# Experimental Tests and Aeroacoustic Simulations of the Control of Cavity Tone by Plasma Actuators
## 4 Results and Discussions  
### Measured Geometric Effects of Actuators on Control  
The variation of the sound-reduction level at the fundamental frequency of 1500 Hz as a function of the voltage \(E_{\text{pa}}\) applied to the actuators was measured, where the spanwise pitch of the lower electrode was either \(s=4\) mm or \(s=10\) mm, and the fixed width of the lower electrode was \(d_{\text{l}}=3\) mm. Figure 14a shows the measured variation. The frequency resolution of spectral analysis was \(\Delta f=4.88\) Hz and it should be noted that the reduction level was different from that in the previous section due to the difference of the frequency resolution.  
As shown in Figure 14a, the amount of noise reduction is greater for higher applied voltages, particularly in the range from \(E_{\text{pa}}=4\) kV\({}_{\text{P-p}}\) to 5.5 kV\({}_{\text{P-p}}\). The sound level drops sharply at lower voltages for the narrower pitch \(s=4\) mm, as compared to the case with \(s=10\) mm. For \(s=4\) mm, the sound reduction level of 31 dB was achieved at \(E_{\text{pa}}=5\) kV\({}_{\text{P-p}}\). However, for a fixed cavity width, more actuators and greater power consumption are necessary for narrower pitches. In the next subsection, the sound-reduction mechanism is discussed for \(s=10\) mm and \(E_{\text{pa}}=5.0\) kV\({}_{\text{P-p}}\).  
According to the investigation by [PERSON] et al. [5], the cavity tone was also reduced by pairs of introduced streamwise vortices by blowing jets in the incoming boundary layer. Additionally, the results at the jet velocity of \(V_{\text{j}}/U_{0}=0.07\), which roughly corresponds to the jet velocity (2 m/s) induced by the present plasma actuators, show that the control effects became smaller for finer spanwise displacement of the jets, such as \(s/L=0.1\) and 0.25. The maximum reduction level was achieved at \(s/L=0.5\). This was because the induced longitudinal vortices were weakened for the finer displacement.  
Meanwhile, the present plasma actuators can most largely reduce cavity tone with a finer displacement of \(s/L=0.2\). This difference from the results of blowing jets is possibly because the electrodes of the actuators are elongated into the streamwise direction making it easier to introduce intense streamwise vortices, while the blowing jets were ejected from simple circular holes. Deliberately SETTING up the inlet shape and blowing direction for the jets for the introduction of the streamwise vortices possibly increases the effects.  
The comparison of the present results with those of the control by blowing jets indicates that the present plasma actuators can effectively introduce longitudinal vortices and reduce cavity tone with a finer displacement. Meanwhile, for a fixed cavity width, more actuators and greater power consumption are necessary for a narrower displacement. The exact estimation of power consumption remains a problem for the future.  
To clarify the effects of the lower-electrode width on control of the cavity tone, the sound-reduction levels were measured for lower-electrode widths of \(d_{\text{l}}=1\), 3, 5, and 7 mm, at a constant pitch of  
Figure 13: Predicted and measured sound-pressure spectra, both with and without control.  
\(s=10\) mm, as shown in Figure 14b. The results show that sound reduction was obtained and that the influence of the lower-electrode width on sound reduction was small, except for the narrowest width, \(d_{1}=1\) mm. Streamwise vortices are not induced at this narrow width, possibly because the body force is not sufficiently large, due to too narrow a width for expansion of the plasma between the exposed electrodes [27].