# Study on Actuator Line Modeling of Two NREL 5-MW Wind Turbine Wakes
## 5 Double NREL 5-MW Wind Turbines Case
### Result of 7\(D\) Separation  
Although changing the tip loss model from Glauert to Shen and other adjustments make the errors of the mean power larger, it is still with the acceptable range. The comparison of the power with improved ALM by [PERSON] et al. (2018) is presented in Table 12, in which the power of WT2 reduces a lot and is only 39.8% of WT1 due to the influence of the WT1 wake effect. The power and thrust coefficients of WT1 and WT2 are described in Figures 20 and 21. The tendency of the WT1 power and thrust curves shows almost no changes. Though the curves of WT2 continue to become lower, the reduction is no more than 2%. Besides, the interval between the two extremum points \begin{table}
\begin{tabular}{c c c} \hline \hline
**Top Speed Ratio of WT2** & **Power Coefficient (WT1)** & **Power Coefficient (WT2)** \\ \hline
3.5 & 0.5206 & 0.0899 \\
4.0 & 0.5205 & 0.1256 \\
4.5 & 0.5205 & 0.1599 \\
5.0 & 0.5204 & 0.1885 \\
5.5 & 0.5204 & 0.2024 \\
6.1 & 0.5203 & 0.2069 \\
6.5 & 0.5203 & 0.2054 \\
7.0 & 0.5202 & 0.1961 \\
7.55 & 0.5201 & 0.1794 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Power coefficient with different tip speed ratios of WT2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mean Power (MW)** & **Turbine 1** & **Turbine 2** & _ap (W/m)_ \\ \hline
6D & 2.0312 & 0.6817 & 901.7270 \\
7D & 2.0345 & 0.8089 & 917.1647 \\
8D & 2.0336 & 0.9275 & 920.1591 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The mean power and _ap_ with different turbine separations. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Mean Power (MW)** & **Turbine 1** & **Turbine 2** \\ \hline Jha & 1.9217 & 0.8644 \\ turbinesFoam & 2.0345 & 0.8089 \\ Error (\%) & 5.87 & 6.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: The comparison of mean power computed by improved ALM. ALM: Actuator Line Model. in WT2 is bigger than WT1. The reason for this is due to the fact that the rotational speed of WT2 is smaller than that of WT1. As can be seen in Figures 20 and 21, the curves between the two extremum points fluctuate significantly. It proves that the WT2 is located in the wake flow field of WT1 and subjected to the flow unsteadiness. Figure 22 shows the radial distributions of average tangential and normal forces of WT1 and WT2. The distribution patterns of WT2 are very similar to those of WT1, and the force amplitude of WT2 is nearly 56% of WT1. It is noted that Figure 22 shows the averaged value of the time but not the instantaneous one, which may not be sufficient to establish a sound conclusion. Considering this, five-points data on the blade are picked up in different times, and their standard deviations are calculated. The outcomes are shown in Figure 23. It can be observed that the standard deviations of WT2 are greater than those of WT1, especially in the case of normal force. This is an indication that the force varies widely, and the forces get their maximums from \(r/R=0.6\) to \(r/R=0.8\). Consequently, the loading distribution of WT2 is lower than that of WT1 across the range. Figure 21: Comparison of thrust coefficient between WT1 and WT2. Figure 20: Comparison of power coefficient between WT1 and WT2. According to the discussion above, the distribution of the forces on the blades and the stabilization of the force both affect the production of the wind turbine. Because of the power of WT1 being higher, the stabilization effect is more crucial than the distribution one. Besides, the distribution is more highly concentrated and the range of change is larger in the middle of the blades, where the blades are easily damaged and need to be paid much more attention during the design. Furthermore, Figure 24 depicts the radial distributions of averaged axial flow interference factors. It can be seen that the WT1 distribution of \(a\) is similar to that in Section 4.3. The tendency of \(a\) is almost the same between WT1 and WT2, but the value is much bigger in WT2.