# Aerodynamic Enhancement of Vertical-Axis Wind Turbines Using Plain and Serrated Gurney Flaps
## 3 Results and Discussion  
### Effect of GFs on an NACA0021 Isolated Aerofoil  
#### 3.1.1 Aerodynamic Forces and Separation Control  
The flap effects on the aerodynamic force coefficients of the NACA0021 airfoil are depicted in Figure 9. The letters P and S represent PGF and SGF, respectively, followed by numbers indicating different flap heights. For instance, P-3 represents PGF with a flap height of 3%. Figure 8: Comparison between simulation values of the power coefficient with experimental results and literature [32; 44; 45; 46]. Figure 9: GFs effects on the NACA0021 airfoil aerodynamic performance with respect to the AoAs. (**a**) Lift coefficient versus angle of attack; (**b**) drag coefficient versus angle of attack; (**c**) lift-to-drag ratio versus angle of attack. In Figure 9a for lift force, flapped airfoils have an increased lift coefficient (\(C_{l}\)) nearly proportional to the flap height. In the case of a 6% chord flap, the PGF airfoil has increased the maximum lift by 89.19% over the baseline, while the SGF airfoil has an increase of 65.6%. For the same flap height, PGF shows better lift than the serrated flap. It is observed that the S-3 airfoil has an equivalent lift to the P-1.5 airfoil. It verifies the assumption that the lift increment is proportional to the effective flap area. It is thus concluded that flap serration is not important for lift enhancement. A notable finding in Figure 9a is that SGF retains the flap's function of increasing the effective airfoil camber, resulting in positive lift at a zero angle of attack, which has been reported for the symmetric NACA0012 airfoil by [PERSON] [6] and the cambered NACA4412 airfoil by [PERSON] et al. [47]. Figure 9b compares the drag coefficients of different flapped airfoils. Drag increases with the raised flap height as the lift does. Related to the lift, the stalling limit is reduced from 14\({}^{\circ}\) to approximately 11\({}^{\circ}\). A flapped airfoil works like a camber one. Due to the penalty of the drag, flapped airfoils normally have higher drag coefficients than the baseline, although the increase is not obvious before \(\alpha=11^{\circ}\). GF is believed to improve the lift-to-drag ratio (\(C_{l}\)/\(C_{d}\)) of airfoil, compared with the PGF. However, the \(C_{l}\)/\(C_{d}\) of the PGF airfoil is higher than that of the SGF airfoil when the flap height is under 6%c. At \(\alpha>14^{\circ}\), the flaps have a negative effect on \(C_{l}\)/\(C_{d}\). When the flap height \(H=6\%c\), the \(C_{l}\)/\(C_{d}\) of SGF is better than PGF under \(\alpha>3^{\circ}\), which indicates that an SGF device with a large flap size has the potential to improve the airfoil's aerodynamic performance. The flap element affects the flow behavior on the airfoil surface. Figure 10 shows the surface distributions of pressure and skin friction coefficients. The flow separation zone is depicted by the negative skin friction and abrupt pressure slope on the airfoil suction (upper) surface. At the separation point, the skin friction coefficient is nearly zero, which can be calculated using the subsequent equation:  
\[C_{f}=\frac{\tau_{W}}{0.5\rho v^{2}} \tag{6}\]  
where \(\tau_{W}\) is the wall shear stress, \(\rho\) and \(v\) are the density and velocity. The distribution of the surface pressure coefficient of the airfoil provides insights into the physical mechanism responsible for the observed lift enhancement by adding flaps. For clarity, three flapped airfoils are compared with the baseline at \(\alpha=6^{\circ}\) in Figure 10.  
Figure 10a presents the surface distribution of the friction coefficient for various flap heights at \(\alpha=6^{\circ}\). The \(C_{f}\) juncture of zero friction on the suction surface indicates the location of laminar separation. Decreased \(C_{f}\) for a short distance followed by a sudden raise-up indicates the exact laminar-to-turbulent flow transition [43]. The turbulent boundary layer captures extra momentum from the mainstream flow.