# Numerical Simulations of Novel Conning Designs for Future Super-Large Wind Turbines
## 3 Results and Discussions
#### 3.1.2 Flow Field Analysis
As most studies available on AOA extraction are for straight blades without coning, Equation (4) is commonly used. To extract AOA, the distance from AC to the up-/down- stream annulus was set to one local chord length \(C\), as shown in Figure 7b, where the axial velocity in the \(YZ\) plane is also illustrated. Figure 7: Sketch of points used by AAT to extract AOA: (**a**) straight baseline; (**b**) coned rotor. The streamlines in the \(YZ\) plane of the two coned configurations are drawn in Figure 8, where the axial velocity contour is also shown. The streamlines of the downwind coned case in Figure 8b were more up-pointing than those of the upwind coned case in Figure 8a. Especially near the blade tip, the upwind cone had a smaller projection angle \(\gamma\) and had streamlines which were more perpendicular to the blade. When projecting the real inflow velocity _Vinflow_ in direction \(n\), the upwind coned rotor had a smaller \(Vn\) value, even if with the same _Vinflow_ value. Therefore, it is more straight forward to analyze \(\alpha_{n}\), which reveals the inflow condition in the normal-wise \(Xn\) plane. To explore the mechanism behind the interesting force distributions shown in Figure 5, the distribution of \(\alpha_{z}\) and \(\alpha_{n}\) are compared in Figure 9. It was found that the \(\alpha_{z}\) of an upwind cone is always smaller than its downwind counterpart, which is not consistent with the force distributions. Interestingly, the \(\alpha_{n}\) curve of the upwind cone intersected with its downwind counterpart. Near the blade root, downwind configurations had a larger \(\alpha_{n}\) than their upwind counterparts, which indicated larger thrust and tangential force. Towards the blade tip, the downwind coning made the \(\alpha_{n}\) gradually decrease below that of upwind cone, which was consistent with the force distribution. Additionally, as shown in Figure 5, there was a phenomenon whereby an up/downwind pair had an almost reversed \(Ft\) distribution relative to the baseline, but had a less symmetric distribution of \(Fz\) curves, especially towards the tip. A reasonable explanation is given below. The upwind cone had  
Figure 8: Streamlines in the YZ plane with axial velocity contours for the two coned configurations: (**a**) upwind coned rotor of \(T_{trans}=5/R\), \(C_{cone}=-4\); (**b**) downwind coned rotor of \(T_{trans}=5/R\), \(C_{cone}=4\). a slightly larger \(\alpha_{n}\) than the straight baseline toward the blade tip, and therefore, also had a larger \(Fn\), which is the normal force parallel to \(n\), as shown in Figure 6. But the force \(Fz\) in Figure 5b was along the axial direction, which has a relationship with \(Fn\) as follows:  
Figure 6.0  
where the force along the span-wise direction is usually small and thus neglected. Although \(Fn\) of the upwind coning was slightly larger than the baseline near the tip, after projecting \(Fn\) to \(Fz\), the \(Fz\) may have been smaller than the baseline, as shown in Figure 6.1 It is known that a cone angle always leads to a \(\cos\beta\) which is smaller than one; however, there is no projection process for the tangential force \(Ft\). Therefore, the \(Ft\) curves of the upwind cone shown in Figure 5 could be higher than the baseline curves, which follow the \(\alpha_{n}\) curves more closely. Lastly, uncertainties still lie in the extraction of AOA, especially near the blade tip [31,32], but it is clear that this provides a view to explain the force distribution shown in Figure 6.2  
To validate the extracted \(\alpha_{n}\) in Figure 9, streamlines and pressure plots around the normal blade section at \(r\) = 77.59 m are shown in Figure 6.3 This slice was normal-cutting, which was parallel to the normal-wise \(Xn\) plane. It was found that the three airfoil sections were all in an attached flow condition. The \(\alpha_{n}\) of these three configurations could be approximately compared by analyzing the slopes of the streamlines ahead of the leading edge.