# Aerodynamic Enhancement of Vertical-Axis Wind Turbines Using Plain and Serrated Gurney Flaps
## 2 Simulation Setup
### Isolated Airfoil
#### 2.1.3 Numerical Solver and Simulation Validation  
The flow field around the static airfoil is resolved at various AoAs ranging from 0\({}^{\circ}\) to 20\({}^{\circ}\) through a commercial software FLUENT 19.2, which solves the incompressible Reynolds-averaged Navier-Stoke equations using the finite-volume scheme. The unsteady solver is based on the coupled pressure-velocity scheme with the second-order upwind scheme for spatial discretization. Considering feasibility and accuracy, the improved delayed detached eddy simulation (IDDES) method is used for the flow over the blades with different flaps. [PERSON] and [PERSON] [33] improved the LES solution at the wall in the DES model and originated the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Total Cells (\(\times\)10\({}^{5}\))** & **y+** & **C\({}_{1}\)** & **Deviation-C\({}_{1}\) (\%)** & **C\({}_{d}\)** & **Deviation-C\({}_{d}\) (\%)** \\ \hline coarse & 8 & 1.2 & 0.66 & \(-\)2.3 & 0.032 & 2.6 \\ medium & 14 & 0.98 & 0.692 & \(-\)0.2 & 0.0311 & \(-\)0.3 \\ fine & 20 & 0.77 & 0.693 & - & 0.0312 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mesh-independence on an NACA0021 airfoil. Figure 3: Zoom view of the computational mesh of the NACA0021 with an SGF. IDDES method, which is widely applied in recent studies [34; 35; 36; 37]. IDDES allows the activation of RANS and LES in different flow regimes, which are suitable for solving complex turbulent flows with high precision [36]. The modified Menter's k-\(\omega\) shear-stress transport (SST) two-equation turbulence model is chosen for the RANS simulation due to its credible predictions of the aerodynamic forces and the flow separations under the adverse pressure gradients [38]. The computational machine involved with these simulations consists of 4 Intel Xeon-Gold 6230 processors @2.1 GHz with 80 cores. The transient formulation of a bounded second-order implicit scheme with a time step of \(\Delta\)t = 5.0 \(\times\) 10\({}^{-5}\) s is used, and several rounds of 20 iterations per time-step are employed to ensure the scaled residuals drop below 10\({}^{-5}\). The airfoil lift coefficient and drag coefficient are calculated by  
\[C_{l} =\frac{F_{L}}{0.5\rho u_{0}^{2}\mathrm{S}} \tag{1}\] \[C_{d} =\frac{F_{D}}{0.5\rho u_{0}^{2}\mathrm{S}} \tag{2}\]  
where \(F_{L}\) and \(F_{D}\) are the lift and drag forces, and \(S\) is the projected area of the airfoil, \(S=c\times L\). The lift and drag coefficients of the clean NACA0021 airfoil at \(\alpha=9^{\circ}\) are employed to assess the mesh-independence. Table 1 summarizes the computational results of lift and drag coefficients by three mesh densities. Compared to the results with the fine grid, a deviation of less than 1% is observed with a grid number of 1.4 million. Considering the balance of the simulation accuracy and computation cost, the medium mesh is selected to be comparable to the fine mesh. The isolated airfoil simulation method has been validated through a comparison with the available experimental measurements of the NACA0018 airfoil by [PERSON] and [PERSON] [39], as well as numerical predictions with the SST turbulence model [13]. Figure 4 compares the lift and drag coefficients with respect to AoAs. The present predictions are overall satisfactory. For moderate angles of attack (6\({}^{\circ}<\alpha<\) 13\({}^{\circ}\)), the predicted lift and drag distributions match with the measured data. Once the flow enters into a stall, the computation predicts a falling trend of lift and an abrupt rise in drag when \(\alpha\geq 13^{\circ}\). Similar unsatisfactory results were also reported by [PERSON] et al. [13] and [PERSON] et al. [40], suggesting that the limitation of the numerical scheme in predicting vortical turbulent flow separation is a common challenge. In comparison, the IDDES model demonstrates a more accurate prediction of the lift and drag coefficients compared to the SST k-\(\omega\) model. Thus, it is believed that IDDES is a reliable method to investigate the following simulations.