# Numerical Simulations of Novel Conning Designs for Future Super-Large Wind Turbines
## 3 Results and Discussions
#### 3.1.2 Flow Field Analysis  
Analyzing the flow field around a wind turbine, such as inflow velocity and angle of attack (AOA), may help to understand the force distributions mentioned above. The inflow velocity decomposition for the upwind and downwind coned rotors is illustrated in Figure 6. This decomposition was made in the \(YZ\) plane, which contained the rotor axis and the pitch axis of a blade. The unit vectors \(z\), \(r\), \(s\) and \(n\) were along the axial, radial, span-wise and normal directions, respectively. At a far upstream position, the axial velocity was \(V_{0}\), the normal velocity component was \(V_{0}\)cos\(\beta\), and the radial velocity was zero. Towards the rotor, the axial and normal velocity decreased and the radial velocity increased. Arriving at the rotor, the axial and normal velocity was reduced to \(V_{0}\)-\(Wz\), \(V_{0}\)cos\(\beta\)-\(Wn\), and the radial velocity increased to \(Vr\). Here, \(Wz\) is the axial induction velocity at the aerodynamic center (AC) and \(Wn\) is the normal induction velocity at AC. Due to the presence of \(Vr\), the resultant velocity _Vinflow_ in the \(YZ\) plane was not horizontal and did not equal to \(V_{0}\)-\(Wz\), as shown in Figure 6. The velocity decomposition was different for the upwind and downwind coned configurations. For an upwind cone  
Figure 5: Force distributions along radial direction: (**a**) tangential force; (**b**) axial force. Figure 6: Inflow velocity decomposition for an upwind and a downwind coned rotor. configuration, projecting the resultant velocity _Vinflow_ to the normal component was different to that on a downwind counterpart, as the projection angle \(\gamma\) was different. However, the radial velocity component is omitted in the traditional BEM method because there is no equation to describe the radial flow. Then, it was assumed that the inflow velocity _Vinflow_ would be along the axial direction and would be equal to \(V_{0}\)-\(W\)z. When projecting the inflow velocity _Vinflow_ to the normal component, the projection angle \(\gamma\) equaled the cone angle \(\beta\). Thus, the upwind and downwind pair had the same value of \(\cos\beta\), _Fn_ and _Fz_. In short, the traditional BEM methods cannot distinguish the upwind and downwind coning, which is clearly in contrast with reality. Another way to analyze the flow is to use the concept of angle of attack, which is conducted on the planes perpendicular to the blade spanwise direction. At present, difficulties or uncertainties remain in the extraction of AOA from 3D CFD simulations or experiments, which is different from that in the 2D situations. There are different kinds of methods to extract AOA from CFD data, which are thoroughly discussed and compared in [31; 32]. Most methods predicted similar AOA at midspan, but it should be kept in mind that the results near the blade root and tip varied from one method to another. The Average Azimuthal Technique (AAT) [31; 32; 33], proposed by [PERSON] et al. [33], was used in the present paper. At a given rotor radius, AAT extracts the inflow velocity on two circles which are just upstream and downstream of the rotor, as shown in Figure 7a. The number of points on a circle is 72 in the present study. AAT estimates the velocity at AC by averaging the up- and down- stream data, and then calculates AOA using Equation (4). However, Equation (4) is only applicable for straight blades without cones. A general form of AOA, which is suitable for coned rotor analyses, is Equation (5). \[\alpha_{z}=\tan^{-1}(\frac{Vz}{Vt})-\theta=\ \tan^{-1}(\frac{V_{0}-Wz}{Vt})-\theta \tag{4}\]  
\[\alpha_{n}=\tan^{-1}(\frac{Vn}{Vt})-\theta=\ \tan^{-1}(\frac{V_{0}\cos\beta-Wn}{Vt})-\theta \tag{5}\]  
where \(Vz\) is the estimated axial velocity at AC, \(Vn\) is the estimated normal-wise velocity at AC, \(Vt\) is the estimated tangential velocity at AC, and \(\theta\) is the local pitch angle. When applied to straight blades without a cone, Equation (5) is reduced to Equation (4), because \(Vn\) becomes \(Vz\).