## 4 Numerical and Experimental Results
### Active Control of the Flow-Induced Resonance Noise  
Based on the system shown in Figure 4, ANC experiments are further carried out to verify the effectiveness of the proposed method. In each experiment, the optimum stepsize is obtained by the trial-and-error method so that the best noise reduction performance could be achieved. For each case, some other adjacent frequencies (with intervals of 1 Hz) are also used as the reference frequencies to test if a better performance could be achieved. The best control results for the narrowband resonance noise with 236 mm, 249 mm and 261 mm cavity depths are summarized in Table 2. The effective reference frequency ranges within which attenuations of resonance noise could be achieved is also given. Although the original flow-induced noise spectrums show two resonance frequencies corresponding to different modes, only the first resonance is under control, i.e., the tonal reference signal of the ANC system only contains the first resonance frequency component. As can be seen from Table 2, resonance noise can be effectively reduced by the narrowband ANC system. The noise energy at the fundamental resonance frequency and its first harmonic could be greatly attenuated at the same time, although only the former is under control in the ANC system. Moreover, it was also observed that both the upstream and downstream noise could be effectively reduced by the control system, which indicates that the total energy of resonance noise is attenuated for the whole duct system and a global control performance can been achieved. These results go against with the ones in early researches [20,21], in which it was concluded that only local noise reduction performance is expected and adaptive algorithms are not effective for multiple modes. It should be noted that in this paper the cavity is installed inside a duct system with extremely low Mach numbers, which might give rise to different noise reduction behaviors. It can also be observed from Table 2 that, in some cases, the optimal reference frequencies are not in accordance with the resonance frequencies. The difference between these two frequencies could be up to 6-8 Hz. Further, the ANC system is effective over a relatively wide range of the reference frequency (approximately 12 Hz for all 3 cases). The specific power spectrums of resonance noise before and after control are given in Figures 8-10 for different cavity depths. These relatively wide reference frequency ranges are very different from linear systems, where the noise reduction performance could be greatly reduced by only 1 Hz FM [23,24]. Furthermore, the optimal reference frequency corresponding to the best noise reduction performance shows some randomness when compared with the resonance frequency. For the 249 mm cavity, the optimal reference frequency is the same as the resonance noise frequency, which is a common result for a narrowband ANC system. For the 236 mm cavity, however, the best control performance could be obtained with a 332 Hz reference, which is much lower than the resonance frequency 340 Hz. While in the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Cavity Depth/mm**} & \multirow{2}{*}{**Number of Grids**} & \multicolumn{4}{c}{**Numerical Prediction**} & \multicolumn{1}{c}{\multirow{2}{*}{**Experiment Result/Hz**}} \\ \cline{3-4} \cline{6-7}  & & **M1/Hz** & **Error** & **M2/Hz** & **Error** & \\ \hline \multirow{3}{*}{261} & 171,595 & 351 & 6.0\% & 358 & 8.2\% & \\  & 361,464 & 336 & 1.5\% & 337 & 1.8\% & \\ \cline{1-1}  & 905,769 & 336 & 1.5\% & 337 & 1.8\% & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Independence verification of grid.