## 2 Methods
### Experimental Setup  
An experiment of an airfoil with VGs was carried out in the wind tunnel of North China Electric Power University (NCEPU), which contains a 2-D airfoil measurement section. The size of the test section is \(1.5\times 3\times 4.5\) m\({}^{3}\), and the maximum wind speed of the wind tunnel is 62 m/s. The measurement section is equipped with 256- and 64-channel electronic scanning valves and a PXI (Platform PCI eXtensionsfor Instrumentation) data acquisition system. A pitot tube was installed on the wall of the upstream wind tunnel of the airfoil and provided a measurement of the total pressure of the inflow. The sidewall of the pitot tube was punctured to provide air holes, which were used to measure the static pressure of the incoming flow. There were 96 pressure taps in the middle section of the airfoil to measure the static pressure distribution on the surface of the airfoil. The static pressure coefficient (\(C_{p}\)) was the time-averaged result found with a sampling time interval of 0.1 seconds. The experimental sampling time was 10 seconds for each working condition. There were 111 total pressure piezometric holes and 5 static pressure piezometric holes (called the wake rake) downstream of the airfoil, which were used to calculate the drag coefficient of the airfoil. The geometric dimensions of the wind tunnel and test airfoils are shown in Figure 4.  
The test airfoil used in the experiment is a special wind turbine airfoil: the DU93-W-210 airfoil. The airfoil was developed and designed by Delft University. The DU93-W-210 airfoil is very representative of the aerodynamic characteristics of wind turbine airfoils in general. The thickness of the airfoil was 21% of \(C\), the chord length of the tested airfoil was 0.8 m, and the span of the airfoil was 1.5 m. The VGs were arranged at 0.2 times the chord length from the leading edge of the airfoil. Figure 5 shows the test airfoil with the VGs installed. The geometric dimensions of the VGs are shown in Table 3. The tunnel wind speed was set to 18.2 m/s, and the Reynolds number based on the chord of the airfoil was \(1\times 10^{6}\). The AoA of the airfoil ranged from \(-10^{\circ}\) to \(25^{\circ}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Settings Angle \(\beta\) (\({}^{\circ}\))** & **Length \(l\) (mm)** & **Height \(H\) (mm)** & \(S\)/H & \(\lambda\)/H \\ \hline
20 & 17 & 6 & 7 & \(3,5,7,9\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: VG geometric parameters. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{3}{c}{**Mesh**} & \multicolumn{3}{c}{**Richardson Extrapolation**} \\ \cline{2-7}  & **Coarse** & **Medium** & **Fine** & **RE** & \(p\) & \(R\) \\ \hline \(C_{Ap}\) & 0.3635 & 0.3628 & 0.3622 & 0.3620 & 2.75 & 0.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mesh independence study results. Figure 6 shows the wind tunnel test results of the DU93-W-210 airfoil without the VGs. NCEPU provided the test results in this paper. NPU is the wind tunnel test results from the Northwest Polytechnic University, and Delft is the wind tunnel test results from Delft University. By comparing the results of the three wind tunnels, it can be seen that the wind tunnel test results in this paper were close to those obtained by NPU and Delft before a stall AoA (8\({}^{\circ}\)) for the airfoil lift coefficient. After the stall AoA, the lift coefficient measured in the wind tunnel was slightly higher than that measured in the other two wind tunnels. For the drag coefficient, before the stall AoA, the drag coefficient matched the results of the other wind tunnels. However, after the stall AoA, the wind tunnel test results in this paper were closer to the Delft University wind tunnel test results. Since the aerodynamic characteristics of airfoils fluctuate after a stall, the lift and drag coefficients must be revised, and the mechanism of each correction method is different.