## 5 Design of Shutters Based on Side Wing Efficiency
### Optimization of Shutters' Geometry
#### 5.1.5 Optimization of Blocking Ratio  
When the blocking ratio \(p\) is close to 1, shutters, similar to a thick plate of porous media, enhance the ability to combine the turbulent flow. However, a larger drag is generated in the rear, and the overall effect worsens. When the blocking ratio is close to 0, the fins become a thin plate, the stiffness of the device is reduced, the interaction between the  
Figure 16: Shutters’ width B is constrained by the inner side of vertical plane wheel.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Fin’s Angle** & \(I_{\textit{prefm}}\) & **Side Wing** & **Overall** & **Side Wing** & **Overall** \\
**of Attack a/\({}^{\circ}\)** & \(I_{\textit{prefm}}\) & **Lift/N** & **Lift/N** & **Drag/N** & **Drag/N** \\ \hline
2 & 6.79 & \(-101.3344\) & \(-95.0846\) & 31.154 & 31.3948 \\
6 & 9.03 & \(-103.8904\) & \(-96.6426\) & 31.0142 & 31.5454 \\
8 & 9.77 & \(-104.3266\) & \(-97.1518\) & 30.7828 & 31.5168 \\
10 & 8.76 & \(-103.9956\)  
fins is weakened, and the shutters fail. Therefore, an optimal blocking ratio should be determined, and the optimal blocking ratio is distinctive for different fin shapes. The analysis of blocking ratio under the flat airfoil fin shape with \(L\) = 90 mm is performed.  
Additional simulations are conducted on four cases with the number of fins \(n\) = 4, 5, 6, and 8 under the same gross height of 220 mm, showing in Figure 17. All the previous data about the flat airfoil form a dataset of 20 groups.  
The maximum thickness \(\delta\) and gross height are eliminated because they are dependent to other parameters, such as n and fin shape. The chord length \(L\), angle of attack \(\alpha\), number of fins \(n\), average interval \(\Delta\), and blocking ratio \(p\) are the independent parameters, and the total negative lift of side wing and shutters are taken as dependent variables. Multivariate regression models with various kernel functions are trained in MATLAB, and the training results show that support vector machine with quadratic kernel (quadratic SVM) has the smallest root mean square and the best fitting degree in this simulation results dataset, with \(R^{2}=0.84\). Kernel function of quadratic SVM is  
\[K\big{(}x_{i},x_{j}\big{)}=\Big{(}ax_{i}^{T}x_{j}+b\Big{)}^{2}, \tag{7}\]  
where \(a\), \(b\) are coefficients to train, \(x_{i}\), \(x_{j}\) can be any data point with the same dimension from the same dataset, and the details of quadratic SVM and quadratic kernel can be found in [16]. This regression model can predict the influence of variables above on the overall negative lift. With other four parameters remain unchanged, and the blocking ratio \(p\) is modified and re-predicted to obtain its influence on \(I_{perfm}\). The prediction result is shown in Figure 18.  
Figure 17: CAD models of additional simulation cases. (**a**) Shutters with number of fin n = 4. (**b**) Shutters with number of fin n = 5. (**c**) Shutters with number of fin n = 6. (**d**) Shutters with number of fin n = 8.  
Figure 18: Prediction of the influence of blocking ratio on \(I_{perfm}\) of side wing with SVM regression model using quadratic kernel function, trained on the dataset with 20 simulation cases mentioned above.  
The results show that when other conditions remain unchanged, \(I_{perfm}\) first increases and then decreases with the increase in blocking ratio, and the negative lift decreases rapidly when \(p>30\%\). This time, the shutters are equivalent to a thick plate, which blocks the air flow. The optimal blocking ratio for flat airfoil shutters is between 10 and 20%. Given that the chord length \(L\) and fin shape are determined, 17.7 is selected as the temporal optimal blocking ratio with simulated \(I_{perfm}=9.77\).