## 4 Case Study and Analysis
### Aerodynamic Analysis
#### 4.3.2 Aerodynamic Analysis of Three-Dimensional Blades
Figure 36: Pressure coefficient distribution and streamlines on different cross-sections of two propellers at State 1: (**a**) Prop A; (**b**) Prop B. Prop B has higher efficiency than Prop A. It is worth noting that the laminar separation bubbles on the three-dimensional blades appear later than that at the cross-sectional airfoils. This is because the radial airflow caused by the rotation of the blades injects energy into the flow and delays the laminar separation. As shown in Figure 37, when the \(Re_{\text{average}}\) is about \(1.8\times 10^{5}\) (State 2), the laminar separation bubble almost disappears and is no longer the main factor affecting the propeller performance. As shown in Figure 39, the pressure difference between the upper and lower surfaces of the propellers at State 2 is much bigger than that at State 1, which indicates that the lift of the blade element is sufficient. In addition, since there is no laminar separation bubble, the drag of blade element is also greatly reduced. In this case, the negative effect  
Figure 37: Pressure coefficient distribution and streamlines on different cross-sections of two propellers at State 2: (**a**) Prop A; (**b**) Prop B.  
Figure 38: Pressure coefficient distribution on different cross-sectional airfoils at State 1: (**a**) \(r/R=0.5\); (**b**) \(r/R=0.75\); (**c**) \(r/R=0.95\). Figure 39: Pressure coefficient distribution on different cross-sectional airfoils at State 2: (**a**) \(r/R=0.5\); (**b**) \(r/R=0.75\); (**c**) \(r/R=0.95\). of the incremental drag caused by the Gurney flap outweighs the positive effect of the incremental lift brought by it. Consequently, the efficiency of Prop B is even slightly lower than that of Prop A. In summary, a Gurney flap can affect the aerodynamic efficiency of the propeller by affecting the aerodynamic performance of the cross-sectional airfoil. The influence of a Gurney flap on the aerodynamic performance of the cross-sectional airfoil can be summarized by three factors. Firstly, Gurney flap can increase the equivalent camber of the airfoil, which can lead to higher lift coefficient to overcome the lift loss caused by laminar separation bubbles and help to improve the lift-to-drag ratio. Secondly, the vortices induced by the Gurney flap can inject energy into the airflow and help to suppress the separation bubble, which can also help improve the performance of the airfoil. Thirdly, a Gurney flap changes the pressure distribution near the trailing edge and increases the pressure drag of the airfoil. With the change of Reynolds number, the three factors account for different priorities. When the Reynolds number is as low as \(4.0\times 10^{4}\), due to the obvious laminar separation bubbles, the first two factors play a major role. As a result, the Gurney flap could improve propeller efficiency. When the Reynolds number increases above \(1.4\times 10^{5}\), the third factor plays a major role as the laminar separation bubble almost disappears. As a result, the Gurney flaps instead slightly reduces the efficiency of the propeller. Therefore, after reasonable design, the propeller with a Gurney flap can achieve better aerodynamic performance at low Reynolds numbers than the conventional propeller. However, due to the small size and high precision requirements, it is not easy to manufacture a Gurney flap on the propeller. In addition, the materials used to make the Gurney flap also require good stiffness to avoid vibration and deformation. These problems may cause difficulties to the practical application of the propeller with a Gurney flap.