolds number was studied by [PERSON] and [PERSON] [25] using Large Eddy Simulation (LES). A lift increase of 70% was obtained when using \(C_{\mu}=0.0123\), \(F^{+}=1.284\) and \(\theta=30.2^{\circ}\). The same airfoil at \(Re=3.9\times 10^{4}\) was experimentally studied by [PERSON] and [PERSON] [26]. The optimum momentum coefficient and actuation frequencies were respectively, \(C_{\mu}=0.0123\)O and \(F^{+}=0.7\) and \(1.3\), being the highest frequency the most effective one. When using these forcing conditions, an improvement of the stall AoA from \(10^{\circ}\) to \(18^{\circ}\) was observed. [PERSON] et al. [27] numerically studied the same airfoil and Reynolds number via LES simulations. They observed that the optimal frequencies coincided with the vortex shedding one obtained from the baseline case (\(f_{wake}\)) and its first harmonic (\(2f_{wake}\)). [PERSON] et al. [28] reached the same conclusion through experimental tests. Flow control using SJAs on a NACA-23012 at \(Re=2.19\times 10^{6}\) was numerically investigated by [PERSON] and [PERSON] [29], [PERSON] et al. [30]. Maximum lift was obtained when the jet was placed nearby the boundary layer separation point and \(F^{+}=1\). When applying SJA tangentially, clear advantages were observed than when injecting/sucking fluid perpendicular to the surface. The separation control generated by SJA on a NACA-0025 airfoil at \(Re=10^{5}\) and AoA = \(5^{\circ}\) were experimentally studied by [PERSON] et al. [31]. Momentum coefficient was found to be the primary control parameter, a drag decrease of nearly 50% was obtained when \(C_{\mu}\) was higher than a certain threshold value. The same Reynolds number and wing profile, but at AoA = \(10^{\circ}\) was evaluated by [PERSON] et al. [32]. They observed that the momentum coefficient needed \(C_{\mu}\) to keep the flow reattached, was an order of magnitude lower when the excitation frequencies happened to be around the vortex shedding one. The same Reynolds number and wing profile but at AoA = \(12^{\circ}\) was analyzed in [33], where the jet position effectiveness in controlling the flow separation was evaluated. The optimum results were obtained when locating the jet groove nearby (whether downstream or upstream) the boundary layer separation point, a small improvement was observed in the upstream location.