## 3 Results and Discussion  
### Flow Characteristics over an Axial Fan  
The flow characteristics over the fan must be understood because the aerodynamic noise was generated by an unsteady flow. Figure 6 shows the iso-surface of the instantaneous vorticity magnitude of \(-2.81\times 10^{2}\) at T* = 9.2. The fan blades generated a wide range of vorticities over the blades after a laminar separation of the bubbles on the surface of each blade consisting of slender airfoils from the root at tip. The presence of the vortices affected the resulting aerodynamic performance and noise. In general, the existence of the separation bubble on an airfoil is considered undesirable because it can have negative effects on the performance owing to the local alteration of the surface pressure distribution and lead to main flow unsteadiness if the bubble bursts [29; 30]. Figure 7 shows the instantaneous pressure contours on the fan's surface and the streamlines and velocity vectors in the X-Z plane at \(Z=0\) (T* = 9.2). Here, X, Y, Z, and D represent each direction of the X, Y, Z coordinates and the fan diameter, respectively, as indicated in the right lower end of Figure 7. The axial flow was more dominant at some locations of Z/D = 0.638 and 0.368 far away from the hub's front side when the fan was rotating. However, at Z/D = 0.114 in the upstream, the radial flow near the ring rapidly flowed into the passages between the blades due to the low pressure of strongly pushing air into the downstream and allowed some dead zones around the ring to be formed, including the wake just after the hub. A comparatively higher pressure on the pressure side of the blade was generated, and the pressure difference caused a flow through the fan. The simulation results for the velocities in the upstream and downstream were validated with experiments (Figures 8 and 9). The flow increased more from Z/D = 0.638 to Z/D = 0.114 due to the increased pressure difference with the ambient pressure. The velocity at Z/D = 0.638 was approximately 1.2 m/s and increased to approximately 7.5 m/s at Z/D = 0.114. The velocity distribution at Z/D = 0.114 calculated from the LES in the upstream showed a comparatively good agreement with the experiments, except 0.75 and 0.92 of dimensionless radius, where the simulation results were slightly overpredicted due to the misalignment of measurement locations between the simulation and the experiment. As previously stated, the high velocities between 0.75 and 0.92 of dimensionless radius were confirmed due to the increase in the radial velocity (Figure 7). Similarly, the velocity distribution in the simulation in the downstream was overall overpredicted; however, it maintained a similar shape  
Figure 6: Iso-Surface of instantaneous vorticity magnitude at T* = 9.2.  
with the experiments. Compared to the upstream, the velocities at the same location between 0.75 and 0.92 of dimensionless radius were decreased due to the influence of the dead zone. Figure 8: Velocity distributions at each section at y = 0 section in the upstream and comparison with experiments. Figure 7: Instantaneous pressure contours on the fan’s surface, and streamlines and velocity vectors in X–Z plane at Z = 0 m (T* = 9.2). The pressure contours at the y = 0 section at different dimensionless times of T\({}^{*}\) = 13.16, 13.19, 13.22, and 13.25 based on one cycle of T\({}^{*}\) = 1 were illustrated by the pressure side of the fan's blades and the wake region (Figure 10). Here, dimensionless time is defined as the ratio of the simulation time to the period corresponding to rotational speed of 2100 rpm. The pressure variations occurred between \(-\)365 Pa and 234 Pa, with a period of approximately 0.004082 s at the first BPF of 245 Hz. The instantaneous pressure contours indicated that a very small pressure pulsation caused by the vortices over the blades was present near the blades when the fan was rotating. A similar phenomenon was observed by [PERSON] et al.