# Accurate RANS Simulation of Wind Turbine Stall by Turbulence Coefficient Calibration
## 5 Verification of the Calibration to the MEXICO Rotor
### Results and Disscussion  
RANS simulations of the three airfoils of the MEXICO blade are carried out, and the resulted lift coefficients are shown in Figure 19. For DU91-W2-250 at Re = 0.5 \(\times\) 10\({}^{6}\), the default \(\beta_{\infty}^{*}\) of 0.09 gives results consistent with the measured data at a wide range of angles of attack. For RISO-A1-21 at Re = 1.6 \(\times\) 10\({}^{6}\), \(\beta_{\infty}^{*}\) = 0.10 looks better. For NACA 64-418 at Re = 0.7 \(\times\) 10\({}^{6}\), \(\beta_{\infty}^{*}\) = 0.105 gives perfect prediction before deep stall. As a result, in the simulations of the MEXICO rotor, different values of \(\beta_{\infty}^{*}\) should be applied at different span locations depending on the airfoil used there. That would be an inconvenience for application. A function might have to be established to give a continuous change of \(\beta_{\infty}^{*}\) in the computational domain, especially along the blade span. The function could be applied to the SST model if an open source solver or a house code were used. However, it cannot easily have been realized in ANSYS FLUENT. As a compromise, three independent rotor simulations are carried out, in which the \(\beta_{\infty}^{*}\) values of 0.09, 0.10, and 0.105 are applied, respectively.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**r/R** & **r (m)** & **Chord (m)** & **Profile** & **Re** \\ \hline
0.25 & 0.563 & 0.224 & DU91-W2-250 & 0.38 \(\times\) 10\({}^{6}\) \\
0.35 & 0.788 & 0.193 & DU91-W2-250 & 0.46 \(\times\) 10\({}^{6}\) \\
0.6 & 1.350 & 0.142 & RISO-A1-21 & 0.58 \(\times\) 10\({}^{6}\) \\
0.82 & 1.845 & 0.113 & NACA 64-418 & 0.64 \(\times\) 10\({}^{6}\) \\
0.92 & 2.070 & 0.099 & NACA 64-418 & 0.62 \(\times\) 10\({}^{6}\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: Information about the five sections and their Reynolds numbers in the present case.  
The rotor simulation results of pressure distributions over the five blade sections of 25%, 35%, 60%, 82%, and 92% span are shown in Figure 20. Measured data from both the MEXICO and the New MEXICO experiments are shown for comparison. For the default \(\beta_{\infty}^{*}\) value of 0.09, notable deviations between the computational and experimental data appear on the suction side at sections of r/R = 0.35, 0.82, and 0.92. The present simulation error of the three sections is at an average level of the CFD results from the Mexnext project [29]. The Figure 20c-e give the results of r/R = 0.6, 0.82, and 0.92 for the calibrated values of \(\beta_{\infty}^{*}\), in which the results for \(\beta_{\infty}^{*}\) = 0.09 are also displayed. At r/R = 0.6, the prediction of = 0.09 is consistent with the New MEXICO data, while the result of \(\beta_{\infty}^{*}\) = 0.10 is closer to the MEXICO data. At r/R = 0.82 and 0.92, the predicted pressure distributions on the suction side become much closer to the experimental data when \(\beta_{\infty}^{*}\) = 0.105 is applied. Also, the present results are better than a collection of the CFD results from the Mexnext project [29]. The comparisons in the Figure 20d,e give strong evidence for the contribution of the present calibration to the accurate simulation of wind turbine stall.  
Figure 19: The predicted lift coefficients of the airfoils DU91-W2-250, RISØ-A1-21, and NACA 64-418 for different values of \(\beta_{\infty}^{*}\), with a comparison to experimental data.  
Figure 20: The predicted pressure distributions over blade sections for different values of \(\beta_{\infty}^{*}\) compared to experimental data and a collection results of the Mexnext project [29].