# Effect of Different Acoustic Parameters on NOx Emissions of Partially Premixed Flame
## 3 Results and Discussion
### Flame Length and Flame Surface Wrinkling  
The flame images were taken by a Canon CMOS (Complementary Metal Oxide Semiconductor) camera to show the flame structures under the different frequencies. In Figure 6, the images are illustrated for case two of partially premixed flames with a range of acoustic frequency from 80 Hz to 280 Hz based on time-average images. Flame surface wrinkles were quite different with acoustic frequencies at a fixed acoustic amplitude of 345 \(\pm\) 10 Pa. The effects of acoustic forcing on flame wrinkling at 80 Hz to 150 Hz were much stronger than 200 Hz to 280 Hz, which was in good agreement with the results in the change of NOx emissions with acoustic frequency.  
Figure 5: NOx emission characteristics with acoustic amplitudes (0–180 Hz) (**a**) Case 1; (**b**) Case 2; (**c**) Case 3.  
Figure 6: Flame surface wrinkling under different frequencies (345 \(\pm\) 10 Pa).  
Figure 7: Flame length characteristics with different acoustic parameters; (**a**) Case 1; (**b**) Case 2. (c) Case 3.  
flame, which could be observed from the velocity contour. It was thought that the periodic acoustic excitation enhanced the mixing of fuel and air, and reduced the flame length. Research results showed that when the flame length reduced, the reaction region of NOx shortened, reaction rate strengthened, and NOx emission decreased [23; 38].  
The interaction between vortex and flame was the important mechanism for reduction of NOx in partially premixed flame with acoustic excitation. Figure 9 shows the interaction of flame-vortex under the acoustic frequency range from 80 Hz to 280 Hz in a fixed amplitude at 241 \(\pm\) 10 Pa. It can be observed that the intensity and position of the vortex showed different characteristics with acoustic frequency. The vortex changed from upstream to downstream with an increase in frequency from 80 Hz to 200 Hz at the same phase. Vortex diameter became larger and the vortex rolled up with surrounding air to the downstream when the acoustic frequency increased. The flame-vortex interaction caused the  
Figure 8: Vortex structure in partially premixed flame under acoustic excitation.  
flame base to broaden when the frequency was less than \(f_{\mathrm{c}}\) (\(f_{\mathrm{c}}^{-}\)), although this broadening effect did not reappear when the frequency was greater than \(f_{\mathrm{c}}\) (\(f_{\mathrm{c}}^{+}\)). This corresponded to an increase of NOx emissions induced by the weakness of the mixing effect. This was the reason that EINOx for \(f_{\mathrm{c}}^{-}\) was much less than for \(f_{\mathrm{c}}^{+}\).  
As Figure 10 shows, the vortex moved upstream and enhanced the interaction at the base of the flame with an increase of amplitude at 110 Hz, but the influence of amplitude on the length of flame was not obvious at 280 Hz. These changes in flame structure with amplitude variation at different frequencies were well matched with changes of flame length shown in Figure 6. Therefore, NOx emission and flame length both shortened observably with increased acoustic amplitude at 110 Hz; however, it was opposite when the frequency was at 280 Hz.