# Design and Testing of a LUT Airfoil for Straight-Baded Vertical Axis Wind Turbines
## 5 Conclusions  
In this study, we designed an asymmetrical airfoil for straight-bladed VAWTs based on the law of motion of the VAWTs by employing the SQP optimization method; we called this design the LUT airfoil. Meanwhile, the aerodynamic performance of the LUT airfoil was investigated at two Reynolds numbers, \(3\times 10^{5}\) and \(5\times 10^{5}\), under the conditions of a low-speed, low-turbulence wind tunnel at the Northwestern Polytechnical University, China; the flow field around the LUT airfoil was observed by PIV technology. The LUT airfoil has a 20.77% moderate thickness and 1.11% moderate camber. Moreover, the position of the maximum camber is close to the trailing edge, which forms a trailing-edge loading \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**Airfoil**} & \multirow{2}{*}{\(\mathbf{R_{\text{c}}}\) (\(\mathbf{\text{l}}\times\mathbf{10^{9}}\))} & **Max.** & **(\(\mathbf{\text{l/d}}\) Max.** & **Max.** & **(\(\mathbf{\text{l/d}}\) Max.** & **Radius Leading** & **Edge (\(\mathbf{\text{q/d}}\))** & **Max. C\({}_{\text{t}}\)/C\({}_{\text{t}}\) (\(\mathbf{\text{a}}\))** & **Max. C\({}_{\text{t}}\) (\(\mathbf{\text{a}}\))** \\ \cline{2-10}  & & & & & & & & & & \\ \hline Do06-W200 [25] & 3 & \multirow{2}{*}{19.8\%} & \multirow{2}{*}{31.1\%} & \multirow{2}{*}{0.5\%} & \multirow{2}{*}{84.6\%} & \multirow{2}{*}{1.7442\%} & 58.05 (9.75\({}^{\circ}\)) & 1.4153 (16.75\({}^{\circ}\)) \\ \cline{2-10}  & & 5 & & & & & & & 71.5 (9.5\({}^{\circ}\)) & 1.4384 (18\({}^{\circ}\)) \\ \hline \multirow{2}{*}{NACA0018 [25]} & 3 & \multirow{2}{*}{18\%} & \multirow{2}{*}{30\%} & \multirow{2}{*}{0} & \multirow{2}{*}{0} & \multirow{2}{*}{3.1017\%} & 57.09 (8.25\({}^{\circ}\)) & 1.24 (18.75) \\ \cline{2-10}  & & 5 & & & & & & 65.8 (9.25\({}^{\circ}\)) & 1.2624 (16.5\({}^{\circ}\)) \\ \hline NACA0015 [28] & 5 & 15\% & 30\% & 0 & 0 & 2.3742\% & 66.43 (7.5\({}^{\circ}\)) & 1.2731 (16.75\({}^{\circ}\)) \\ \hline DU12W26 [21] & - & 26.2\% & 37\% & - & - & - & - & - & - \\ \hline AIR013 [20] & - & 34.9\% & - & 2.29\% & - & 7.8\% & - & - \\ \hline \hline \end{tabular} Note: “-” indicates that the data of the corresponding locations are not presented in the literature.  
\end{table} 
Table 1: Main geometrical parameters and aerodynamic parameters of a part of commonly used airfoils for straight-bladed VAWTs. Figure 12: Contours of the velocity and stream lines at different angles of attack: (\(\mathbf{\text{a}}\)–\(\mathbf{\text{g}}\)) the contours of the velocity at different angles of attack. This figure shows the transient contours from the angle of attack \(\alpha=-20^{\circ}\) to the angle of attack \(\alpha=22^{\circ}\) at \(R_{\text{c}}=3\times 10^{5}\). However, only the varying velocity on the upper surface of the LUT and the larger vortex are captured in this figure due to the picture being limited by the ability of the Particle Image Velocimetry (PIV) equipment. to improve the efficient lift of the LUT airfoil. The maximum thickness of the LUT airfoil is achieved by restricting the thickness of the upper surface while adding the thickness of the lower surface. It is conducive to delay flow separation on the upper surface. Moreover, the moderate thickness helps to ensure the structural strength of the blade and to improve the performance of VAWTs with the LUT airfoil at high tip speed ratio. Ultimately, the main objectives of achieving a higher maximum lift coefficient, higher maximum lift-drag coefficient, and gentle stall characteristics were achieved. Compared with the airfoil commonly used for VAWTs, the LUT airfoil displays a better aerodynamic performance at a low \(R_{e}\). Additionally, the maximum lift coefficient of the LUT airfoil is steady with the increase in \(R_{e}\) between 3 \(\times\) 10\({}^{5}\) and 5 \(\times\) 10\({}^{5}\). The LUT airfoil retains the desirable characteristic of low drag over a wide range of angles of attack in the range \(-10^{\circ}<\alpha<10^{\circ}\), that is, the LUT airfoil has a wide drag bucket.