# Accurate RANS Simulation of Wind Turbine Stall by Turbulence Coefficient Calibration
## 6 Conclusions  
An approach of turbulence coefficient calibration has been proposed for accurate simulation of wind turbine stall. The similarity of error between the rotor and airfoil simulations is investigated on the S809 airfoil and the NREL Phase VI rotor. It is an important foundation of the present work, which provides a way to improve rotor simulation using airfoil experimental data. The simulation of the NREL Phase VI rotor is significantly improved by making the calibration on the S809 airfoil. Furthermore, the procedure of calibration is applied to the MEXICO rotor, and it also significantly improves the simulation. The following conclusions are drawn from the present study:  
* RANS simulations using the SST turbulence model tend to over-predict the aerodynamic force of airfoils and rotors in light stall. The present study involves four airfoils of S809, DU91-W2-250, RIS\(\O\)-A1-21, and NACA 64-418, three of which face the problem of over-prediction at given Reynolds numbers. The over-prediction of the NREL Phase VI rotor and the MEXICO rotor is dependent on the airfoils of their blades.
* There is a high degree of similarity of error between the airfoil and the rotor simulations. In conditions of stall, the rotor simulation error is approximately at the same level of the airfoil simulation error. That means the rotor simulation error is not mainly caused by the rotational effect or the 3-D effect. For example, the range and amplitude of the simulation error at the mid-span section (r/R = 0.47) of the NREL Phase VI blade overlaps much with those of the S809 airfoil, and the peak error at the root section (r/R = 0.3) and the tip section (r/R = 95) is not higher than that of the airfoil.
* The closure coefficient \(\beta_{\infty}^{*}\) of the SST turbulence model has a great impact on the prediction of light stall for both airfoils and rotors. The predicted airfoil lift in light stall reduces with the increase of \(\beta_{\infty}^{*}\). For example, the lift coefficient of the S809 airfoil, which was over-predicted about 30% in light stall conditions, is reduced to a level consistent with experimental data as \(\beta_{\infty}^{*}\) is adjusted to 0.11. Also, the error of predicted torque of the NREL Phase VI rotor is reduced when the same adjustment is made.
* The optimal \(\beta_{\infty}^{*}\) obtained from the calibration in airfoil simulation can significantly improve the stall prediction in rotor simulation, and thus the rotor aerodynamic performance is predicted more accurately. For the NREL Phase VI rotor, the relative error of the predicted maximum torque is reduced from 34.4% to 3.2%. For the MEXICO rotor, the predicted pressure distributions over typical sections are better than the CFD results from the Mexnext project.  
In essence, the present study provides an approach for calibrating the rotor simulation by using airfoil experimental data and enhances the potential of RANS in accurate simulations of the wind turbine aerodynamic performance. In future work, more simulations of various airfoils and rotors will be carried out to obtain a more comprehensive evaluation of the approach.  
Conceptualization, W.Z.; Data curation, H.T.; Funding acquisition, W.Z. and T.W.; Investigation, W.Z., H.T., and C.Z.; Methodology, W.Z.; Project administration, W.Z. and T.W.; Supervision, W.Z. and T.W.; Visualization, H.T. and C.Z.; Writing--original draft, W.Z.  
This research was funded jointly by the National Natural Science Foundation of China (No. 51506088), the National Basic Research Program of China (\"973\" Program) under Grant No. 2014 CB046200, the Priority Academic Program Development of Jiangsu Higher Education Institutions, and the Key Laboratory of Wind Energy Utilization, Chinese Academy of Sciences (No. KLWEU-2016-0102).  
Part of the present study was once discussed in [PERSON]. [PERSON]'s research team, department of Wind Energy, DTU. The corresponding author wishes to express special acknowledgement to him and his team members.  
The authors declare no conflict of interest.