# The Aerodynamic Analysis of a Rotating Wind Turbine by Viscous-Coupled 3D Panel Method
## 3 Results  
In order to assess the validity of the current method's results, pressure distribution data was computed at a number of radial locations and compared with RANS predicted pressure data, solved in Fluent 6.2.16 via the SIMPLEC algorithm and one-equation Spalart-Allmaras turbulence model (a more detailed description of the model may be found in [22]), for a commercial 2 MW wind turbine rotor under normal operating conditions. Also included for comparison are 2D pressure data computed around identical airfoils in uniform flow using Xfoil [45], a 2D viscous-coupled panel method which is very popular for airfoil analysis, and is finding more use in wind turbine applications. The considered rotor blade is divided into a cylindrical section at the root, a transitional section, a so-called \"aerodynamic\" section, and a tip section. The rotor airfoil sections considered for analysis, as well as their non-dimensionalised radial locations and thickness-to-chord ratios, are summarised in Table 1 and Figure 5.  
The combined airfoil-wake geometries, as predicted by the current method, are shown on the left hand side (LHS) of Figure 6, with the airfoils' separation regions highlighted in red, and the undisturbed relative flow velocity vectors given as the vector sums of the free stream velocity \(U_{\infty}\) and the rotor's local rotational velocities \(-\omega r_{i}\). The right hand side (RHS) of Figure 6 shows the pressure data predicted by the current method, with the constant pressure distributions assumed to exist throughout the separation regions also highlighted in red, and the compared RANS and Xfoil data. Along the outboard region of the rotor, namely at the rotor tip (Figure 6a) and at the outermost of the three considered \"aerodynamic\" sections (Figure 6b), the predicted separation regions extend over 26% of the suction surfaces, but the thickness of the separated wakes appears almost negligible. It is perhaps interesting to note that the orientation of the thick wake at these outboard sections appears to initially be more closely aligned with rotor's plane of rotation, but, further downstream, is observed to veer away towards \(U_{\text{rel}}\). The pressure data predicted by the current method show excellent agreement with the RANS data, with suction-side-minimum to pressure-side-maximum pressure differentials respectively 8% and 6% greater than those predicted by RANS, while Xfoil was found to significantly overpredict the suction peaks, with pressure differentials respectively 42% and 69% greater than those predicted by RANS. At midspan (Figure 6c), the separation point was predicted to have advanced further towards the leading edge, with a predicted separation region of 31%. The separated wake is also noticeably thicker, and appears to undergo a slight undulation. The predicted pressure data at this section is slightly more conservative than that predicted by RANS, with a 19% greater pressure differential, while Xfoil's predicted pressure differential exceeds that of the RANS data by 42%. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Section Label** & **(f)** & **(e)** & **(d)** & **(c)** & **(b)** & **(a)** \\ \hline \begin{tabular}{c} Section type \\ Radial location \\ Thickness/chord \\ \end{tabular} & \begin{tabular}{c} cylindrical \\ \(r_{i}/R=0.045\) \\ \(t_{i}/c_{i}=1.0\) \\ \end{tabular} & \begin{tabular}{c} transitional \\ \(r_{i}/R=0.107\) \\ \(t_{i}/c_{i}=0.8\) \\ \end{tabular} & \begin{tabular}{c} aerodynamic \\ \(r_{i}/R=0.193\) \\ \(t_{i}/c_{i}=0.8\) \\ \end{tabular} & \begin{tabular}{c} aerodynamic \\ \(r_{i}/R=0.395\) \\ \(t_{i}/c_{i}=0.4\) \\ \end{tabular} & \begin{tabular}{c} aerodynamic \\ \(r_{i}/R=0.395\) \\ \(t_{i}/c_{i}=0.285\) \\ \end{tabular} & \
\begin{tabular}{c} step \\ \(t_{i}/c_{i}=0.225\) \\ \end{tabular} &
\begin{tabular}{c} step \\ \(t_{i}/c_{i}=0.17\) \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 1: Wind turbine rotor blade airfoil sections. Figure 5: Wind turbine rotor blade airfoil sections.