# Accurate RANS Simulation of Wind Turbine Stall by Turbulence Coefficient Calibration
## 3 Investigation of the RANS Simulation Error  
### Simulation of the S809 airfoil  
The wind tunnel experiments of the S809 airfoil, which were conducted in Delft University of Technology (DUT) [11], Ohio State University (OSU) [37], Colorado State University (CSU) [38], and University of Glasgow [39], respectively, cover a range of Reynolds number (Re) between 0.3 \(\times\) 10\({}^{6}\) and 2 \(\times\) 10\({}^{6}\). In the present study, full turbulence RANS simulation of the S809 airfoil is firstly made at Re = 1 \(\times\) 10\({}^{6}\). It is close to the Reynolds number experienced by the blades of the NREL Phase VI rotor (The Reynolds number varies between 0.7 \(\times\) 10\({}^{6}\) and 1.4 \(\times\) 10\({}^{6}\) at the blade root and between 1.0 \(\times\) 10\({}^{6}\) and 1.1 \(\times\) 10\({}^{6}\) at the blade tip, at the wind speeds between 7 m/s and 25 m/s [40].) The simulation results of the airfoil lift coefficient (C\({}_{\rm L}\)) for a wide range of AoA between 0\({}^{\circ}\) and 40\({}^{\circ}\) are shown in Figure 4. The experimental data from two different sources are referenced in the figure. One is from the OSU [37] experiment, the other is the measured data of the r/R = 0.63 section of a parked NREL Phase VI blade [41]. The r/R = 0.63 section is close to the mid-span of the blade, and thus its performance can be approximately recognized equal to the 2-D S809 airfoil. The two sets of experimental data are consistent when AoA < 20\({}^{\circ}\) but deviate from each other when AoA > 20\({}^{\circ}\) where deep stall occurs. It is worth asking why such deviation occurs and which set of data is the appropriate reference for the simulation results in deep stall. [PERSON] [41] once made an analysis of the parked NREL Phase VI blade. The data collected in his article showed that the deviation does not become more notable at the r/R = 0.8 and r/R = 0.95 sections, although the 3-D effect is more significant there. Therefore, the primary reason for the deviation might not be attributed to the 3-D effect of the blade. The present study pays attention to the tunnel blockage effect. The size of the test section of the NASA Ames wind tunnel, in which the NREL Phase VI experiment was conducted, is 24.4 m \(\times\) 36.6 m. The chord length of the NREL Phase VI blade (between 0.355 m and 0.737 m) is very small compared to the wind tunnel, and therefore the tunnel blockage effect can be ignored in standstill cases. The wind tunnel experiment of the S809 airfoil was faced with a completely different situation. Figure 5 shows the present simulation result of the flow field around the airfoil at AoA = 40\({}^{\circ}\) in the wind tunnel of OSU. It is found that the actual blockage in deep stall is determined by the size of the vortices rather \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Wind Speed**} & \multicolumn{3}{c}{**Mesh ID**} & \multicolumn{3}{c}{**Richardson Extrapolation**} \\ \cline{2-7}  & **M01** & **M02** & **M03** & **p** & **R\({}^{*}\)** & **TE** \\ \hline
7 m/s & 744.2 & 756.5 & 757.4 & 4.18 & 0.073 & 757.5 \\
10 m/s & 1597.4 & 1778.6 & 1802.6 & 3.19 & 0.132 & 1806.5 \\
15 m/s & 850 & 1309.5 & 1408.8 & 2.36 & 0.216 & 1439.1 \\
20 m/s & 1047.6 & 1006.4 & 1001.4 & 3.33 & 0.121 & 1000.7 \\ \hline \hline \end{tabular}  
* TE represents the extrapolated torque, R* the ratio of errors, and p the order of accuracy.  
\end{table} 
Table 4: Results of the mesh independency study based on Richardson extrapolation 1. Figure 3: Demonstration of the mesh adopted for the rotor simulation. (**a**) The rotational plane; (**b**) the blade; (**c**) a profile. than the airfoil geometry. Therefore, the blockage effect correction applied to the experimental data was inaccurate, since only the size of the airfoil was considered [37]. Figure 6 shows the lift coefficient from the airfoil simulation with tunnel walls compared with the measured data of the OSU experiment.