# The Influence of Tilt Angle on the Aerodynamic Performance of a Wind Turbine
## 3 Results and Discussion
### Wind Shear  
The change in wind speed with height was determined according to the power function given in International Electrotechnical Commission (IEC) 61400-1 [21] and presented as follows:  
\[\frac{V_{Z}}{V_{Z_{r}}}\ =\ \left(\frac{Z}{Z_{r}}\right)^{\gamma} \tag{12}\]  
where \(V_{Z}\) refers to the wind speed at height z, \(V_{Z_{r}}\) refers to the reference wind speed at height \(Z_{r}\) and \(\gamma\) refers to the wind shear exponent. \(Z_{r}\) refers to the hub height. In this study, the reference wind speed is 11.4 m/s. In this paper, wind shear exponents are 0.09, 0.2 and 0.41. The wind shear exponent of 0.09 indicates a very unstable atmospheric state, 0.20 represents a neutral state and 0.41 represents a very stable state [4]. The turbulence intensity was calculated according to the formula in IEC 61400-1 [21] and given as follows:  
\[I_{T}\ =\ I_{ref}(0.75V_{hub}+5.6)/V_{hub} \tag{13}\]  
where \(I_{T}\) is the turbulence intensity, \(I_{ref}\) is the expected value of the turbulence intensity and \(V_{hub}\) is the reference velocity at the hub. In this paper, \(I_{ref}\) values are 0.12, 0.14 and 0.16. \(I_{ref}\) of 0.12 represents lower turbulence characteristics, 0.14 describes medium turbulence characteristics and 0.16 describes higher turbulence characteristics. Table 8 shows the average power along one rotation of the wind turbine after it has stabilized. It can be seen from Table 8 that, compared with uniform wind, wind shear will cause the average power of the wind turbine to decrease by about 14%. At the same time, it can be found that the average power of the 4\({}^{\circ}\) tilt angle is close to that of the 0\({}^{\circ}\) tilt angle and is higher than the average power of the 8 and 12\({}^{\circ}\) tilt angles under uniform wind or wind shear conditions. The deviation (\(|P_{a}-P_{m}|\)) of the power relative to the average power at an azimuth angle of 180\({}^{\circ}\) gradually decreases as the tilt angle increases (see Figure 23, Table 8). When the tilt angle reaches 8\({}^{\circ}\) and continues to increase, \(|P_{a}-P_{m}|\) will remain unchanged. This means that as the tilt angle increases, the interaction between the blade and the tower gradually weakens. When the tilt angle exceeds 4\({}^{\circ}\), the influence of the tilt angle on the interaction between the blade and the tower can be ignored. However, when the tilt angle exceeds 4\({}^{\circ}\), it will cause a significant decrease in the average power of the wind turbine. Therefore, considering the power of the wind turbine and the interaction between the blade and the tower, it is more appropriate to set the wind turbine tilt angle to about 4\({}^{\circ}\). Figure 22: The distribution of instantaneous axial velocity along blade span at the wind turbine downstream positions of 0.5D, 2.5D, 3.5D and 4.5D. Figure 24 describes the influence of wind shear exponents (\(\gamma\)) on the aerodynamic performance of the wind turbine. It can be seen from Figure 24 that the thrust and power of the wind turbine when the wind shear exponent is 0.41 are higher than the values when the wind shear exponents are 0.09 and 0.20. It can be found from Table 9 that the average thrust and power of the wind turbine under different wind shear exponents have the smallest error when the wind shear factor is 0.41 compared with the uniform wind, and the average thrust and power of the wind turbine are almost the same when the wind shear factors are 0.09 and 0.2. In Table 9, the wind shear exponent of 0.00 means uniform wind inlet conditions. In Figure 24, it can be seen that the fluctuation of the wind turbine thrust and power curve when the wind shear factor is 0.09 is significantly higher than the other two cases. This means that the wind shear exponent has an effect on the interaction between the blade and the tower. Figure 23: Thrust and power versus azimuth angle for various tilt angles at \(V_{hub}=11.4\) m/s (\(\gamma=0.2\), \(I_{ref}=0.14\)).