# Numerical Simulations of Novel Conning Designs for Future Super-Large Wind Turbines
## 3 Results and Discussions
### Special Coned Configurations: C4S0, C4S1, C4S2, C4, C-4S0, C-4S1, C-4 S2 and C-4
#### 3.2.2 Distributed Force Performances  
The axial force \(Fz\) and tangential force \(Ft\) per unit length are compared in Figure 11. Figure 2b is redrawn in Figure 11a, where the upwind configurations are denoted by the dashed lines and downwind by the dotted lines. Clearly, C4S0 and C-4S0 had the same configuration as the straight baseline when \(r>2R/3\), or in other words, without coning. As a result, the \(Ft\) and \(Fz\) curves of C4S0, C-4S0 and the straight baseline were very close. In the same spanwise range, C4 and C-4S1 had the same cone angle, as did C-4 and C4S1. Correspondingly, the same cone angle led to close \(Ft\) and \(Fz\) curves. The discrepancy between the close curves increased towards \(r=2R/3\), because the coning point at \(r=2R/3\) distorted the nearby flow. In short, the same cone angle near the tip will lead to close force distribution.  
When \(R/3<r<2R/3\), the four configurations C4S2, C4, C4S0, C4S1 had the same cone angle as shown in Figure 11a. Additionally, their counterparts C-4S2, C-4, C-4S0, C-4S1 had the same cone angle as well. However, none of the \(Ft\) and \(Fz\) curves coincided, even if the same cone angles existed, as shown in Figure 11b,c, which indicated that the cone effect in this range was not solely controlled by the cone angle itself. Additionally, traditional BEM methods will predict the same force distribution under the same cone  
Figure 11: Comparison of special coning: (**a**) redrawn of special cone configurations; (**b**) tangential force; (**c**) axial force; (**d**) zoomed view of axial force.  
angle, which implies that such an approach is not applicable here. When \(r<R/3\), all the cone configurations coincided with the straight baseline. However, only C4S1 and C-4S1 had close force distributions comparable to the straight baseline. The force distribution of C \(\pm\) 4S2, C \(\pm\) 4 and C4 \(\pm\) S0 varied from configuration to configuration. It was found that C4S1 and C-4S1 were totally different cone configurations at \(r>R/3\), but that they had the same blade tip position as the straight baseline. This implies that the influence of the coned part on the straight part is mostly determined by the blade tip position. Traditional BEM will predict the same force distribution again, or fail at \(r<R/3\), even if all the configurations have a zero cone angle.  
There are many interesting phenomena between the curves in Figure 11. Looking closely at group C4S2, C4, C4S0, and C4S1, the \(Ft\) and \(Fz\) curves (especially \(Ft\) lines) are nearly parallel with each other in the range of \(R/3<r<2R/3\). The case C4S2 had the highest force curves, and C4, C4S0, and C4S1 had successively lower forces. Coincidently, this was consistent with the successively upstream-moving of the tip positions from \(Z=3Z_{tip}\) to \(2Z_{tip}\), \(Z_{tip}\) and 0 m (\(Z_{tip}=7.4292\) m). If the blade tip is located at a more upstream position, it will cause the blade sections to be further immersed in the wake, which will lead to a stronger axial induction velocity \(Wz\), a smaller axial inflow velocity, and a lower \(\alpha_{z}\) and \(\alpha_{n}\). The variation of \(\alpha_{z}\) and \(\alpha_{n}\) will be validated later in Section 3.2.3. In short, the upwind transformation of the blade tip is consistent with the successive reduction of the \(Fz\) and \(Ft\) curves. Focusing on the four counterparts, C-4S2, C-4, C-4S0, and C-4S1, the curves were nearly parallel and successively ascending with the downstream-moving of the blade tips. Transforming the blade tip into a further downstream position, the blade sections immerse less heavily into the tip vortex trace, leading to a smaller \(Wz\) and a higher \(\alpha_{n}\). Additionally, the nearly parallel curves of C4S2, C4, C4S0, and C4S1 had different slopes compared with those of C-4S2, C-4, C-4S0, and C-4S1, and apparently different slopes compared with the baseline rotor.