## 3 Numerical Simulation
### Analysis Conditions and Far-Field Boundary Condition  
The study was conducted using ANSYS FLUENT 19.4, which is a general-purpose commercial CFD code based on a cell-centered finite-volume method. There are several types of solver algorithms available in FLUENT, including coupled explicit, coupled implicit and segregated solvers. For the computations presented in this paper, we selected the segregated solver to speed up the convergence. The pressure-velocity coupling was obtained through the SIMPLE algorithm, and a green-gauss cell-based scheme was used for the gradient spatial discretization. Second-order upwind schemes were employed for pressure, momentum, and turbulence equations. The steady state computation was performed for approximately 20,000 iterations where the convergence tolerance for all relevant variables was less than 0.001% and changed from a default value of 0.1% due to the experimental data with five decimal places. Note that the results were taken using the average of the last 2000 datapoints acquired at each iteration step due to the oscillation problem for each variable occurring in the convergence history. However, the occurrence of the oscillation phenomenon, which means unsteady physical flow characteristics, is general and natural in the wall-bounded transitional flows with separation bubbles when the convergence criterion becomes very low. Therefore, averaging the last data is a reasonable method to accurately predict aerodynamic coefficients.  
Figure 4: Close-up view of the mesh in the vicinity of the airfoil.  
Figure 3: C-type grid topology used in this study, showing the overall grid resolution and boundary conditions.  
The analysis was carried out at a low Reynolds number of \(2.0\times 10^{6}\) for the angles of \(0^{\circ}\), \(1.02^{\circ}\), \(5.13^{\circ}\), \(6.04^{\circ}\), \(8.04^{\circ}\), \(9.22^{\circ}\), \(14.24^{\circ}\), and \(20.15^{\circ}\). The Reynolds number corresponds to Mach number of 0.04797 converted to velocity of 16.31 m/s. A TI of 0.03% was applied from the experimental results as the turbulence level in the test section of NREL wind tunnel varied from 0.02% at 10 m/s to 0.04% at 60 m/s [26]. The free-stream turbulent kinetic energy and the specific dissipation rate of turbulent energy were \(3.59\times 10^{-5}\) m\({}^{2}\)/s\({}^{2}\) and 0.44 1/s, respectively. This is based on TI of 0.03% and density (\(\rho\)) of 1.226 kg/m\({}^{3}\) using Equations (21) and (22), where \(C_{\mu}\) is an empirical constant specified in the turbulence model and \(\frac{\mu_{t}}{\mu}\) is the turbulent viscosity ratio.  
\[k\ =\ \frac{3}{2}\cdot(U\cdot I)^{2} \tag{21}\]  
\[\varepsilon\ =\ \rho\cdot C_{\mu}\cdot\frac{k^{2}}{\mu}\left(\frac{\mu_{t}}{ \mu}\right)^{-1} \tag{22}\]  
A pressure far-field condition for all the boundaries except for the airfoil was used to model a free-stream condition at infinity, with a free-stream Mach number. The pressure far-field boundary condition is often called a characteristic boundary condition, since it uses characteristic information to determine the flow variables at the boundaries. This boundary condition is applicable only when the density is calculated using ideal-gas law.