# Wind Turbine Enhancement via Active Flow Control Implementation
## 3 Main Parameters Definition of the DTU 10 MW RWT  
In order to increase the accuracy of the 2D-CFD simulations, it is important to consider the flow's three-dimensional effects over the airfoil section under study. Two induction factors, axial (\(a\)) and tangential (angular) (\(a^{\prime}\)), which consider some flow three-dimensional effects, are used to more precisely calculate the axial and radial velocities for 2D simulations [52]. The decrease in streamwise velocity from the free-stream conditions to the rotor plane is called the axial velocity deficit, and the fraction by which it is reduced is called the axial induction factor (\(a\)). The tangential induction factor (\(a^{\prime}\))considers the increase of the tangential speed in the rotor plane. Figure 7 introduces the typical velocity and force components acting on a generic HAWT airfoil, and considering the corresponding induction factors, the main angles associated are also depicted. The aerodynamic forces (lift and drag) are decomposed into radial and tangential directions. For the present study, the values of the induction factors corresponding to each of the two airfoil sections studied, Sections 54 and 81, were obtained from [53]. Additionally, for the computation of essential metrics such as net force, torque, angle of attack, and relative wind speed for each blade section, as described by Formulas (27)-(30) from [54,55], the framework necessitates the establishment of two distinct angles. These angles serve as pivotal factors in the analytical processes. The initial angle, referred to as \(\theta\), corresponds to the angle formed between the section chord and the plane of rotation, designated as the section twist angle. This angle, which is different for each section, is defined in the design process of each HAWT and cannot be modified. In fact, and in order to obtain the maximum power for each given wind speed, HAWT traditionally uses the blade pitch angle, not depicted in Figure 7; note that the pitch angle is constant for all blade sections and just depends on the wind speed. For the present DTU10 MW RWT,  
Figure 6: Pressure (**a**) and friction (**b**) coefficients comparison for the four meshes evaluated in Section 54. Figure 7: Wind, rotor velocities, and forces on a generic blade section. when the wind speed is 10 m/s, the pitch angle is zero. Lastly, the other angle that plays a crucial role in the calculations is labeled as \(\varphi\) and characterizes the inflow angle. This angle quantifies the divergence between the relative wind speed of each blade section and the plane of rotation, as delineated in Figure 7. Notice that the angle of attack (AoA) is given as \(\alpha=\varphi-\theta\). Based on the information just presented, the relation between the relative velocity \(u_{rel}\), the free stream velocity \(u_{\infty}\), and the tangential one \(\Omega r\), \(r\) being the section (airfoil) radius and \(\Omega\) standing for the wind turbine turning speed, is given as Equation (27). \[u_{rel}=\sqrt{\left(\Omega r(1+a^{\prime})\right)^{2}+\left(u_{\infty}(1-a) \right)^{2}} \tag{27}\]  
The equation defining the angle of attack (given in degrees) for any blade section takes the following form:  
\[\alpha=\arctan\left(\frac{u_{rel}(1-a)}{\Omega r(1+a^{\prime})}\right)\cdot \frac{360}{2\pi}-\theta \tag{28}\]  
For a given section, the resultant force acting on the rotor plane direction \((T)\) and the force acting in a plane perpendicular to it \((N)\), are expressed as. \[T=\frac{1}{2}C\rho u_{rel}^{2}(C_{l}\sin\varphi-C_{d}\cos\varphi) \tag{29}\]  
\[N=\frac{1}{2}C\rho u_{rel}^{2}(C_{l}\cos\varphi+C_{d}\sin\varphi) \tag{30}\]  
From Equation (29), several insights can be derived regarding the significance of lift and efficiency across different parts of the blade: when dealing with high inflow angles at the root region (close to 90 deg. ), the contribution of the lift coefficient becomes more significant than that of drag in torque generation.