# The Aerodynamic Analysis of a Rotating Wind Turbine by Viscous-Coupled 3D Panel Method
## 4 Discussion  
Along the outboard region of the wind turbine rotor, the rotor blade airfoils are better aligned with the undisturbed relative flow, and flow separation, although present to a lesser extent, does not significantly affect aerodynamic performance. The strong correlation between the current method and the RANS data in this flow-aligned region is thus not surprising. The significantly overpredicted data from the compared 2D panel method is most likely due to the inability of the method to account for tip losses; such 2D methods being restricted to the analysis of infinite wings in uniform flow. Moving inward toward the root, however, \(\omega r_{i}\) decreases with decreasing \(r_{i}\), as is clearly illustrated by the velocity vectors in Figure 6, resulting in higher angles of attack, and, consequently, more severe separation. Furthermore, the increased angles of attack combined with increased thickness-to-chord ratios result in a thicker separated wake, and, therefore, a more marked transition from displacement body streamline to separation streamline, which further exacerbates the adverse pressure gradient responsible for flow separation. The slight discrepancy between the pressure data predicted by the current method and that predicted by the RANS solver highlights the difficulty of numerically simulating a separated flow behind a rotating body. Of course, it is important to note that, despite a vast body of work on the accuracy and limitations of the RANS equations closed by appropriate turbulence models for the resolution of the turbulent boundary layer along wind turbine rotor blades, without \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Velocity (m/s)**} & \multicolumn{3}{c}{**Power (kW)**} & \multicolumn{3}{c}{**Error (\%)**} \\ \cline{2-6}  & **Official Data** & **Current Method** & **RANS** & \(\frac{P_{\text{CM}}}{P_{9}}\) & \(\frac{P_{\text{RMS}}}{P_{9}}\) \\ \hline
3 & 4 & 10 & 25 & 150.0 & 525.0 \\
4 & 32 & 66 & 59 & 106.3 & 84.4 \\
5 & 103 & 125 & 114 & 21.4 & 10.7 \\
6 & 219 & 219 & 194 & 0.0 & -11.4 \\
7 & 373 & 346 & 308 & \(-7.2\) & \(-17.4\) \\
8 & 570 & 512 & 452 & \(-10.2\) & \(-20.7\) \\
9 & 816 & 721 & 628 & \(-11.6\) & \(-23.0\) \\
10 & 1110 & 991 & 879 & \(-10.7\) & \(-20.8\) \\
11 & 1430 & 1323 & 1111 & \(-7.5\) & \(-22.3\) \\
12 & 1770 & 1716 & 1539 & \(-3.1\) & \(-13.1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Wind power data. Figure 7: Compared wind power curves. corroborating experimental data, we cannot comment on the real-world accuracy of the compared RANS data, which therefore serve merely as code-to-code comparison. With this in mind, the current method's predictions are considered highly satisfactory, especially in light of the substantial reduction in computational expense afforded by the current method, which employed around 2000 quadrilateral panels compared to the one million polyhedral cells employed by the RANS model. Finally, along the inboard region of the rotor blade, aerodynamic efficiency has been sacrificed in favour of greater structural integrity, which has been achieved by very high thickness-to-chord ratios ranging from 0.4 at the innermost aerodynamic section to 1.0 at the cylindrical root section. Due to the combination of high thickness-to-chord ratios and supercritical angles of attack, the flow has completely separated from the suction surface of this section of the rotor blade. However, despite such severe flow separation, the current method's predicted pressure data is still highly comparable with the RANS data, especially at the transitional and cylindrical sections. In addition to accuracy and speed, this also illustrates the robustness of the current panel method in modelling severely separated flows behind rotating bodies, considering that the compared 2D panel method was unable to produce converged results for these sections in uniform flow.