## 2 Materials and Methods
### CFD Simulation
#### 2.4.6 Sensitivity Analysis  
Assumptions for the numerical analysis such as the angular increment of the rotor angle and the size of the computational domain were made on the basis of reference studies for similar but not identical vertical-axis wind turbines. Therefore, to further confirm the assumptions made, sensitivity analyses were performed considering the specific geometry of the carousel rotor analyzed in this study. The effect of angular increment of the rotor angle was examined for the cases presented in Table 5. In turn, the effects of the main dimensions of the computational domain were checked concerning the cases summarized in Table 6.  
The results of the sensitivity analysis of the rotor angular increment are shown in Figure 8. Figure 8a presents the moment coefficient for a single blade, whereas Figure 8b show the average turbine power for various values of the rotor angle angular increment. It can be noted that for values \(d\alpha=0.2^{\circ}\) and \(d\alpha=0.5^{\circ}\), a convergent solution is obtained. Therefore, the adopted value of \(d\alpha=0.5^{\circ}\) is considered to be correct. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameter** & _di_ & _do_ & \(W\) & _(D/W)_ & _dc_ & **Domain Size (L \(\times\) W)** & _d\(\alpha\)_ \\ \hline Distance to inlet (_di_) & 2.5 & 15 & 20 & 5\% & 1.5 & 17.5 \(\times\) 20 & d\(\alpha\) = 0.5\({}^{\circ}\) \\  & 5 & & & & & 20 \(\times\) 20 & \\  & 10 & & & & 25 \(\times\) 20 & \\ \hline Distance to outlet (_do_) & 5 & 5 & 20 & 5\% & 1.5 & 10 \(\times\) 20 & d\(\alpha\) = 0.5\({}^{\circ}\) \\  & & 10 & & & & 15 \(\times\) 20 & \\  & & 15 & & & & 20 \(\times\) 20 & \\ \hline Domain width (_W_) & 5 & 15 & 5 & 20\% & 1.5 & 20 \(\times\) 5 & d\(\alpha\) = 0.5\({}^{\circ}\) \\  & & & 10 & 10\% & & 20 \(\times\) 10 & \\  & & & 20 & 5\% & & 20 \(\times\) 20 & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Cases for sensitivity analysis of computational domain dimensions _di_, _do_, and \(W\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline _d\(\alpha\)_ & _dt_ & _y+\_ave_ & _y+\_max_ & _Co\_BW_ & _Co\_BD_ & _Co\_RD_ & _Co\_FD_ \\ \hline
0.5\({}^{\circ}\) & 1.93925 \(\times\) 10\({}^{-3}\) & 0.107 & 0.46 & 0.59 & 5.82 & 15.37 & 0.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Resulted _y+_ and Courant number for rotor angle of 200\({}^{\circ}\). \begin{table} \begin{tabular}{c c c c c c c c} \hline \hline
**Parameter** & _da_ & _dt_ & _di_ & _do_ & \(W\) & _D/W_ & **Domain Size (L \(\times\) W)** \\ \hline Angular increment & 0.2\({}^{\circ}\) & 7.75702 \(\times\) 10\({}^{-4}\) & 10\(D\)\({}^{*}\) & 15\(D\) & 20\(D\) & 5\% & 25\(D\)\(\times\) 20\(D\) \\ \hline \hline \end{tabular} 
\begin{tabular}{c c c c c c c} Angular & 0.5\({}^{\circ}\) & 1.93925 \(\times\) 10\({}^{-3}\) & & & & & \\ increment & 1\({}^{\circ}\) & 3.87851\(\times\) 10\({}^{-3}\) & & & & & \\  & 2\({}^{\circ}\) & 7.75702 \(\times\) 10\({}^{-3}\) & & & & & \\  & 5\({}^{\circ}\) & 1.93925 \(\times\) 10\({}^{-3}\) & & & & & \\  & 10\({}^{\circ}\) & 3.87851\(\times\) 10\({}^{-3}\) & & & & & \\ \hlineThe results of the sensitivity analysis of the computational domain dimensions, such as the distance to inlet di and distance to outlet do, are presented in Figure 9a,b. Figure 9a presents the moment coefficient for three different values of the distance to inlet \(di\). It can be noticed that the value of \(di=2.5D\) was too small and affected the moment coefficient, whereas \(di=5D\) and \(di=10D\) revealed negligible differences. Therefore, the adopted value of \(di=10D\) was considered acceptable. Figure 9b presents the moment coefficient for three different values of the distance to the outlet \(do\). The obtained values almost coincided for each of the analyzed cases. Some minor discrepancies were observed for \(di=5D\) in the angle ranges of \(220^{\circ}\)-\(240^{\circ}\), \(260^{\circ}\)-\(270^{\circ}\), and \(290^{\circ}\)-\(295^{\circ}\).