## 4 Results and Discussion
### Laminar Separation-Induced Transition
#### 4.2.1 Laminar Separation-Induced Transition
**} & \multicolumn{2}{c}{**\% Error**} \\ \cline{2-7}  & \multicolumn{2}{c}{**Standard \(k\)-\(\epsilon\)**} & \multicolumn{1}{c}{**Transition Model**} & \multicolumn{1}{c}{**Maxed Laminar/ Turbulent**} & \multicolumn{1}{c}{**Standard \(k\)-\(\epsilon\)**} & \multicolumn{1}{c}{**Transition Model**} & \multicolumn{1}{c}{**Maxed Laminar/ Turbulent**} \\ \hline
0\({}^{\circ}\) & 0.07822 & 0.1495 & 0.1558 & 0.1469 & \(-\)46.8 & 1.8 & 6 \\
1.02\({}^{\circ}\) & 0.13455 & 0.2718 & 0.2755 & 0.2716 & \(-\)50.5 & 0.1 & 1 \\
5.13\({}^{\circ}\) & 0.5898 & 0.7595 & 0.7542 & 0.7609 & \(-\)22.5 & \(-\)0.2 & \(-\)1 \\
9.22\({}^{\circ}\) & 1.1069 & 1.1144 & 1 TO in this study is defined as the location where the TI just starts to increase after the separation. Using this definition, it can be observed that at the AoA of 0\({}^{\circ}\), a TI of 0.03% at the far-field condition suddenly increases on the pressure and suction airfoil surfaces at the TO points of X/C = 0.476 and 0.526. This is observed to occur after the LS points at X/C = 0.455 and 0.50, and after the TR points at X/C = 0.523 and 0.518 reach maximum values of 0.83% and 0.75% at X/C = 0.524 and 0.592, respectively (Figure 7a). Similarly, as the AoA is increased to 5.13\({}^{\circ}\), the TI starts to increase at the TO points of X/C = 0.495 and 0.508 after the LS points of X/C = 0.471 and 0.496, and after the TR points of X/C = 0.523 and 0.518 reach maximum values of 0.88% and 0.91% at X/C = 0.543 and 0.547 on the pressure and suction airfoil surfaces, respectively (Figure 7b). Hence, with increase in AOA the TO on the suction side moves closer to the leading edge and moves downstream on the pressure side since the separation occurs at a smaller and larger distance to the leading edge, respectively. The distribution of TI and the overlapped distribution of the velocity vector and TI at AoAs of 0\({}^{\circ}\), 5.13\({}^{\circ}\), and 14.4\({}^{\circ}\) and close-up views of the LSB on the S809 airfoil are shown in Figure 8. The points of LS, TR, TO, and SBL are also shown. The shift of the LS point closer to the leading edge and trailing edge on the suction and pressure surfaces by increasing AoA can be seen in Figure 8. The Figure 8 shows that at the AoA of 0\({}^{\circ}\), the separated shear layer reattaches on the upper (suction) surface around the mid-chord length and on the lower (pressure) surface just forward of the mid-chord length, resulting in the formation of different sizes of separation bubbles on each surface. This is primarily due to the increased adverse pressure along each surface gradient prior to the onset of turbulence, as stated earlier. As the AoA increases, the adverse pressure gradient on the suction surface increases near the leading edge of the airfoil, leading to earlier separation of the laminar boundary layer and consequently the increased turbulence level up to a maximum of 30%. From a close-up view at the AoA of 14.24\({}^{\circ}\), earlier TO and TR are triggered upstream. Therefore, the SBL on the suction surface decreases as the bubble moves upstream with increasing AoA. Figure 7: Comparison of x-direction skin friction coefficient (\(C_{f,x}\)) and turbulence intensity (TI) at the AoAs of 0\({}^{\circ}\) (a) and 5.13\({}^{\circ}\) (b) for both surfaces of the airfoil (pressure and suction sides).