# CFD Simulations of Flows in a Wind Farm in Complex Terrain and Comparisons to Measurements
## 2 Methodology
### Actuator Disc Reynolds-Averaged Navier-Stokes Simulation  
The \(k\)-\(\epsilon\)-\(f_{P}\) eddy-viscosity model [3; 17] is used to model the turbulence in RANS. A log-law is used with a surface roughness of \(z_{0}=0.1\) m over the entire domain to simulate the site vegetation. Ideally, \(z_{0}\) should be based on measurement data, e.g., by considering the inflow profile according to measurements in the wind farm, however a rough estimate for \(z_{0}\) was used instead. Figure 2a depicts the terrain and wind turbine setup for the AD-RANS where the wind turbine rotor diameter,  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **CSIC HZ93-2.0 MW** \\ \hline Diameter & 93 m \\ Power rating & 2.0 MW \\ Hub height & 67 m \\ Power control & Variable speed, collective blade pitch control \\ \hline \hline \end{tabular}
\end{table}
Table 1: China Shipbuilding Industry Corporation (CSIC) Haizhuang (HZ) wind turbine specifications.  
Figure 1: Comparison of the manufacturer’s data and the developed model for the (**a**) electrical power and (**b**) rotor thrust as a function of the wind speed.  
\(D\), is 93 m. In the AD-RANS setup, the mesh is cylindrical in shape with a radius of 28 km and a height of approximately 25 km. The 7.8 km\({}^{2}\) terrain grid is situated at the center of the mesh at WT10, since WT10 is approximately located at the center of the wind farm. The cylindrical mesh allows variable wind directions without changing the grid. Inflow/outflow boundary conditions are applied on the outer-boundary of the mesh according to the wind direction. The velocities at the top and inlet boundaries are prescribed. The mesh contains 280 blocks with each block having 48\({}^{3}\) grid points. The terrain grid is 10 \(\times\) 10 blocks. There are approximately 6 (horizontal) \(\times\) 16 (vertical) grid cells on each AD.  
Given an amount of computational resources to work with, since the amount of computational resources is limited, the computational mesh is designed such that there is more grid points at the center to capture terrain effects and the effect of each AD on the flow field. At the center, the velocities gradients due to complex terrain and the wind turbine presence is greatest. Further away from the center and towards the cylindrical boundary of the mesh, a much coarser grid is used over a long distance to minimize the computational cost and at the same time reduce the effect of the boundary conditions on the flow field at the center. The computational grid gave slightly less than the recommended amount of grid points on each AD, which based on experience should be a minimum of 8 horizontal and 8 vertical grid cells [17]. The effect of a refined mesh, where the terrain grid is 24 \(\times\) 10 blocks, is shown in Section 3.1.  
Sensors are placed at hub height for all twenty-five wind turbines as well as on the met masts in the CFD setup. The (a) outer and (b) terrain computational grids for the AD-RANS computations are shown in Figure 3. Each AD-RANS computation is performed using one-hundred-and-forty 2.8 GHz processors on a Linux cluster, where each processor is allocated for two blocks out of the 280 blocks. Each AD-RANS computation requires approximately 3 to 4 h for completion.  
Figure 2: Computational layouts of the (**a**) Shaanxi wind farm with twenty-five wind turbines and of (**b**) wind turbine 14 with met masts M1 and M3. The wind turbines are labeled from 1 to 25.