# Accurate RANS Simulation of Wind Turbine Stall by Turbulence Coefficient Calibration
## 3 Investigation of the RANS Simulation Error
### Simulation of the NREL Phase VI Rotor  
Full turbulence simulation of the NREL Phase VI rotor in non-yawed condition is carried out at the wind speeds between 7 m/s and 25 m/s. Figure 7 shows the predicted rotor torque versus the wind speed, with a comparison to the measured data. The curves can also be divided into three stages. At stage \"A\", the predicted torque agrees with the measured data and increases linearly with the wind speed. The torque is overestimated at stage \"B\", while it is underestimated at stage \"C\". That is similar to the results of the airfoil simulation shown in Figure 6, which raises a question: Why is there such a similarity of simulation error between the airfoil lift coefficient (see Figure 6) and the rotor torque (see Figure 7)?  
Figure 8 shows the simulated limiting streamlines on the suction side of the NREL Phase VI blade at different wind speeds. At 7 m/s, all streamlines are directed from the leading edge to the trailing edge, indicating the flow on the entire blade is attached and no stall occurs. At 10 m/s, the flow pattern on the blade is a combination of trailing edge flow separation (light stall) and attached flow (no stall). At 15 m/s, it becomes a combination of complete flow separation (deep stall) and trailing edge flow separation (light stall). When the wind speed increases to 20 m/s, complete flow separation (deep stall) covers the entire blade. The flow patterns at five sections of the blade are listed in Table 5. It is found that the simulation error of the rotor torque in Figure 7 is closely related to the flow patterns. At 7 m/s, no stall occurs, and the torque is well predicted. At 10 m/s, most sections are in light stall, and the torque is remarkably overestimated. At 15 m/s, three sections are under deep stall, while two sections are under light stall, and the overestimation of the torque is reduced. At 20 m/s, deep stall occurs on the entire blade, and the torque is underestimated. The above results indicate that the simulation accuracy of rotor torque is much affected by the flow patterns on the blade. The similarity of the simulation error between the airfoil lift coefficient (see Figure 6) and the rotor torque (see Figure 7) is raised by the fact that light stall leads to overestimation of the aerodynamic force, while deep stall leads to underestimation for both the airfoil and the blade sections.  
Figure 9 shows the C\({}_{t}\)\({}^{\prime}\) versus the wind speed, in which C\({}_{t}\)\({}^{\prime}\) is the dimensionless coefficient of the aerodynamic force contributing positive torque of the blade. The shown three sections of r/R = 0.3, r/R = 0.47, and r/R = 0.95 represent the root, the mid-span, and the tip of the blade, respectively. The predicted curves exceed the experimental ones at the wind speeds between about 9 m/s and 17 m/s. The simulation error at the root section (r/R = 0.3) and the tip section (r/R = 0.95) is found not greater than that at the mid-span section (r/R = 0.47), although the flow at the root and the tip is more complex due to the rotational effect and the 3-D effect. It suggests that the rotational effect and the 3-D effect are not the primary cause of the inaccuracy of the rotor simulation.