# Performance Characteristics of an Orthopter-Type Vertical Axis Wind Turbine in Shear Flows
## 3 Numerical Approach
### Numerical Setup
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Flow** \\ **Type** \\ \end{tabular} } & \multirow{2}{*}{\(\Gamma\)} & \multirow{2}{*}{\(\Phi\)} & \multicolumn{2}{c}{**Range of**} & \multicolumn{2}{c}{**Velocity**} & \multicolumn{2}{c}{**Range of**} \\  & & & \(U_{H}\) & \(U_{H}\) & **Distribution in** & **Transition Region** & \(U_{L}\) & \(U_{L}\) \\  & & & [**m/s**] & **Region** & **Transition** & **[m]** & **[m]** & **[m/s]** & **Region** \\ \hline Uniform & 0 & - & 8 & 8 & & 8 & \\ ASF-SF & 0.51 & 0.67 & 13.2 & \(y\leq-0.24\) & \(U_{H}\cdot(y/0.24)^{0.3}\) & \(-0.24\leq y\leq-0.01\) & 4.3 & \(y\geq-0.01\) \\ ASF-SF & 0.40 & 0.60 & 12.1 & \(y\leq-0.22\) & \(U_{H}\cdot(y/0.22)^{0.35}\) & \(-0.22\leq y\leq 0.02\) & 5.2 & \(y\geq-0.02\) \\ ASF-SF & 0.28 & 0.49 & 10.8 & \(y\leq-0.18\) & \(U_{H}\cdot(y/0.18)^{0.2}\) & \(-0.18\leq y\leq-0.01\) & 6.1 & \(y\geq-0.01\) \\ RSF-SF & 0.51 & 0.67 & 13.2 & \(y\geq 0.24\) & \(U_{H}\cdot(y/0.24)^{0.3}\) & \(0.01\leq y\leq 0.24\) & 4.3 & \(y\leq 0.01\) \\ RSF-SF & 0.40 & 0.60 & 12.1 & \(y\geq 0.22\) & \(U_{H}\cdot(y/0.24)^{0.35}\) & \(0.02\leq y\leq 0.22\) & 5.2 & \(y\leq 0.02\) \\ RSF-SF & 0.28 & 0.49 & 10.8 & \(y\geq 0.18\) & \(U_{H}\cdot(y/0.24)^{0.2}\) & \(0.01\leq y\leq 0.18\) & 6.1 & \(y\leq 0.01\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Distribution of \(u\) at the inlet boundary. Here, \(\Gamma\) is the velocity ratio; \(\Phi\) is the shielding ratio of a perforated panel; \(U_{H}\) and \(U_{L}\) are the maximum and minimum velocities in a shear flow. The separated shear flow from a building with an aspect ratio of 1:1:2 reaches an amplification factor of 1.2 [35]. In addition, the separated shear flow from a building with an aspect ratio of 1:1:6 reaches an amplification factor of 1.7 [36]. At \(x=0\), the values of \(\Gamma\) do no change, as shown in Figure 6c,d. However, due to the momentum diffusion, the horizontal gradients of the time-mean streamwise velocity become weaker. One of the reasons for the relatively large discrepancies between the profiles obtained by the experiment and the CFDs can be that the turbulence intensities of the CFDs are significantly small compared to those of the experiments, as shown in Figure 7. Even though very high values of turbulence intensity were set at the inlet boundary, the turbulence intensities dissipated rapidly and became very small at \(x=0\) as compared to those of the experiments. As the setting of high turbulence intensity at the inlet boundary leads to computational instability, we set no perturbation condition at the inlet boundary. Table 4 shows the values of \(U_{0}\) computed by Equation (8) and the Reynolds number which is defined as:  
\[Re=\frac{U_{0}D}{\
u} \tag{18}\]  
At the outlet boundary, the pressure outlet condition with \(p=0\) was imposed. On the surface of the O-VAWT and the splitter plate, the no-slip boundary conditions were set. The sliding mesh technique was used to couple the rotational domains and the stationary domain. The direction of the rotor and the blade rotations are counterclockwise and clockwise, respectively, when viewed from the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Flow Type**} & \multirow{2}{*}{\(\Gamma\)} & \multicolumn{2}{c}{\(\mathbf{U_{0}}\) **[m/s]**} & \multicolumn{2}{c}{\(\mathbf{Re}\)} \\ \cline{3-6}  & & **Experiment** & **CFD** & **Experiment** & **CFD** \\ \hline Uniform & 0 & 8 & 8 & \(2.79\times 10^{5}\) & \(2.79\times 10^{5}\) \\ ASF-SF & 0.51 & 10.08 & 9.78 & \(3.52\times 10^{5}\) & \(3.41\times 10^{5}\) \\ ASF-SF & 0.40 & 9.38 & 9.22 & \(3.28\times 10^{5}\) & \(3.22\times 10^{5}\) \\ ASF-SF & 0.28 & 8.73 & 8.72 & \(3.05\times 10^{5}\) & \(3.05\times 10^{5}\) \\ RSF-SF & 0.51 & 7.76 & 7.48 & \(2.71\times 10^{5}\) & \(2.61\times 10^{5}\) \\ RSF-SF & 0.40 & 7.72 & 7.36 & \(2.70\times 10^{5}\) & \(2.57\times 10^{5}\) \\ RSF-SF & 0.28 & 7.52 & 7.33 & \(2.62\times 10^{5}\) & \(2.56\times 10^{5}\) \\ \hline \hline \end{tabular}
\end{table}