# Evaluation of Tip Loss Corrections to AD/NS Simulations of Wind Turbine Aerodynamic Performance
## 6 Simulation Results  
### Results of Glauert-Type Corrections  
#### 6.1.1 Glauert-A/B/C Corrections  
The blade loads for Cases 1, 2 and 3 are gathered in Figure 4, which represent results obtained from the _NREL Phase VI_ rotor. The _NREL Phase VI_ blade has a linear change of chord distribution starting from \(r=1.3\) m with a constant slope of 0.1. The chord length is 0.358 m at the tip, which is about 48% of the largest chord length in the blade inboard part. Therefore, the loads do not converge to zero without a tip loss correction. It is noticed that there is a certain degree of difference between the results of the Glauert-A/B/C corrections in the tip region (e.g., at \(r/R>0.8\)). In general, Glauert-C leads to lower loads which are closer to the experimental data, Glauert-A gives results close to, but slightly higher than, those of Glauert-C, while Glauert-B results in relatively higher loads near the tip. Taking the \(F_{n}\) in Figure 4a as an example of quantitative comparison, the relative difference between the results of Glauert-B and Glauert-C is about 4% at \(r/R=0.95\). The difference in other cases is not larger than this value. At a wind speed of 7 m/s, all the curves of \(F_{n}\) generally agree with the five experimental data except that at \(r/R=0.95\) where an overestimation is observed. This overestimation becomes much more remarkable as the wind speed increases to 10 m/s and 13 m/s. At 10 m/s, there is no much difference around \(r/R=0.9\) between the results with no correction and with the Glauert-type corrections, indicating that almost no effective correction is made here. At 13 m/s, the curves of the Glauert-type corrections even exceed the uncorrected curve in a \(r/R\) range of about [0.66, 0.88]. It is clear that the corrections perform much worse at the higher wind speeds as compared with 7 m/s. The overestimation at \(r/R=0.95\) is also observed in the results for \(F_{t}\), although it looks better to some extent, especially at 7 m/s. Considering the fact that the Glauert correction was derived based on the potential hypothesis, it is reasonable to believe that the unusually poor performance at the higher wind speed is caused by the flow separation. According to the results of the _NREL UAE Phase VI_ experiments [50], the angle of attack at most cross-sections of the blade exceeds the linear range of their aerodynamic polar when the wind speed is increased to be higher than 10m/s. Taking the cross-section of \(r/R=0.63\) as an example, the angles of attack are \(5.9^{\circ}\), \(11.8^{\circ}\), \(16.9^{\circ}\) at a wind speed of 7 m/s, 10 m/s, 13 m/s, respectively. The exact operating points for three cases on the lift polar of the S809 airfoil (the airfoil of all cross-sections  
Figure 4: Normal force \(F_{n}\) and tangential force \(F_{t}\) along the _NREL Phase VI_ blade. of the _NREL Phase VI_ blade) are depicted in Figure 5. It clearly shows that Case 2 and Case 3 are in the nonlinear lift region corresponding to flow separation, while Case 1 is in the linear lift region corresponding to attached flow, which implies that flow separation occurs at 10 m/s and 13 m/s. The normal and tangential forces along a blade of the _NREL 5 MW_ rotor are plotted in Figure 6. As a widely studied virtual rotor, full CFD solutions [33] are often used as the reference data. Although the typical rotating speed of the _NREL 5 MW_ rotor is a few times less than the _NREL Phase VI_ rotor, the resulted tip speed ratio is higher, which is closer to the optimal design point. The blade tip of the _NREL 5 MW_ rotor is smoothly sharpened where the slope at the last 4 m is 0.46, and the chord length at the tip is only 4.3% of the largest chord length in the blade inboard part. It can be seen in Figure 6 that the loads at the tip naturally approach to zero even without a tip loss correction. Figure 5: Operating points of the cross-section of \(\tau/R=0.63\) on the lift polar of the S809 airfoil. (The Reynolds number of the airfoil is \(1\times 10^{6}\) which is close to that of the cross-section).