# Wind Turbine Enhancement via Active Flow Control Implementation
## 4 Results
### Jet Injection Angle Optimization  
To optimize the jet inclination angle (\(\theta_{\rm jet}\)), the momentum coefficient obtained in the previous subsection (\(C_{\mu}=0.007\)) will be kept constant, along with SJ pulsating frequency (\(f_{0}=7.1\,Hz\)) (\(F^{+}=1\)), the groove position (\(x/C=0.4\)), and width (\(h=0.5\%\)C). Ten different jet inclination angles ranging between 2 and 50 degrees were simulated. Table 7 presents the time-averaged values for the aerodynamic coefficients and their respective peak-to-peak amplitudes corresponding to each jet angular position evaluated. From these data, it is highlighted that the optimal angle obtained from the parametric optimization is \(\theta_{\rm jet}=5\) deg., with its associated efficiency of \(\eta=41.067\); however, it should be mentioned that \(\theta_{\rm jet}=2\) deg. yields a higher lift coefficient, although the efficiency drastically decays to \(\eta=16.151\). Concerning the oscillations of the lift and drag coefficients in relation to the jet angle, it can be observed that the lift coefficient's PTP values remain relatively stable for injection angles below 25 degrees. Furthermore, in the case of the drag coefficient, oscillations decrease notably within the region of minimum drag, specifically within the range of jet angles where \(5\leq\theta_{\rm jet}\leq 20\). The observed reduction in PTP values for both lift and drag coefficients, see Table 7, signifies an improvement in the dynamic forces, which reduce vibration when compared with the baseline case.  
When exploring the lift coefficient as a function of the jet angle in Figure 11, it is observed that the lift keeps increasing as the jet angle decreases, suggesting a delay of the boundary layer separation. Additionally, studies such as [58; 59; 60] have extensively explored the effects of tangential flow injection and have demonstrated its ability to promote flow reattachment and lift increase. The Coanda effect refers to the tendency of a fluid jet to adhere to a nearby surface due to the curvature of the solid body. By decreasing the jet angle, the airflow is directed closer to the airfoil surface, effectively leveraging the Coanda effect to enhance boundary layer reattachment. Thus, regarding the results obtained in this research, the observed increase in lift coefficient with decreasing jet angle aligns with the predictable outcomes of previous research.  
Figure 11: Lift coefficient (**a**), drag coefficient (**b**), and aerodynamic efficiency (**c**) variation as a function of the jet angle; the vertical bars characterize the corresponding peak-to-peak amplitude. Constant momentum coefficient (\(C_{\mu}=0.007\)) and forcing frequency (\(F^{+}=1\)).  
Figure 10: Lift coefficient (**a**), drag coefficient (**b**), and aerodynamic efficiency (**c**) variation as a function of momentum coefficient; the vertical bars characterize the corresponding peak-to-peak amplitude. Constant jet angle (\(\theta_{\rm jet}=10\) deg.) and forcing frequency (\(F^{+}=1\)).  
When considering the choice of \(\theta_{\rm jet}=5\deg\). as the optimal jet angle for the AFC implementation, it is essential to examine the effects on drag coefficient and aerodynamic efficiency, Figures 11b and 11c, respectively. The drag coefficient remains relatively low for most of the studied jet angles; however, as the injection direction approaches tangential flow, the drag coefficient experiences a notable increase, even higher than the baseline case, leading to a rapid decrease in aerodynamic efficiency. Considering the airfoil efficiency in Figure 11c and Table 7, it is obvious that the maximum efficiency is obtained at \(\theta_{jet}=10^{\circ}\), but as explained before, the final jet inclination angle chosen is based on a trade-off between maximum lift and maximum efficiency.