# Collaborative Optimization of Aerodynamics and Wind Turbine Blades
## 3 Discipline Analysis
### Aerodynamic Discipline
#### 3.1.2 Aerodynamic Shape Design
The twist angle \(\theta_{i}\) is then determined according to (12). Figure 10: Forces and velocities relating to airfoil. In the study, the blade is divided into 18 parts alongside the length of the blade. Based on the above calculation, the results for chord length and twist are as shown in Table 3.  
Based on the obtained chord length and twist angles, CAESES is employed to run the parameterized modeling. The results are shown in Figure 12, in which Figure 12a shows the 3D model of the blade while Figure 12b depicts the variation in blade elements along the length of the blade. Figure 11: Aerodynamic shape design process. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Station No.** & **Radius Ratio** & **Chord Length** & **Twist Angle** \\  & _r/R_ & _c (m)_ & _\# (Degree)_ \\ \hline  
(-\)0.6485 \\
18 & 1 & 0.1621 & \(-\)1.7784 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Chord length and twist angle. Based on the model, a CFD calculation is carried out to analyze the aerodynamics of the wind turbine blade. Considering the rotation of the rotor blade, a multiple reference frame (MRF) technique is employed. The calculation domain is divided into two areas, a rotational in-fluid area and a stationary out-fluid area. The number of blades is selected as three. Therefore, both the in-fluid area and out-fluid area are set as one-third cylinders to save calculation time. The distance from the inlet to the blade is set as \(3D\) while the distance from the blade to the outlet is \(5D\) (where \(D\) is the length of the wind turbine blade). The radius of the out-fluid one-third cylinder is set as \(2D\) while that of the in-fluid is set as \(1.05D\). The length of the in-fluid one-third cylinder is set as \(6.6\) times the maximal chord length, i.e., \(6.6c_{\text{max}}\). The calculation domain relating to the wind turbine blade is shown in Figure 13. Corresponding boundary conditions are set as follows. The inlet is set as a velocity inlet while the outlet is set as a pressure outlet. The boundary of the rotational in-fluid area is set as frame motion while that of the out-fluid is set as stationary. Correspondingly, the cylindrical wall of the out-fluid area is set as a stationary wall. The boundary of the interface relating to the in-fluid and out-fluid areas is set as interior. Since only a one-third cylinder is considered in the CFD calculation, the plane walls of the out-fluid are set as a periodic boundary. The boundary of the blade is set as a moving wall. Considering the complex curves of the blade, an unstructured grid is employed in the meshing. In generating surface grids, shared topology is used to deal with interfaces. In generating volume grids, the Poly-Hexcore mosaic meshing technique is employed. Refinement is conducted for the rotational in-fluid area. After an independence check, the number of grids is determined as 1,170,775, out of which 677,134 grids make up the in-fluid area and 493,641 grids the out-fluid area. The meshing results are shown in Figure 14.  
Figure 12: Parameterized model of wind turbine blade. (**a**) 3D blade model, (**b**) blade element distribution. Figure 13: Calculation domain relating to wind turbine blade. Combined with the SST \(k-\omega\) turbulence model, the FLUENT calculation results are shown in Figure 15. The blade is assumed to be rotating counterclockwise. As can be seen, the windward surface is a pressure side since positive high pressure exists on this side, while the leeward surface is a suction side since most pressure on this side is negative. Moreover, the high pressure concentrates on the front edge of the blade. In general, the pressure distribution obtained from the CFD calculation is consistent with reality.