## 3 Numerical Results
### Validation of the Simulation Framework  
Before going further to discuss the performance of a wind turbine in different operation setups, the accuracy of the simulation code should be verified first. The 2.3 MW NM80 wind turbine was used here. The design geometry of the LM 38.8 blade and aerodynamic airfoil data for the generic 2.3 MW variable speed and pitch controlled NM80 wind turbine were provided through a confidential agreement of using the DANAERO database. The airfoil data were used directly in AL/FLEX5, and the structural data originally prepared for HAWC2 were used to produce an equivalent FLEX5 input file. We assume the wind turbine operates in an ideal situation, so the tilt angle and tower shadow effects are neglected. Some key parameters of the wind turbine are listed in Table 1.  
Specific parameters for the two verification cases are listed below in Table 2.  
In the computations, a relatively fine mesh of about 19 million cells was used with \(192\times 192\times 512\) cells in the transversal, vertical and streamwise directions in a domain of \([-16\)R, \(16\)R\(]\times[0\)R, \(19\)R\(]\times[-16\)R, \(34\)R\(]\) (R is the rotor radius), respectively. A time-step based on \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline Rotor diameter & 80 m & Rated wind speed & 16 m/s \\ Hub height & 60 m & Max rotor speed & 16.2 rpm \\ Rated power & 2.3 MW & & \\ Cut-in wind speed & 4.5 m/s & Cut-out wind speed & 25 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Key wind turbine parameters. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Case I** & **Case II** \\ \hline Pitch angle & \(-4.75^{\circ}\) & \(-4.75^{\circ}\) \\ Rotor speed & 16.2 rpm & 16.2 rpm \\ Hub height wind speed & 9.792 m/s & 8.429 m/s \\ Shear exponent & 0.249 & 0.262 \\ Air density & 1.22 kg/m\({}^{3}\) & 1.22 kg/m\({}^{3}\) \\ Yaw angle & \(-6.02^{\circ}\) & \(-38.34^{\circ}\) \\ Ambient pressure & 1005 Pa & 1020 Pa \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of Case I and Case II. Figure 3: Configuration of a wind turbine under wind shear and yaw. rotor radius and inflow wind speed of 0.002 was used. A resolution of 30 cells per rotor radius was used in the rotor plane and 18 cells per rotor radius were uniformly distributed from 1D (rotor diameter) in front of the turbine to 11D behind the turbine in order to have a good resolution in the wake region. The airfoil data used in the computations were 2-dimensional airfoil data provided from the International Energy Agency (IEA) Task 29 consortium. To take into account the dynamic stall effects, the \(\O\)ye dynamic stall model [34] was used as this is a part of FLEX5. The boundary condition used in the computations is that at the inlet (min z), spanwise boundary (x direction) and up-boundary (max y), a sheared wind velocity profile is used, at the ground (y = 0) no-slip condition is used, and at the outlet (max z) the convective boundary condition is used. In this study, no synthetic inflow turbulence is used. Figures 4 and 5 illustrate the comparisons between the measured data and simulation results. The simulation results were extracted from a cycle after the flow was stabilized. The forces normal and tangential to the local airfoil chord at 33%, 48%, 76% and 92% rotor radius noted as Fn33, Ft33, Fn48, Ft48, Fn76, Ft76, Fn92, Ft92, respectively, are shown below:  
Figure 4: _Cont_. Figure 4: Forces normal and tangential to the local chord at 33%, 48%, 76% and 92% rotor radius for Case I (**a**) Fn33; (**b**) Ft33; (**c**) Fn48; (**d**) Ft48; (**e**) Fn76; (**f**) Ft76; (**g**) Fn92; (**h**) Ft92. Figure 5: _Cont._  
As observed, the magnitudes between the measurements and simulations are similar for most of the quantities. In Case I, the computed normal force does not follow with the measured one and this is probably due to the \(\mathcal{O}\)ye dynamic stall model used in the computations, which does not perform well at small angles of attack.