# The Influence of Tilt Angle on the Aerodynamic Performance of a Wind Turbine
## 3 Results and Discussion
### The Effect of the Tilt Angle on the Wind Turbine Wake  
The instantaneous isovorticities occurring when the blade is in front of the tower are presented in Figure 19. One can clearly see that these instantaneous diagrams with nacelle tilt angle shows that there is a strong flow interaction between the wake generated by the blade root, hub and tower regions. Because of the existence of the tower, there are strong unsteady flow interactions between tower vortex and blade tip vortex during downstream propagation. This interaction caused the blade tip vortex to break behind the tower. In addition, an increase in tilt angle will cause the blade tip vortex tube to tilt.  
The instantaneous x-vorticities at different sections in four tilt angles are presented in Figure 20. We can observe that there is a clear difference in the blade tip vortex at different tilt angles. At 0 and 4\({}^{\circ}\) tilt angles, the blade tip vortex has only negative x-vorticities. When the tilt angle is changed to 8\({}^{\circ}\), positive x-vorticity and negative x-vorticity appear in the right half of the blade tip vortex. When the tilt angle is changed to 12\({}^{\circ}\), the left part of blade tip vortex is negative and right part is positive. At the same time, it can be seen that there are slight differences in the tower-generated vortexes of the four cases. By comparison, at the positions of x/D = 0.25 and x/D = 0.5, the vortex generated by the tower behind the rotor at the tilt angle of 4\({}^{\circ}\) is slightly less than other cases. When the tilt angle reaches 12\({}^{\circ}\), the vortex generated by the tower is broken.  
Figure 19: Side-view of instantaneous isovorticity contours for different nacelle tilt angles.  
Figure 18: Tangential force per unit of span along the rotor span for Blade 1.  
The corresponding vertical x-velocity profiles are presented in Figure 21. When the tilt angle is \(0^{\circ}\), as the downstream distance increases, the velocity field behind the wind turbine is approximately symmetrical about the centerline and keeps a circular shape. However, as the tilt angle increases, the velocity field behind the wind turbine shows asymmetry and gradually moves to the upper right. Meanwhile, the low-velocity region at the end of the wake gradually decreases with increasing tilt angle.  
Figure 20: Instantaneous x-vorticities at different sections for four tilt angles.  
Figure 22 shows 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, which represent the development of the velocity in the wake. Observing the instantaneous axial velocity distribution at the position of X/D = 0.5, it can be seen that the upper half of the curve does not change much with the tilt angle, but the lower half of the curve changes significantly with the tilt angle. In addition, it can be seen that the lower half of the curve has the smallest fluctuation at the 4\({}^{\circ}\) tilt angle, which means that the interaction between the blade tip vortex downstream of the wind turbine and the tower wake vortex is the weakest at a tilt angle of 4\({}^{\circ}\). We can also observe a similar phenomenon in Figure 21. Observing the instantaneous axial velocity distribution at the positions of X/D = 2.5 and X/D = 3.5, we can see that as the tilt angle increases, the minimum velocity in the wake gradually increases and shifts upwards. However, at the position of X/D = 4.5, there is a slight decrease in the minimum velocity as the tilt angle increases. This is due to the upward shift of the wake-end deceleration zone.  
Figure 21: Vertical section x-velocity profiles at y = 0 m.  
Figure 22: _Cont._