# Wind Turbine Enhancement via Active Flow Control Implementation
## 4 Results
### Momentum Coefficient \(C_{\mu}\) Optimization  
Synthetic jet actuators (SJA) generate zero net mass flux, which means that the mass flow through the AFC groove must be equal during both the suction and blowing phases. In order to achieve this statement, the time-dependent velocity profile for the AFC simulations is often chosen to be a sinusoidal trigonometric function, which is usually expressed as  
\[u_{\text{jet}}(t)=u_{\text{max}}\cdot\sin(2\pi f\cdot t) \tag{31}\]  
where \(f\) is the synthetic jet actuation frequency, \(u_{\text{max}}\) is the maximum SJ outgoing/incoming velocity, and \(t\) is the time. Based on previous studies [39; 40; 41; 42; 43; 44], for optimum performance, the synthetic jet actuation frequency should be the same as or a multiple/submultiple of the vortex shedding one. This is why in our parametric analysis we will initially set the SJ pulsating frequency constant and equal to the vortex shedding one, which was \(f_{0}=7.1\) Hz. The second parameter which will be initially kept constant is the jet inclination angle. A reasonable initial guess would be to inject the flow almost tangentially to the airfoil surface, taking advantage of the Coanda effect [57]. Thus, by injecting the pulsating flow tangentially to the airfoil surface, the Coanda effect can help to maintain the incoming flow attached to the airfoil. Based on several previous studies [22; 23], we have decided to start the parametric analysis, maintaining a constant 10-degree SJ injection angle. At this point, four AFC parameters are initially set, and the parametric optimization starts via evaluating the effect of the momentum coefficient on the flow dynamics. The relation of the maximum velocity amplitude (\(u_{\text{max}}\)) and the momentum coefficient can be extracted from (22). According to [43], relatively low momentum coefficients for AFC at high Reynolds numbers can lead to improvements in the aerodynamic forces of airfoils. [PERSON] and [PERSON] [43] numerically investigated flow separation control with SJAs on a NACA23012 airfoil at \(Re=2.19\times 10^{6}\), and they found that as momentum coefficient increased, lift improvement in comparison to the one obtained at small \(C_{\mu}\) decreased. Moreover, to prevent reaching compressible flow effects on the groove exit, \(C_{\mu}\) should be kept low. Therefore, momentum coefficients ranging between \(C_{\mu}=0.0001\) and \(C_{\mu}=0.01\) have been selected as an initial guess for the present application. Table 6 presents a comprehensive overview of the AFC simulations for all \(C_{\mu}\) evaluated as well as for the baseline case, offering numerical insights into the averaged lift and drag coefficients, aerodynamic efficiency, and peak-to-peak values for lift and drag coefficients. Notably, the data reveal that the momentum coefficient yielding the highest lift force is \(C_{\mu}=0.007\), the drag being particularly small under these conditions. Significantly, it is observed that there is a reduction in the amplitude of lift and drag coefficient oscillations when compared with the baseline case. It's worth noting that for the iterative process involving the momentum coefficient, this reduction isn't exceptionally pronounced; however, it can be deduced that, especially for high lift coefficients and low drag coefficients (i.e., high efficiencies), there is a slight decrease in the PTP values when compared with lower efficiency scenarios. In conclusion, it can be affirmed that delaying the boundary layer results in lift enhancement and drag reduction, accompanied by a dampening of the fluctuations of lift and drag forces. To gain further insight into the relationship between the lift coefficient and the momentum coefficient, Figure 10a is presented. The graph illustrates that at very low momentum coefficients, the jet fails to inject sufficient energy into the boundary layer, and the BL is likely to remain separated.