# Numerical Simulations of Novel Conning Designs for Future Super-Large Wind Turbines
## 3 Results and Discussions
#### 3.1.1 Force Performances  
Firstly, the overall aerodynamic performance of the configurations presented in Figure 2a are compared. The two configurations of \(C_{cone}\) = \(\pm\) 4 and \(T_{trans}\) = 1/3 also appear in Figure 2b, where they are abbreviated as C4S2 and C-4S2. These configurations are not discussed here, and will be explored in Section 3.2. In Table 2, the thrust \(T\) and torque \(Q\) of the other four configurations in Figure 2a are listed. As high torque and low thrust are beneficial, the torque-to-thrust ratio (\(QT\)) was used to compare different conning configurations. The relative variations of these parameters are denoted as \(\delta T\), \(\delta Q\) and \(\delta QT\); for example, \(\delta T\) means  
\[\delta\;=\;\frac{\mid T\mid_{cone}\;-\;\mid T\mid_{straight}}{\mid T\mid_{ straight}}\times 100\% \tag{3}\]  
The most upwind-coned configuration \(C_{cone}\) = \(-\)4 gives the lowest thrust, i.e., 4.53% lower than that of the baseline without coning. Although \(C_{cone}\) = \(-\)4 reduces the torque by 1.07% compared with the baseline, it has the highest \(QT\) due to the obvious decline of thrust. The downwind counterpart \(C_{cone}\) = 4 produces the highest \(T\), lowest \(Q\), and lowest \(QT\), which is unfavorable. Among the pair of \(C_{cone}\) = \(\pm\)8, the upwind configuration also has a smaller \(T\), a higher \(Q\) and a higher \(QT\) than the downwind counterpart.  
To understand the overall performance differences shown in Table 2, the tangential and axial force per unit span length is shown in Figure 5. The axial force \(Fz\) is parallel to the rotor axis, and the tangential force \(Ft\) is perpendicular to \(Fz\). The aforementioned forces are the summation of all the three blades. Near the blade tip, the upwind configurations had a larger \(Ft\) and \(Fz\) than the downwind counterparts. For example, the \(Ft\) and \(Fz\) curves of \(C_{cone}\) = \(-\)4 were higher than those of \(C_{cone}\) = 4. Towards the blade root, the situation reversed, i.e., the upwind configurations had a lower \(Ft\) and \(Fz\). For the distribution of \(Ft\), the upwind and downwind counterparts had an almost reversed \(Ft\) distribution of the baseline rotor with straight blades. The upwind configurations had a higher \(Ft\) near the blade tip, which is more beneficial to an increase of torque. As a result, the torque of \(C_{cone}\) = \(-\)4 and \(-\)8 was slightly higher than \(C_{cone}\) = 4 and 8, as listed in Table 2. However, all four  
\begin{table}
\begin{tabular}{c c c} \hline
**Wind Speed (m/s)** & **Pitch (Degree)** & **Rotational Speed (RPM)** \\ \hline
9.000 & 0.000 & 7.229 \\ \hline \end{tabular}
\end{table}
Table 1: The operational parameters.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **Straight** & \(C_{cone}\) = 8 & \(C_{cone}\) = \(-\)8 & \(C_{cone}\) = 4 & \(C_{cone}\) = \(-\)4 \\ \hline \(T\)(KN) & 1046.06 & 1057.24 & 1025.85 & 1060.77 & 998.63 \\ \(\delta T\) & 0.00\% & 1.07\% & \(-\)1.93\% & 1.41\% & \(-\)4.53\% \\ \hline \(Q\)(KNLm) & 7283.11 & 7254.96 & 7268.08 & 7195.15 & 7205.48 \\ \(\delta Q\) & 0.00\% & \(-\)0.39\% & \(-\)0.21\% & \(-\)1.21\% & \(-\)1.07\% \\ \hline \(QT\)(m) & 6.96 & 6.86 & 7.08 & 6.78 & 7.22 \\ \(\delta QT\) & 0.00\% & \(-\)1.44\% & 1.76\% & \(-\)2.58\% & 3.63\% \\ \hline \end{tabular}
\end{table}
Table 2: Thrust and torque of different configurations (\(T_{trans}\) = 5/\(R\)).  
coned configurations had a smaller torque than the baseline. For the distribution of \(Fz\), the baseline did not lie in the middle of an up/downwind pair, especially toward the blade tip. Although upwind lines gradually surpassed their downwind counterparts and approached the baseline near the blade tip, they barely went above the baseline. The largest upwind cone \(C_{\text{core}}=-4\) showed the overall lowest \(Fz\), which was consistent with the results shown in Table 2. It is difficult to understand why the force distribution behaved like this, so more analyses are needed.