# Aerodynamic Enhancement of Vertical-Axis Wind Turbines Using Plain and Serrated Gurney Flaps
## 2 Simulation Setup
### The Vertical-Axis Wind Turbine
#### 2.2.3 Numerical Solver and Simulation Validation  
The fundamental solution schemes utilized are similar to those employed on the isolated airfoil, with the exception that only the shear stress transport (SST) k-\(\omega\) turbulence closure is used. It is regarded as reliable for accurately capturing the boundary layer (BL) and stall phenomena around rotating airfoils [42]. We follow the work by [PERSON] et al. [43] who obtained satisfactory predicting results.  
A constant freestream velocity of 9 m/s is set as an the inlet boundary condition [43]. An averaged zero-gauge pressure is set on the domain outlet. The airfoil surface is conditioned as a non-slip wall. The domain top and bottom are considered periodic ones. A steady-state solution is obtained to initiate the flow field for later unsteady flow simulations around the rotating blades. In the first 20 revolutions, the time step was equivalent to 0.5\({}^{\circ}\). In the last 2 revolutions, the time step was reduced to 0.2\({}^{\circ}\). The final stable data of the 22 nd revolution are used to calculate the aerodynamic performance. The fluctuation in the moment coefficient (\(C_{m}\)) between the last and previous rotation cycles is less than 1%, indicating a high consistency. The turbine power coefficient (\(C_{p}\)) is employed to evaluate the mesh quality.  
The definitions are the following:  
\[C_{p}=\frac{T\omega}{0.5\rho U_{\infty}^{3}A} \tag{4}\]  
\[C_{m}=\frac{T}{0.5\rho U_{\infty}^{2}A} \tag{5}\]  
where \(T\) is the torque generated from the rotor blades, \(\rho\) is the air density, and \(A\) is the rotor through-flow area of the rotor diameter multiplied by the blade height.  
Table 3 shows that similar results are generated by the medium and the fine meshes, but a relatively small value is obtained by the coarse mesh. Considering the low computation cost, we chose the medium mesh to calculate the primary VAWT performance and thus employed it in later analysis of the flow fields.  
Several well-known cases are used to validate the present computation ability. The measured turbine power coefficient (\(C_{p}\)) values by [PERSON] et al. [44] and the simulated \(C_{p}\) values by [PERSON] et al. [32], [PERSON] et al. [45], and [PERSON] et al. [46] are used to verify the present computation reliability. Figure 8 shows the comparison and elucidates our ability to predict correct aerodynamic parameters for the former simulation and experiment.  
Our prediction moderately overestimates the power coefficient of the experiment in all tested conditions, which is the same as the selected simulation results. However, the difference does not change the behavior of the \(C_{p}\) with the TSR variation. There is a slight difference among the simulation results, though compared with the experimental data, the maximum error of \(C_{p}\) is 38.4% at TSR = 3.3 and the minimum error is 8.3% at TSR = 2.35. The similar results are reported by [PERSON] [46]. This leads to the conclusion that our simulation configuration and grid distribution are reliable in predicting the aerodynamic performance and flow field of this rotor model.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Mesh Set** & **Number of Cells** & \(C_{p}\) & **Relative Change in \(C_{p}\) concerning the Fine Mesh** \\ \hline coarse & 2,156,466 & 0.388 & \(-2.5\%\) \\ medium & 5,181,680 & 0.399 & 0.25\% \\ fine & 6,995,051 & 0.398 & - \\ \hline \end{tabular}
\end{table}
Table 3: Sensitivity of grid size for the 1.5%c PGF VAWT at TSR = 2.62.