## 4 Results and Discussion
### Laminar Separation-Induced Transition
#### 4.2.2 Effects of the Separation Bubble  
The LS, TR, and TO points on the suction airfoil surface for each AoA are plotted in Figure 9. The TR points overall show a very good agreement with the experiments between AoAs of 0\({}^{\circ}\) and 15\({}^{\circ}\), except those between 6.03\({}^{\circ}\) and 8.04\({}^{\circ}\), between which a sudden jump of the separation point to the upstream occurred because the transition model approaches could represent regions at which the LSB changed. The simulations showed that the transition model was not able to detect the unsteady characteristics of the flow for AoAs between 6.03\({}^{\circ}\) to 8.04\({}^{\circ}\), which will be further studied in future using large eddy simulation. It must also be noted that the TO points indicating the turbulence onset could not be compared to the experiment by [PERSON] et al. and [PERSON] as it was not reported in [26]. According to Figure 9, as the AoA increases from 0\({}^{\circ}\) to 5.13\({}^{\circ}\), the transition location moves from 0.523 to 0.504 X/C, which shows that the minor effect of small AoAs on the transition location of the suction side. At the AoA of 9.22\({}^{\circ}\), which is smaller than the 2D stall angle of 16\({}^{\circ}\), the separation bubble on the upper surface jumps to the leading edge of the airfoil [32]. When the AoA is greater than 9.22\({}^{\circ}\), the transition always occurs at the leading edge. Figure 8: Distribution of TI and overlapped distributions of velocity vector and TI at selected AoAs of 0\({}^{\circ}\) (**a**), 5.13\({}^{\circ}\) (**b**), and 14.24\({}^{\circ}\) (**c**) (left panels) and close-up views of the LSB on the S809 airfoil (right panels). The points of laminar separation (LS) followed by turbulent reattachment (TR), the transition onset (TO) between them, and SBL are also marked for the pressure and suction surfaces of the airfoil. The LS, TR, and TO points on the pressure side of the airfoil for each AoA are plotted in Figure 10. The TR points show a good agreement with the experiments, except for small deviations at higher AoAs. With increasing AoA from 0\({}^{\circ}\) to 20.15\({}^{\circ}\), the TO point moves downstream from 0.476 to 0.591 X/C without abrupt jumps along the surface. This shows that increasing the AoA gives rise delays separation on the pressure side with the weak adverse pressure gradient. The SBL on the suction airfoil surface and the airfoil lift-to-drag ratio (C\({}_{l}\)/C\({}_{d}\)) are presented in Figure 11. As the AoA increases, the extent of the LSB decreases from 5.74% of the chord length at 0\({}^{\circ}\) to 0.841% the chord length at 20.15\({}^{\circ}\), except for a little increase to 5.86% the chord length at 1.02\({}^{\circ}\). The change in the size occurs primarily because of upstream movement of the TR point due to a  
Figure 10: Movement of LS, TR, and TO points on the pressure airfoil surface with increasing AoA. The blue squares represent experimental data points. Figure 9: Movement of LS, TR, and TO points on the suction airfoil surface with increasing AoA. The red squares represent experimental data points. strong adverse pressure gradient in the separated shear layer. According to [PERSON] and [PERSON] [31], a separation bubble with a size of less than a maximum of 5.86% the chord length can be classified as a short separation bubble. The simulation results also show that the lift-to-drag ratios obtained by using the transition model are 104.1 and 118.4 at the AoAs of 5.13\({}^{\circ}\) and 6.03\({}^{\circ}\), respectively, when the corresponding bubble sizes are 2.24% and 2.11% of the chord length, whereas the C\({}_{\rm{I}}\)/C\({}_{\rm{d}}\) value obtained by using the standard \(k\)-\(\varepsilon\) model (Tables 2 and 3) is 17.2 at the AoA of 5.13\({}^{\circ}\). A maximum C\({}_{\rm{I}}\)/C\({}_{\rm{d}}\) ratio at a designed AoA is an important factor in accurately predicting and maximizing the power of wind turbine blade, based on the BEM theory [7].