# CFD Simulations of Flows in a Wind Farm in Complex Terrain and Comparisons to Measurements
## 3 Results
### Actuator Disc Reynolds-Averaged Navier-Stokes Results  
Prior to simulating the entire wind farm using AD-RANS, the inputs for the far upstream wind direction and speed should be modified to include the effect of the turning angle and speed-up. The wind direction and speed throughout the complex terrain will not be equal to the far upstream wind direction and speed where the terrain is assumed to be flat (see e.g., Figure 3). The flow will change direction and gain or lose speed when encountering, e.g., hills, valleys, and cliffs. For an accurate comparison with the measurements, the computed wind direction and speed at the reference met mast and wind turbine must take into account the effect of the turning angle and speed-up. The turning angle and speed-up are obtained from a pre-computation without wind turbines at the reference met mast and wind turbine locations, respectively. The turning angle and speed-up are calculated using the reference wind speed and direction as shown in Table 2. Table 4 summarizes the turning angles and speed-ups obtained for FC1. In the pre-computation without wind turbines, e.g., FC 1.1 in Table 4, the far upstream wind direction and speed were set to 180 degrees and 4 m/s, respectively. The wind direction and speed computed at M3 and WT14 was \((180+4.28)\) degrees and \((4\times 1.25)\) m/s, respectively. The far upstream wind direction and speed are then set to \((180-4.38)\) degrees and \((4/1.25)\) m/s to obtain approximately 180 degrees and 4 m/s at M3 and WT14, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**FC1** & **1.1** & **1.2** & **1.3** & **1.4** & **1.5** & **1.6** & **1.7** & **1.8** & **1.9** \\ \hline Turning angle (degrees) & 4.28 & \(-\)4.78 & 1.29 & 4.28 & \(-\)4.76 & 1.29 & 4.28 & \(-\)4.75 & 1.28 \\ Speed-up (-) & 1.25 & 1.12 & 1.13 & 1.25 & 1.12 & 1.13 & 1.25 & 1.12 & 1.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Turning angles and speed-ups obtained for FC1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**FC1** & **Sector** & **Wind Speed, h = 67 m** & **Reference Wind Speed** & **Reference Wind Direction** \\ \hline
1.1 & \(180\pm 5^{\circ}\) & \(4\pm 1\) m/s & WT14, h = 67 m & M3, h = 70 m \\
1.2 & \(300\pm 5^{\circ}\) & \(4\pm 1\) m/s & WT11, h = 67 m & M1, h = 70 m \\
1.3 & \(330\pm 5^{\circ}\) & \(4\pm 1\) m/s & WT11,  
Figure 5 contains the results for the flow cases defined in Table 2, which consist of the AD-RANS results and the comparisons with the measurement data from SCADA. The notation _wd_ and _ws_ shown in the title for each figure denotes wind direction and wind speed, respectively. The wind direction corresponds to the measurements on met masts M1 and M3, while the wind speed corresponds to the measurements on the reference wind turbine (ref. WT). The figure contains the predicted, labeled as AD# and AD# \(\pm\) 5\({}^{\circ}\) where # is the wind direction in degrees, and measured, labeled as SCADA, electrical power output for all 25 WTs. Each WT is labeled between 1 and 25, refer to Figure 2a. The AD# results represent a single run with the wind direction, #, which is also specified in the sub-figure titles. The AD# \(\pm\) 5\({}^{\circ}\) results represent the average of five runs: \(-\)5, \(-\)2, 0, \(+\)2, and \(+\)5 degrees relative to _wd_. For example, AD# for FC 1.1 is a single run at 180 degrees (# = 180\({}^{\circ}\)), and AD# \(\pm\) 5\({}^{\circ}\) is the average of 5 runs: 180 \(-\) 5, 180 \(-\) 2, 180, 180 \(+\) 2, and 180 \(+\) 5 degrees. The SCADA measurements represent averaged values in \(\pm\)5 degree bins. Although difficult to see, the standard error (SE) in Figure 5 is equal to SCADA \(\pm\) 5\({}^{\circ}\) but includes the error bars (may require zoom-in). In Figure 5, AD# \(\pm\) 5\({}^{\circ}\) should more closely represent the SCADA measurements than AD#, since the SCADA measurements are grouped and averaged in \(\pm\)5 degree bins.