# Study on Actuator Line Modeling of Two NREL 5-MW Wind Turbine Wakes
## 4 A Single NREL 5-MW Turbine Case
### Wake Structures  
The vortex isosurfaces to illustrate the downstream development of the wake vortices are depicted in Figure 13. The wake vortices are identified by the Q criterion, where Q is adjusted as 0.003 for the three cases. It is shown that the tip and hub vortices are clear behind the rotor. They persist for nearly two turns, diffuse at \(U_{0}=11.4\) m/s, and spread out early when the wind speed decreased, corresponding to the increase in the tip speed ratio. Additionally, they become a continuous vortex sheet at \(U_{0}=5\) m/s.  
The axial flow interference factors represent the influence on the performance of the wind turbine and the distribution of the loading on the blades, which can be calculated by:  
\[a=1-\frac{U_{x}}{U_{0}} \tag{30}\]  
where \(U_{x}\) is the velocity behind the rotor and \(U_{0}\) is the wind speed. Figure 14 depicts the radial distributions of averaged axial flow interference factors at different wind speeds. From Figure 14, it can be seen that the curves at the wind speed of 5 m/s and 8 m/s are more generally steady than that of 11.4 m/s, but the values are too large under the wind speed of 5 m/s, which means the loading on the blade is not balanced and the influence on the performance is worse than that under 8 m/s.  
Figure 14: Radial distributions of averaged axial flow interference factors at different wind speeds.  
Figure 13: Computed Q field showing the formation of wake structure (Q = 0.003): (**a**) \(U_{0}=11.4\) m/s; (**b**) \(U_{0}=8\) m/s; (**c**) \(U_{0}=5\) m/s.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **Mean Power (MW)** & \(\mathbf{C_{p}}\) & **Difference (\%)** \\ \hline Glauert model & 5.243 & 0.4634 & 4.858 \\ No model & 5.600 & 0.4950 & 12.018 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of the power with Glauert model and without the tip loss model.  
It is common that the wind turbine turns the wind energy into mechanical energy and the reduction of the wind speed is described as the velocity deficit. It depicts the efficiency of the energy transformation and can affect the performance of the downstream wind turbine. The velocity deficit can be seen through the axial velocity distribution, which is simply shown in Figure 15. It is worthwhile to note that the axial velocities have been normalized with the corresponding wind speed and so the normalized velocities at the upstream station are 1. Figure 15 illustrates the curves of the average axial velocity ratio at the hub height. It is easy to see the velocity deficit in the wake and the velocity is recovering with the growing distances. The location of the maximum velocity deficit is around 1D-3D. With the wind speed becoming greater, it moves away from the rotor and becomes higher. That is as indication that the utilization of the wind energy is getting smaller and the rate of the recovery gets slower.  
From the above analysis, it can be seen that the utilization of the wind energy and the ratio of the velocity recovery is larger at the low wind speed, but the loading on the blades is so unsteady and the power is too small. It can thus be simply concluded that the wind turbine can work in an oppositely fine status under the wind speed of 8 m/s. In that case, the power coefficient may become coincidently maxima. Thus, it is reasonable that the wind speed has been set as 8 m/s in many documented studies. For further investigation, some representative numerical results are given at 8 m/s in the next section.