# Design and Testing of a LUT Airfoil for Straight-Baded Vertical Axis Wind Turbines
## 4 Results and Discussion
### Static LUT Airfoil Performance at Low Reynolds Number
#### 4.1.4 Lift-Drag Ratios of the LUT Airfoil  
Figure 11 presents the lift coefficient versus the drag coefficient at different values of \(R_{e}\) for the LUT airfoil, where the lift coefficient and drag coefficient are described in and were obtained according to Sections 4.1.1 and 4.1.2. The lines in black and red of the lift-drag ratios correspond to \(R_{e}\) = 3 \(\times\) 10\({}^{5}\) and \(R_{e}\) = 5 \(\times\) 10\({}^{5}\), respectively. The results show that the LUT airfoil has the maximum lift-drag ratio \(\rm{C_{L}/C_{d-max}}\) = 64.4 at an angle of attack of \(\alpha\) = 10\({}^{\circ}\) when \(R_{e}\) = 3 \(\times\) 10\({}^{5}\), and it has the maximum lift-drag ratio \(\rm{C_{L}/C_{d-max}}\) = 79.8 at an angle of attack of \(\alpha\) = 10\({}^{\circ}\) when \(\rm{R_{e}}\) = 5 \(\times\) 10\({}^{5}\). Moreover, combined with Figure 10, the lift-drag ratios linearly increase in the range \(-\)10\({}^{\circ}\) \(<\)\(\alpha\) \(<\) 10\({}^{\circ}\). Therefore, the LUT airfoil presents a wider drag bucket, which is a desired characteristic for the airfoil of VAWTs due to the law of motion of the VAWTs [19]. Figure 11 shows the lift-drag ratios versus the lift coefficients, where the colors of the lines have the same meaning as in Figure 11. The lift-drag ratios of the LUT increase almost linearly with the increase in the lift coefficient in the range \(-\)1 \(\leq\) C\({}_{L}\)\(\leq\) 1.25. Figure 10: Drag coefficient for the LUT airfoil at different values of \(R_{e}\): (**a**) the case of \(R_{e}\) = 3 \(\times\) 10\({}^{5}\); and (**b**) the case of \(R_{e}\) = 5 \(\times\) 10\({}^{5}\). The lines in black and red of the drag coefficient correspond to the experimental results and the numerical simulation results, respectively. In Figure 12, the flow separation on the surface of the LUT is displayed at different angles of attack when the \(R_{e}\) is \(3\times 10^{5}\), measured using PIV technology. Figure 12 shows that the separation point gradually moves from the trailing edge to the leading edge with the increase in the angle of attack, which is consistent with the results in Figures 7 and 8. Moreover, the separation vortex becomes high due to the gradual flow separation. Especially at the angle of attack \(\alpha\) = 22\({}^{\circ}\) in Figure 12g, the leading-edge separation results in the formation of the wake vortex and the detached vortex. At this moment, the pressure distribution on the upper surface of the LUT airfoil keeps a constant value, as shown in Figure 8a. Figure 12d-f displays the development of the flow separation on the upper surface of the LUT airfoil, which results in decreasing pressure on the upper surface of the airfoil, as shown in Figure 7a. However, the development of the vortices on the upper surface of the LUT airfoil are slow; combined with Figure 8a, it indicates that the LUT airfoil has good stall performance. Meanwhile, the changes in flow separation on the lower surface of the LUT airfoil are presented in Figure 12a-c when the angle of attack is a negative value. The pressure distribution on the LUT airfoil surface at a negative angle of attack is shown in Figure 8. However, due to the limited field range of the PIV here, it is difficult to observe the development of the wake vortices. Meanwhile, at a large negative angle of attack, the flow separation on the lower surface is obvious, and the separation point on the lower surface moves toward the leading edge with increasing angles of attack. However, because the placement of the PIV equipment was only convenient for photographing the upper surface of the LUT model, the phenomenon of flow separation was not obviously surveyed. Consequently, we could only survey the vortices near the trailing edge of the LUT. Table 1 shows the main geometrical and aerodynamic parameters of a part of the commonly used and special-purpose airfoils for straight-bladed VAWTs when \(R_{e}\) is \(3\times 10^{5}\) and \(5\times 10^{5}\).