# Wind Turbine Enhancement via Active Flow Control Implementation
## 4 Results
### Forcing Frequency Optimization  
At this point, the two previously optimized AFC parameters, momentum coefficient \(C_{\mu}=0.007\) and jet angle \(\theta_{\rm jet}=5\deg\), are going to be held constant. Being the remaining parameter to be optimized, the jet pulsating frequency \(f\). Eight different non-dimensional frequencies are analyzed in this part of the study; their values range between \(0.1\leq F^{+}\leq 10\). The results obtained after the corresponding CFD simulations are presented in Table 8, where the baseline case data are introduced in the last line for comparison. Based on the information presented, it can be concluded that the optimal value for the jet non-dimensional forcing frequency is \(F^{+}=3\). This choice is supported by the highest lift-to-drag ratio, excellent lift capabilities \(C_{l}\), and a particularly low drag coefficient \(C_{d}\).  
Figure 12a is presenting the lift coefficient and its peak-to-peak amplitude for the different pulsating frequencies evaluated. The first thing to observe is that variations of the pulsating frequency are slightly modifying the lift; a small decrease in lift is observed when considering the smallest forcing frequencies. However, once the forcing frequency reaches approximately \(F^{+}=2\), the lift coefficient remains relatively constant suggesting that the optimal value for the forcing frequency should be greater than 2 (\(F^{+}\geq 2\)). Moreover, it is important to mention that at higher forcing frequencies, the peak-to-peak values for the lift coefficient increase significantly, which indicates the presence of larger amplitude fluctuations and thus, higher structural loads. When checking the drag coefficient values obtained at the different pulsating frequencies evaluated, Figure 12b shows minimum drag values are observed at \(F^{+}=0.1\) and around \(F^{+}=3\). It therefore seems that an analysis of the aerodynamic efficiency needs to be made in order to determine the optimal forcing frequency. From Figure 12c it can be seen that there is a high aerodynamic efficiency at \(F^{+}=0.1\), although it will not be chosen as the optimal value due to its lower lift coefficient. In contrast, regarding the remaining values for frequency, there is an efficiency peak at \(F^{+}=3\), which offers a significant increase in lift coefficient, leading to an increase in torque generation while maintaining a low drag coefficient (see Figure 12b). Additionally, the amplitude of oscillation at this frequency is relatively low, suggesting that it will  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\theta_{\rm jet}\) & \(C_{l}\) & \(C_{d}\) & \(\eta\) & \(PTP_{C_{l}}\) & \(PTP_{C_{d}}\) \\ \hline
2 & 2.633 & 0.163 & 16.151 & 0.163 & 0.087 \\
5 & 2.537 & 0.062 & 41.067 & 0.090 & 0.050 \\
7 & 2.490 & 0.057 & 43.510 & 0.085 & 0.041 \\
10 & 2.450 & 0.050 & 48.712 & 0.114 & 0.046 \\
15 & 2.345 & 0.052 & 45.297 & 0.092 & 0.035 \\
20 & 2.249 & 0.057 & 39.114 & 0.110 & 0.036 \\
25 & 2.225 & 0.066 & 33.505 & 0.110 & 0.070 \\
30 & 2.242 & 0.063 & 35.466 & 0.075 & 0.028 \\
40 & 2.033 & 0.082 & 24.795 & 0.309 & 0.111 \\
50 & 2.079 & 0.070 & 29.592 & 0.095 & 0.036 \\ \hline
**BCS S54** & 1.562 & 0.106 & 14.71 & 0.281 & 0.104 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Time-averaged aerodynamic coefficients \(C_{l}\), \(C_{d}\), and \(\eta\), and their respective peak-to-peak values \(PTP_{C_{l}}\) and \(PTP_{C_{d}}\), for a set of different jet inclination angles \(\theta_{jet}\). Momentum coefficient (\(C_{\mu}=0.007\)), forcing frequency (\(F^{+}=1\)), groove position (\(x/C=0.4\)), and width (\(h=0.5\%\)C) are kept constant.  
have minimal impact on structural loads. It is relevant to highlight that the optimization methodology just introduced may not generate the optimum AFC values, but it allows obtaining rather close ones.