# 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
#### 4.1.3 Drag Coefficient of the LUT Airfoil  
The relationship between the drag coefficient and the angles of attack are displayed for the two Reynolds numbers, \(R_{e}=3\)\(\times\)\(10^{5}\) and \(R_{e}=5\)\(\times\)\(10^{5}\), in Figure 10, where the drag coefficient was obtained via Equations (15) and (16).  
In Figure 10, the lines in black and red of the drag coefficient correspond to the experimental results and the numerical simulation results (design results), respectively. In the cases of \(R_{e}=3\)\(\times\)\(10^{5}\) and \(R_{e}=5\)\(\times\)\(10^{5}\), the values of the drag coefficient are smaller and remain almost constant in the range \(-10^{\circ}<\alpha<10^{\circ}\), because the most attached flow is on the surface of the LUT airfoil. The numerical simulation results agree with the experimental results in this region. However, the values of the drag coefficient increase rapidly when the angle of attack is greater than \(\alpha=13^{\circ}\) or less than \(\alpha=-10^{\circ}\). The results of the experiment and the numerical simulation show a slight difference, but these errors are acceptable. Therefore, the results of the numerical simulation (design results) are in agreement with the results of the experiment reported in this paper.  
Figure 9: Lift 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 lift coefficient correspond to the experimental results and the numerical simulation results, respectively.  
Figures 9 and 10 demonstrate that the results of the experiment agree with the results of the numerical simulation at low angles of attack. However, at high angles of attack where the flow separation occurs, there are some slight differences between the results of the experiment and the numerical simulation. On the one hand, the characteristics of the lift and drag of the LUT airfoil are obtained through integral surface pressure in this experiment, while the results of the numerical simulation with the _SST_\(k\)-\(\omega\) turbulence model are acquired with solving the Reynolds-averaged Navier-Stokes equation; on the other hand, even though the current numerical methods have been greatly improved, for example, the predicted result of the _SST_\(k\)-\(\omega\) turbulence model is accurate, but the _SST_\(k\)-\(\omega\) turbulence model cannot completely solve the turbulence problem [34; 35]. In addition, the wall of the LUT model is infinitely smooth in the numerical simulation, but in the current experiment, although the surface of the LUT model has very low roughness, the roughness of the surface is limited. Therefore, the results of the experiment and the numerical simulation have some differences in the region of the flow separation, while the results of the experiment and the numerical simulation are almost the same at low angles of attack.  
Additionally, the maximum lift coefficient of the LUT airfoil has slow change with the increase in \(R_{e}\) from \(R_{e}\) =3 \(\times\) 10\({}^{5}\) to \(R_{e}\) = 5 \(\times\) 10\({}^{5}\).