## 3 Results and Discussions
### Vertical Velocity Distribution in the Flow Field  
According to Formula (11), the wind turbine power is mainly determined by the wind speed at the wind turbine location. By analyzing the vertical velocity distribution in the flow field, we can have a deep understanding of the characteristics of the flow field. The actuator disk model of OpenFOAM software is used to conduct numerical research on the flow field, and the vertical velocity distribution at the feature position is extracted for comparison, as shown in Figures 4-7.  
\[P=C_{\rm P}\frac{1}{2}\rho Au^{3} \tag{11}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Inflow 7 m/s** & **Case 0** & **Case 1** & **Case 2** & **Case 3** & **Case 4** \\ \hline Power of downstream wind turbine & 7028.1 & 6910.3 & 6996.2 & 6961.1 & 7076.5 \\ Increase & / & \(-1.67\%\) & \(-0.45\%\) & \(-0.96\%\) & 0.69\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of the power of downstream large wind turbines under different wind tunnel test cases (unit: W).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Diameters of large turbine \(D_{e}\) (mm) & 1000 \\ Hub height of large turbine \(H_{e}\) (mm) & 1200 \\ Diameters of small turbine \(d_{e}\) (mm) & 340 \\ Hub height of small turbine \(h_{e}\) (mm) & 300 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Experimental wind turbine parameters.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Inflow 11.2 m/s** & **Case 0** & **Case 1** & **Case 2** & **Case 3** & **Case 4** \\ \hline Power of upstream large wind turbine & 4839.40 & 4833.47 & 4837.80 & 4839.02 & 4839.31 \\ Power of downstream large wind turbine & 4218.30 & 4194.38 & 4202.52 & 4215.43 & 4239.35 \\ Total power of the larger wind turbines & 9057.70 & 9027.85 & 9040.32 & 9054.45 & 9078.66 \\ Total power of the smaller wind turbines & 0 & 604.36 & 603.24 & 602.52 & 601.46 \\ Total power of the larger turbines and small wind turbines & 9057.70 & 9632.21 & 9643.56 & 9656.97 & 9680.12 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of the power of downstream large wind turbines under different number simulation cases (unit: kW).  
Figure 4: Comparison of vertical velocity wind profiles between Case 1 and Case 0.  
Figure 5: Comparison of vertical velocity wind profiles of Case 2 and Case 0.  
Figure 6: Comparison of vertical velocity wind profiles of Case 3 and Case 0.  
Figure 4 compares and analyzes the dimensionless velocity in the vertical direction at \(2D\), \(2D+5d\), \(2D+10d\) and \(2D+15d\) in the flow field under Case 0 and Case 1 conditions. It is found that under the Case 1 working condition, the speed within the height of \(z/D=[0,0.65]\), that is, within the height range of a small wind turbine; in the figure, we can see that the curve of Case 1-1 shifts significantly upstream in this region compared to the curve of Case 0-1. We calculate the results for both operating conditions at \(z/D=0.35\) and find that Case 1-1 has a loss of about 3.34% compared to Case 0-1, decreasing by approximately 3.34%. However, at the positions of \(2D+5d\), \(2D+10d\) and \(2D+15d\), the loss gradually weakened. This indicates that the surface roughness in the flow field is increased under Case 1 conditions. In addition, within the range of \(z/D=[0.65,2.10]\) of the large wind turbine, the wake of the wind turbine gradually recovers, and the influence of the small wind turbine on the vertical speed gradually weakens.  
Figures 5-7 respectively show the dimensionless velocity analysis of Case 2, Case 3, Case 4 and Case 0 in the vertical direction. By comparing and analyzing the above three groups of data, the velocity reduction of Case 2, Case 3 and Case 4 gradually decreases with the increase in distance between the small wind turbine and large upstream wind turbine. Its speed loss is divided into 5.40%, 3.8% and 2.92% compared with Case 0.