# Accurate RANS Simulation of Wind Turbine Stall by Turbulence Coefficient Calibration
## 4 Simulations with Turbulence Coefficient Calibration
### Rotor Simulation Using the Calibrated Coefficient  
\(\beta_{\infty}^{*}=0.11\), the optimal value for the S809 airfoil, is applied to the simulation of the NREL Phase VI rotor. The predicted rotor torque versus the wind speed is shown in Figure 16. Both the results for \(\beta_{\infty}^{*}=0.09\) and \(\beta_{\infty}^{*}=0.11\) are consistent with the experimental data when the wind speed is lower than 9 m/s. They diverge from each other at the wind speeds between 9 m/s and 20 m/s. \(\beta_{\infty}^{*}=0.09\) leads to a notable overestimation of the maximum torque, while \(\beta_{\infty}^{*}=0.11\) makes it accurately predicted. Table 7 shows the relative simulation error of the rotor torque. At 10 m/s, where the maximum torque is achieved for both the predicted curves, the relative error is reduced to 3.2% from 34.4% by the application of \(\beta_{\infty}^{*}=0.11\). At 17 m/s, the result for \(\beta_{\infty}^{*}=0.09\) looks better than that of \(\beta_{\infty}^{*}=0.11\). However, it is a mere coincidence due to the change from positive error to negative error of the curve for \(\beta_{\infty}^{*}=0.09\) at this wind speed. When the wind speed increases to 20 m/s or higher, the two curves overlap again and are lower than the experimental data. The maximum difference of the two predicted curves is located at the wind speed of 10 m/s. The pressure distributions of five typical blade sections at this wind speed are given in Figure 17. It is shown that the application of \(\beta_{\infty}^{*}=0.11\) leads to accurate prediction of the pressure distributions. Taking the section of r/R = 0.47 as an example, \(\beta_{\infty}^{*}=0.11\) makes the onset of deep stall accurately captured and properly gives the flat pressure distribution on the suction side of the blade. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**AoA (\({}^{\circ}\))** & **8** & **10** & **12** & **14** & **16** & **18** & **20** & \(\overline{\delta}\) \\ \hline \(\beta_{\infty}^{*}=0.09\) & 5.8\% & 18.1\% & 23.0\% & 18.9\% & 22.7\% & 39.4\% & 82.2\% & 30.0\% \\ \(\beta_{\infty}^{*}=0.11\) & 2.2\% & 1.3\% & \(-0.3\%\) & 0.5\% & 6.1\% & 17.5\% & \(-3.9\%\) & 4.5\% \\ \hline \end{tabular}
\end{table} 
Table 6: The relative simulation error of lift coefficient for different values of \(\beta_{\infty}^{*}\). Figure 15: The simulation results of lift coefficient at different Reynolds numbers compared to experimental data. The limiting streamlines on the suction side of the blade at the wind speeds of 10 m/s, 15 m/s, and 20 m/s are shown in Figure 18. As compared to \(\beta_{\infty}^{*}=0.09\), the results for \(\beta_{\infty}^{*}=0.11\) have two differences at 10 m/s. Firstly, the area of trailing edge flow separation (light stall) is larger and the area of attached flow (no stall) is correspondingly smaller. Secondly, a small piece of complete flow separation (deep stall) occurs at about r/R = 0.47, which has been corroborated by the experimental pressure distribution at this section shown in Figure 17. At 15 m/s, a large part of the blade is under complete flow separation (deep stall) for both \(\beta_{\infty}^{*}=0.09\) and \(\beta_{\infty}^{*}=0.11\). The difference is that the area of deep stall is larger for \(\beta_{\infty}^{*}=0.11\). At 20 m/s, complete flow separation (deep stall) covers the whole blade, and there is little difference between the two results for \(\beta_{\infty}^{*}=0.09\) and \(\beta_{\infty}^{*}=0.11\). The above results suggest that the simulation using \(\beta_{\infty}^{*}=0.11\) predicts an earlier onset of trailing edge flow separation (light stall) and also an earlier conversion to complete flow separation (deep stall) compared to the simulation using \(\beta_{\infty}^{*}=0.09\). Figure 16: The predicted rotor torque for different values of \(\beta_{\infty}^{*}\) compared to the measured data of the NREL Phase VI experiment. Figure 17: The simulation results of pressure distributions for different values of \(\beta_{\infty}^{*}\), with a comparison to the measured data of the NREL Phase VI experiment.