## 3 Results and Discussion
### Effects of Airfoil on Fan Performance  
#### 3.1.1 Lift-to-Drag Ratios of Different Airfoils  
The selected models are BE10307B (A airfoil), NACA0012 (B airfoil), NACA2412 (C airfoil), and NACA4412 (D airfoil), which are used to design the airfoil of centrifugal fan blades. The shapes of the airfoil and grid distribution are shown in Figures 9 and 10, respectively. The chord length of the airfoil used in the calculation is the chord length of the single-arc blade, and the value is 17 mm. The velocity of the impact airfoil is V = 50.0 m/s, Re = 2.0 \(\times\) 105. The calculation conditions are the same for all airfoils. The boundary conditions of the airfoil are set as follows: the semicircular arc and the upper and lower regions of the computational domain are given velocity boundaries and the outlet pressure is given at the exit position. Turbulence intensity is calculated according to Equation (1), and the value is 3.6%. The turbulence model is Realizable k-\(\varepsilon\), and the solution algorithm adopts the Coupled Algorithm. The values for the constants in SST k-\(\omega\) turbulence model are typically taken as follows: \(\beta^{*}=0.09\); \(\beta=0.075\); \(\sigma_{k}=0.5\); \(\sigma_{\omega}=0.5\); \(a_{1}=0.31\); \(\sigma_{k1}=1.0\); \(\sigma_{k2}=1.0\); \(\sigma_{\omega 1}=0.5\); and \(\sigma_{\omega 2}=0.865\). The residual convergence value is set to \(1\times 10^{-6}\), the lift coefficient and drag coefficient are tested, and the relaxation factor adopts the default value of the simulation software. \[I=0.16\cdot Re^{-0.125} \tag{1}\]  
The grid numbers for the numerical calculation of the two-dimensional airfoil are shown in Table 3. The lift coefficient \(\rm C_{L}\) and drag coefficient \(\rm C_{D}\) at the angle of attack of \(5^{\circ}\) are taken as the independent verification data. The maximum difference of \(\rm C_{L}\) is 0.26%, and the maximum difference of \(\rm C_{D}\) is 0.032%. The errors of the three grids are all very small, which well verifies the grid independence. In order to save computation time and minimize computational errors, Grid 2 was utilized for numerical calculations. Figure 10: Meshing of A airfoils. \begin{table}
\begin{tabular}{c c c c} \hline  & **Total Elements** & \(\rm C_{L}\) & \(\rm C_{D}\) \\ \hline Grid 1 & \(2.9\times 10^{6}\) & \(7.51\times 10^{-1}\) & \(3.23\times 10^{-2}\) \\ \hline Grid 2 & \(4.7\times 10^{6}\) & \(7.52\times 10^{-1}\) & \(3.25\times 10^{-2}\) \\ \hline Grid 3 & \(6.8\times 10^{6}\) & \(7.50\times 10^{-1}\) & \(3.23\times 10^{-2}\Four types of airfoils, A, B, C, and D, shown in Figure 9, are used in fans to study the effects of airfoils on fan performance by numerical simulation. The numerical calculation entails the lift-to-drag coefficients of the four airfoils under the attack angle of 0-10\({}^{\circ}\). The calculated data of the lift-to-drag ratio coefficients of these four airfoils are shown in Figure 11. Within the range of angle of attack from 0\({}^{\circ}\) to 10\({}^{\circ}\), the lift-to-drag ratio of the four types of airfoils first increased and then decreased. The A and D airfoils have a maximum lift-to-drag ratio of 3\({}^{\circ}\), while B and C are at 2\({}^{\circ}\). Overall, the four airfoils are sorted by a lift-to-drag ratio in descending order as follows: A, D, C, and B. The static pressure diagrams of the four airfoils (as shown in Figure 12) indicate that the pressure gradients on the upper surfaces of the four airfoils change gently. The low-pressure area on the upper surface of the A airfoil is larger, followed by the D, C, and B airfoils. Therefore, the lift-to-drag ratio of the A airfoil is larger than that of the other airfoils, which is consistent with the trend in Figure 11. In addition, the B, C, and D airfoils all have a small range of high-pressure areas at the leading edge, and the pressure gradient is large. From the streamline diagram of the four airfoils shown in Figure 13, under the attack angle of 5\({}^{\circ}\), there is no flow separation such as vortices for the four airfoils.