# Wind Turbine Enhancement via Active Flow Control Implementation
## 4 Results
### Energy Assessment  
The present section determines the energy gained by the AFC implementation in Section 54. The power required by the synthetic jet to delay the boundary layer separation is compared with the power increase obtained from this airfoil section due to the AFC implementation and considering an airfoil span of 1m. The power required to activate the synthetic jet is defined as follows [19; 22]:  
\[W_{j}=\frac{1}{2}\rho_{j}A_{j}\sin\theta_{\rm jet}\overline{u_{j}^{3}} \tag{32}\]  
where \(\rho_{j}\) states for the density of the exiting fluid (in this case air at sea level ISA conditions, \(\rho_{j}=\rho_{\infty}=1.225\,\rm kg/m^{3}\)), \(A_{j}\) is the cross-sectional flow area of the synthetic jets (\(A_{j}=h\cdot\rm extrusion\ length=h\cdot 1=0.03045\,m\)) and \(\overline{u_{j}^{3}}\) is the jet time dependent velocity profile defined as follows [19; 61]:  
\[\overline{u_{j}^{3}}=\frac{1}{T/2}\int_{0}^{T/2}u_{\rm max}^{3}\sin^{3}(2\pi ft )\rm d\it t=\frac{4}{3\pi}u_{\rm max}^{3} \tag{33}\]  
T being the SJ oscillation period. The incremental torque represents the difference between the torque generated by the actuated section and the baseline one. It is initially essential to determine the resultant aerodynamic force (\(F_{rot}\)) for both cases, which is obtained by decomposing the lift and drag  
Figure 16: Pressure and tangential wall shear stress coefficients between the baseline case and the optimal AFC implementation on Section 54. Figure 17: Mean velocity profiles tangent to the airfoil surface at several streamwise locations, from \(x/C=0.1\) to \(x/C=0.99\), and as a function of the normalized wall normal distance. Comparison of the baseline with the optimum AFC case. forces in the plane of rotation using the inflow angle (\(\varphi\)). It is important to note that the provided aerodynamic coefficients are time-averaged values, ensuring a representative analysis of the aerodynamic forces. \[F_{rot\;AFC}=\frac{1}{2}\rho_{\infty}u_{rel}^{2}c(c_{I\;AFC}\sin\varphi-c_{d\;AFC }\cos\varphi) \tag{34}\]  
\[F_{rot\;BSC}=\frac{1}{2}\rho_{\infty}u_{rel}^{2}c(c_{I\;BCS}\sin\varphi-c_{d\;BCS }\cos\varphi) \tag{35}\]  
By considering the forces generated by the airfoil section in both the actuated and baseline cases, the increase in torque \(\Delta Q\) can be determined. \[\Delta Q=Q_{AFC}-Q_{BCS}=z_{554}\cdot(F_{rot\;AFC}-F_{rot\;BCS}) \tag{36}\]  
\(z_{554}\) represents the \(z\) coordinate of the improved section, its value being \(31.42\;m\). At this stage, the increase in output power resulting from the lift and drag improvement on the studied airfoil section can be expressed as follows,with \(\Omega\) denoting the wind turbine angular velocity in radians per second (\(rad/s\)). \[\Delta W=\Delta Q\cdot\Omega \tag{37}\]  
To evaluate the net power (\(W_{G}\)) obtained by the AFC implementation on the studied airfoil section and when considering a span of \(1\)m, the power needed to delay the boundary layer separation on this section (\(W_{j}\)) must be considered; the resulting equation reads  
\[W_{G}=\Delta W-W_{j} \tag{38}\]  
The numerical values for the previous equation give the following:  
\[W_{G}=27.982-1.794=26.188\;\mathrm{kW} \tag{39}\]  
If \(W_{G}\) becomes negative, it means that the AFC implementation could improve the lift and aerodynamic efficiency of the section but without a net power saving to the theoretical wind turbine composed of this single airfoil section. In contrast, whenever the power balance becomes positive, there is a gain in total energy and enhanced aerodynamic capabilities of the mentioned section. In the current case, the power required by the synthetic jet to fully attach the flow to the airfoil represents \(6.41\,\%\) of the power gained resulting from the increased lift and reduced drag achieved through the AFC implementation.