# Performance Prediction and Design of Stratospheric Propeller
## 6 Result and Discussion
### Performance of the Designed Propeller  
According to the performance calculation process, chord length \(b\) and pitch angle \(\theta\) are the initial input condition. In the different sections, \(b\) is fixed once the diameter of the propeller is determined. To meet the rated thrust, \(\theta_{char}\) is adjusted, and the iterative calculation needs to be performed with the data of airfoil performance.  
The shape parameters are shown in Figure 12. The pitch angle decreased with the increase of \(\bar{r}\). The chord length first increased, reached a maximum value near \(0.5R\), and then decreased. The 3D solid model of the propeller is shown in Figure 13 and was constructed according to the design parameters.  
Figure 14 shows the angle of attack and interference angle of the propeller, which were designed according to the vortex theory and standard strip analysis. The interference  
Figure 11: FX63 airfoil performance at \(Re\) = 200,000.  
Figure 12: Shape parameters of the propeller.  
Figure 10: FX63 airfoil performance at \(Re\) = 8000.  
angle \(\beta\) affects the angle of attack \(\alpha\) and, consequently, the aerodynamic performance of the blade. The AOA was negative near the root, and most of the blade section showed a small AOA.  
The deviation of four different mesh qualities is shown in Figure 15. The cell number of the coarse mesh was 5.65 million, the mesh used consisted of 7.52 million cells, the refined mesh comprised 10.2 million cells, and the other mesh 8.65 million cells. The maximum deviation from the mesh used was less than 1.41% for the thrust coefficient, 2.14% for the power coefficient, and 1.44% for the efficiency. The results of mesh independency verification showed that the number of cells had a little influence on the results; a mesh with 7.52 million cells was reliable and was chosen for CFD simulation in this paper.  
The CFD simulation at \(H\) = 15 km, 18 km, and 20 km was performed using the mesh model mentioned above, and the results are shown in Figure 16. The variation tendencies  
Figure 14: Angle of attack and interference angle of the propeller.  
Figure 13: Solid model of the propeller.  
Figure 15: Mesh independency verification.  
of \(C_{T}\), \(C_{P}\), and \(\eta\) were approximately the same. The \(C_{T}\) and \(C_{P}\) of \(H=15\) km and \(H=18\) km deviated slightly towards those of \(H=20\) km when \(\lambda<0.7\), and the deviation decreased with the increase of \(\lambda\). The \(\eta\) values at the three altitudes were almost identical within the change range of \(\lambda\). The altitude had almost no effect on the aerodynamic performance of the designed propeller, and the simulation method was reliable and correct.  
Figure 17 shows the pressure contour of the designed propeller at the design point. The pressure on the upper surface decreased from the root to the tip and from the leading edge to the trailing edge, and the minimum pressure occurred from \(0.75R\) to \(0.98R\). The pressure on the lower surface increased from root to tip and from the middle to the trailing and leading edges, and the maximum pressure occurred from \(0.61R\) to \(0.99R\).  
Figure 16: Propeller performance at different altitudes: (**a**) thrust coefficient; (**b**) power coefficient; (**c**) efficacy.  
Figure 17: Pressure contour of the propeller at the design point: (**a**) upper surface of the blade; (**b**) lower surface of the blade.