## 4 Study of the TE Noise Reduction with Serrated Treatment Using Linear Microphone Array
### Results and Discussions  
Firstly, the influence of the sawtooth amplitude on the TE noise characteristics is investigated. Figure 12 shows the sound source identification maps of different serration amplitudes under the flow condition of U = 40 m/s and with sawtooth wavelength \(\lambda\) = 3 mm. It can be seen from the figure that both the LE noise and TE noise sources can be separated correctly. The LE noise is barely affected by the serrated TE modification, while the TE noise can be significantly reduced with the serrated treatment. It can also be found from Figure 10(b) that the sawtooth H5\(\lambda\)3 has an obvious noise reduction effect for high-frequency noise. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**No.** & **Blade** & _2h (mm)_ & _2h/c_ & \(\lambda\) (mm)_ & _\(\lambda\)/c_ & _\(\lambda\)/h_ \\ \hline
0 & Baseline & 0 & 0 & - & - & - \\
1 & H5\(\lambda\)3 & 5 & 0.033 & 3 & 0.02 & 1.2 \\
2 & H10\(\lambda\)3 & 10 & 0.067 & 3 & 0.02 & 0.6 \\
3 & H15\(\lambda\)3 & 15 & 0.100 & 3 & 0.02 & 0.4 \\
4 & H20\(\lambda\)3 & 20 & 0.133 & 3 & 0.02 & 0.3 \\
5 & H25\(\lambda\)3 & 25 & 0.167 & 3 & 0.02 & 0.24 \\
6 & H30\(\lambda\)3 & 30 & 0.200 & 3 & 0.02 & 0.20 \\
7 & H40\(\lambda\)3 & 40 & 0.267 & 3 & 0.02 & 0.15 \\
8 & H30\(\lambda\)1.5 & 30 & 0.200 & 1.5 & 0.01 & 0.10 \\
9 & H30\(\lambda\)5 & 30 & 0.200 & 5 & 0.03 & 0.33 \\
10 & H30\(\lambda\)10 & 30 & 0.200 & 10 & 0.07 & 0.67 \\
11 & H30\(\lambda\)15 & 30 & 0.200 & 15 & 0.10 & 1.00 \\
12 & H30\(\lambda\)30 & 30 & 0.200 & 30 & 0.20 & 2.00 \\ \hline \end{tabular}
\end{table} 
Table 1: Design parameters of the serrated TE configuration. Figure 11: The serrated trailing-edge (TE) blade and parameter definitions. Figure 12: The sound source distribution of the blade with different sawtooth amplitudes (U = 40 m/s). It could be seen from the beamforming results that the main lobes of LE and TE noise all have some width in space. The magnitude of the LE and TE noise should be the sum of sound level in specified space. In this study, the sound pressure levels of LE and TE noise are evaluated using the following equation:  
\[L_{LE}=10\cdot\mathrm{lg}\left(\frac{\sum\limits_{n=N_{\mathrm{min}}}^{N_{ \mathrm{max}}}10^{0.1L_{n}}}{N_{\mathrm{max}}-N_{\mathrm{min}}+1}\right) \tag{1}\]  
where \(L_{n}\) is the sound pressure level at position \(n\). Suppose that the LE and TE noise source center is at the position of maximum overall sound pressure level OASPL (in frequency band of 1000 to 10,000 Hz), \(N_{\mathrm{min}}\) and \(N_{\mathrm{max}}\) are, respectively, the upstream and downstream positions where the OASPL is 3 dB smaller than the maximum OASPL. Figure 13 shows the 1/3 octave spectra of the TE noise for the blade possessing different sawtooth amplitudes and with the wavelength of 3 mm at airflow speeds of 20 m/s, 40 m/s, 60 m/s and 70 m/s. It can be seen from Figure 13 that the TE serrations can effectively reduce the TE noise. At flow speed of 20 m/s, the noise can be decreased by 4-5 dB below 8000 Hz for most of the serrated airfoils tested. However, the serrations have a negligible noise reduction effect for high frequency above 8000 Hz. Moreover, no obvious noise reduction law is obtained about the serration amplitude. When the airflow velocity is 40 m/s, except for the H5\(\lambda\)3 blade, the noise reduction effect of other serrated treatments has insignificant differences. The TE noise can be reduced by 3-7 dB below 5000 Hz. However, when the frequency is above 5000 Hz, the noise reduction effect is obviously weakened. With the increase in airflow velocity to 60 m/s and 70 m/s, the noise reduction difference between different sawtooth configurations increases. The low-frequency noise can even be enlarged by the H5\(\lambda\)3 blade. In general, the TE serrations can effectively reduce the low- to mid-frequency noise, while they might have a negligible noise reduction effect in the high-frequency range. The serrations with a larger amplitude generally obtain a higher noise reduction level.