## 5 Conclusions  
Numerical simulations using the \(\gamma\)-\(Re_{\theta}\) transition model coupled with SST \(k\)-\(\omega\) transport equations around the 21% thick NREL S809 airfoil were performed to achieve a better understanding of the characteristics and effects of LSBs existing at a low Reynolds number and low TI. The computational  
Figure 11: Extent of the separation bubble on the suction airfoil surface as a percentage of the chord length (line with empty circles) and effects on the airfoil lift-to-drag ratio (line with empty squares). The solid line with green squares represents experimental data points. domain had a C-type grid topology with a pressure far-field condition, and the analysis was carried out under various AoAs. The reliability and validity of the simulations were verified using published results of experiments. The transition model case showed very good agreement with the experimental case in terms of aerodynamic lift and drag coefficients, and characteristics of LSBs owing to the higher predictive accuracy relative to the standard \(k\)-\(\varepsilon\) model case. These comparisons provide sufficient evidence that the predictions of the LSB are accurate, as evidenced by the fact that the aerodynamic characteristics of the airfoil are closely related to the characteristics of the LSB. Consequently, the transition model-based approaches, which have a high predictive accuracy, presented herein can elucidate the characteristics and effects of the LSB on airfoil aerodynamic performance. Important findings arising from this research are as follows:  
The transition ramp, which is defined as the region over which the LSB moves with increasing AoA, was clearly observed on the suction airfoil surface. It was confirmed that the TO point on the suction side of the S809 airfoil moved upstream due to an earlier LS caused by increased adverse pressure gradients as the AoA increased. Therefore, the accurate predictions of the pressure coefficients along the airfoil using the transition model offered the necessary validation for the subsequent LSB analysis. At the AoA of 0\({}^{\circ}\), the location of the LSB on the pressure and suction airfoil surfaces was observed to be generated at X/C = 0.455 and 0.50 and to be reattached at X/C = 0.499 and 0.557, causing SBLs of 4.44% and 5.74% the chord length, respectively, between LS and TR. Furthermore, when the AoA increased to 5.13\({}^{\circ}\), the location of the LSB moved to X/C = 0.471 downstream and to X/C = 0.496 upstream, resulting in an SBL that is taller by 0.73% the chord length and shorter by 3.5% the cord length for the pressure and suction airfoil surfaces, respectively. Therefore, the suction surface prediction featured a slightly earlier LS compared to the pressure surface. It was observed that the TI increased suddenly on the pressure and suction airfoil surfaces at the TO points of X/C = 0.476 and 0.526 after the LS points at X/C = 0.455 and 0.50, respectively, at the AoA of 0\({}^{\circ}\). At the AoA of 5.13\({}^{\circ}\), this increase occurred at X/C = 0.495 and 0.508 after the LS points of X/C = 0.471 and 0.496, respectively, which caused the production of turbulent kinetic energy in the separated laminar shear layer. Moreover, at the AoA of 0\({}^{\circ}\), the TI reached maximum values of 0.83% and 0.75% at X/C = 0.524 and 0.592 after the TR points of X/C = 0.523 and 0.518, respectively. At the AoA of 5.13\({}^{\circ}\), the TI reached maximum values of 0.88% and 0.91% at X/C = 0.543 and 0.547 after the TR points of X/C = 0.523 and 0.518, respectively. Therefore, the simulation results demonstrated a sharp increase in turbulence levels during the transition process, immediately after the LS, and a maximum TI value after the TR. The separation bubble on the suction surface jumped to leading edge of the airfoil at the AoA of 9.22\({}^{\circ}\), whereas on the pressure surface, it moved downstream. In addition, the maximum SBL was 5.86% the chord length at the AoA of 1.02\({}^{\circ}\).