# Collaborative Optimization of Aerodynamics and Wind Turbine Blades
## 3 Discipline Analysis
### Aerodynamic Discipline
#### 3.1.1 Airfoil Design and Optimization  
The design of the airfoil is fundamental to blade design and crucial to the overall performance of the wind turbine. Due to the complex geometry of airfoils, parameterized modeling is preferred in most studies. In general, the perturbation-based shape function method, orthogonal basis function method, parametric section method, and CST method are available. Comparatively, CST has the advantages of better fitting efficiency, numerical stability, and universality. In the study, the CST method is employed. According to the CST method [49], the coordinates of an airfoil \((\psi,\xi)\) can be described as  
\[\left\{ \begin{array}{l}\xi_{U}(\psi)=C(\psi)\cdot S_{U}(\psi)+\psi\cdot \Delta\xi_{U}\\ \xi_{L}(\psi)=C(\psi)\cdot S_{L}(\psi)+\psi\cdot\Delta\xi_{L}\end{array} \right. \tag{4}\]  
where \(C(\psi)\) is the class function while \(S_{i}(\psi)\) is the shape function; \(\Delta\xi_{i}\) is the trailing edge thickness; and the subscripts \(U\) and \(L\) denote the upper and lower surfaces of the airfoil, respectively. The class function \(C(\psi)\) is calculated as  
\[C(\psi)=\psi^{N_{1}}.(1-\psi)^{N_{2}} \tag{5}\]  
where \(N_{1}\) and \(N_{2}\) are constants indicating the class of geometry shape of airfoil. For a representative airfoil shape with a rounded front and pointed rear, one can choose \(N_{1}=0.5,N_{2}=1.0\). Based on the Bernstein polynomial, the shape function \(S_{i}(\psi)\) in (4) can be expressed as  
\[S_{i}(\psi)=\sum_{j=0}^{N_{i}}A_{i}(j)\frac{N_{i}!}{j!(N_{i}-j)!}\cdot\psi^{j} \cdot(1-\psi)^{N_{i}-j},(i=U,L) \tag{6}\]  
where \(A_{i}(j)\) are the coefficients of shape function and \(N_{i}\) is the order of polynomial. To verify the CST method, the NACA4412 airfoil is investigated. The order of the Bernstein polynomial is selected as 7. Given the original discrete points on the surfaces of the airfoil, the coefficients \(A_{i}(j)\) can be calculated. The shape function \(S_{i}(\psi)\) can be further determined. The approximation results on the basis of (4) are shown in Figure 2. As calculated by using 18 points, the standard deviation \(\sigma\) is \(8.68\times 10^{-5}\), which verifies the CST method. After the parameterized model of the airfoil is obtained, optimization can be performed to obtain an optimal airfoil that relates to the optimal aerodynamic performance. In the study, a high-fidelity numerical simulation, namely computational fluid dynamics (CFD), is conducted to analyze the aerodynamics of the airfoil. Computer simulation is very useful in the design of wind turbine blades since it helps improve the blade design before manufacture. By computer simulation, one can predict the blade's performance in various environmental conditions and modify the designs to achieve optimal efficiency. An automatic optimization framework is established on the Isight platform to obtain the optimal airfoil. The framework consists of four modules: the modeling module, meshing module, CFD module, and optimization algorithm module. Several different software packages are employed in the four modules. In detail, CAESES is used in the parameterized modeling of the airfoil; ICEM is used for meshing, based on the model obtained by CAESES; and FLUENT is used in the CFD calculation, based on the meshingresults by ICEM. Based on the CFD calculation results, optimization is conducted in combination with an optimization algorithm. Note that CAESES, ICEM, and FLUENT can be integrated as a Workbench module. A brief optimization framework of the airfoil in Isght is shown in Figure 3, in which the maximization of the lift-to-drag ratio (Cl/Cd) is set as the optimization objective. In the CFD calculation, the calculation domain is set as shown in Figure 4, where c denotes the chord length of the airfoil. The inlet is set as a velocity inlet while the outlet is set as a pressure outlet. Bound 1 and bound 2 are set as walls when the angle of attack of the airfoil is zero and as velocity inlets when the angle of attack is nonzero. The boundary of the airfoil is set as a wall.