## 3 Results and Discussion
### Aerodynamic Noise Characteristics  
The fast Fourier transform (FFT) data were compared between the experiments and the simulations at the locations of 0.5 m and 1.0 m and \(\theta\) = 90\({}^{\circ}\) in the downstream direction from the fan (Figure 11). The expression of \(2\times\log_{10}\left(\frac{P_{rms}}{P_{ref}}\right)\) was used to compute the SPL, where \(P_{rms}\) and \(P_{ref}\) denote the root mean square of the sound pressure and the reference of the sound pressure (20 \(\times 10^{5}\) Pa), respectively. The FFT analysis was performed on the temporal signals obtained with 2004 samples during 8.87 revolutions in the simulations, which induced spectral resolutions of 4 Hz, compared with 1 Hz in the experiments. To obtain a frequency resolution in the simulations that is equivalent to that in the experiments requires four times more computational time than the approximately 168 h required for 13 revolutions. Thus, the difference in the resolution can affect the determination of the absolute noise level in each BPF. The experimental result at the location of 0.5 m showed that the highest SPL of 57.8 dB was observed at a 245 Hz frequency corresponding to the first BPF and its first and second harmonics of 53.8 dB and 47.9 dB at doubled and tripled frequencies of 490 Hz and 735 Hz, which corresponded to the 2 nd and 3 rd BPFs, respectively. Similarly, the location of 1.0 m also showed the highest SPL of 51.1 dB at the same frequency corresponding to the first BPF and its first and second harmonics of 46.9 dB and 40.4 dB at the doubled and tripled frequencies of 490 Hz and 735 Hz corresponding to the 2 nd and 3 rd BPFs, respectively. The experimental results illustrate that the dipole sources at each BPF had a major  
Figure 9: Comparison of a velocity distribution with experiments at y = 0 section in the downstream. contribution to the generation of the fan's aerodynamic noise. Furthermore, at the location of 1.0 m, SPL decreases of 6.7 dB, 6.9 dB, and 7.5 dB at each BPF were observed per distance doubling. The BPF noise level of the fan can be very intense and can vary with the number of blades (N) and the rotation speed of the fan (RPM):  
\[\text{BPF = N}\times\text{RPM/60} \tag{14}\]  
The frequency histories of the SPL using the FW-H method based on the LES results were compared with the experimentally measured values and showed an acceptable agreement to 800 Hz. For the location of 0.5 m, the highest SPL of 66.6 dB at the first BPF was overp  
Figure 11: Frequency histories of SPL at 0.5 m (**left**) and 1m (**right**), \(\theta\) = 90\({}^{\circ}\) in the downstream. Figure 10: Pressure contours on the pressure side of the fan’s blades an in the wake region at y = 0 section at different dimensionless times of T* = 13.16, 13.19, 13.22, and 13.25.  
experimental value of 57.8 dB. However, the peaks at the 2 nd and 3 rd BPFs were lower than those in the experiments. Similarly, for the location of 1.0 m, the highest SPL was 60 dB at the first BPF and became lower than that in the experiments at the 2 nd and 3 rd BPFs. These discrepancies might be due to the shorter data acquisition duration, particularly at high frequencies, and the insufficient mesh resolution close to the fan blades. Therefore, a longer data acquisition duration and sufficient mesh resolution may improve these discrepancies. During the transient flow simulation, the time histories of the instant surface pressure values were written into the acoustic data files with which an operation was performed for the surface zones of the fan that were selected as acoustic sources. Figure 12 shows the SPL visualization of the fan noise source on the suction and pressure sides for the first BPF dipole sources that were between the 242.7 Hz and 246.6 Hz band range. A strong tonal noise existed near the leading edge of the blades under approximately \(\mathrm{Re}=9.75\times 10^{5}\) at the blade tip, which amounted to 111 dB SPL and a pressure side higher than the suction side in the SPL.