## 3 Results and Discussion
In the case of diffusion flames of liquid fuel, a convection cooling effect would be produced on the fuel bed by the acoustic flow, which made the fuel evaporation rate drop below the critical value needed to sustain a flame; thus, acoustic extinction was achieved [11]. Although it was also a diffusion flame, the fuel here was gaseous and there was no evaporation process. Consequently, an alternate explanation was needed. As shown in Figure 3b, as the flame displacement increased, there was a gap between the flame root and the burner outlet, meaning that the new fuel from the burner would exist in an unburned state instead of being ignited immediately, which can be observed in the schlieren image in Figure 8c. The motion parameters of three points were further extracted, representing the flame, unburned fuel, and membrane (probe) (Figure 8). The time dependence results in Figure 8a were fitted in Figure 8b. After dimensionless treatment, the three lines can be expressed as two sine functions as follows:  
\[x_{\rm F}^{*}=0.391\sin(\omega t-2.844),\ R^{2}=0.95 \tag{2}\]  
\[x_{\rm m,f}^{*}=2.611\sin(\omega t+0.8644),\ R^{2}=0.98 \tag{3}\]  
where \(x_{\rm F}^{*}\) representing the position of unburned fuel is equal to \(x_{\rm F}/d_{\rm i}\), \(x_{\rm m,f}^{*}\) representing the position of the flame and membrane is equal to \(x_{\rm m,f}/d_{\rm i}\), \(d_{\rm i}\) is the nozzle inner diameter, and \(\omega=2\pi f\). As illustrated in Figure 8c, the oscillation frequencies of the flame, unburned fuel, and membrane were the same, but the displacement amplitude of unburned fuel was less than 15% of that of the flame and membrane. In fact, the newly ejected fuel would exist in an unburned state only when the flame was far away from the burner outlet. However, due to the attributes of the periodic oscillation movement, the speed of the whole flow field first increases to the peak value and then decreases to zero in half a period. Therefore, when the flame was far away, it corresponded to the deceleration phase, and oscillation amplitude of the unburned fuel at the end of the deviation stroke was, consequently, very small. In addition, an abnormal phenomenon was noted in Figure 8b: the temporal characteristics of unburned fuel were not synchronous with that of macroscopic oscillation of the whole flow field, and there was a dislocation equal to about 1/4 period. It should be pointed out that the oscillation of the flame and induced wind was completely consistent, and the  
Figure 2:0 Comparison of \(\zeta_{\rm f}\) and \(\zeta_{\rm m}\) under the same sound pressure, and the reduction trend with increasing frequency \(f\). frequency and amplitude were equal to the excitation source (membrane); thus, the speed was no longer distinguished and was uniformly expressed by \(u^{*}\), which was calculated per Equation (4). Figure 2:1  
When \(x_{\text{F}}^{*}\), \(x_{\text{m,f}}^{*}\), and \(u^{*}\) were compared together in Figure 8d, an interesting case could be seen wherein the nonidentity in time (mentioned above) between \(x_{\text{F}}^{*}\) and \(x_{\text{m,f}}^{*}\) always started when \(u^{*}\) reached its peak and ended when \(u^{*}=0\), i.e., the flame and unburned fuel moved in opposite directions during the deceleration period of induced wind (marked by pink stripes in figures). As illustrated in Figure 9a, the velocity of unburned fuel \(U_{\text{F}}\) was actually the vector sum of \(u\) and ejection velocity \(v_{\text{F}}\). Thus, the horizontal component of \(U_{\text{F}}\) decreased continuously during the deceleration period of induced wind. As a result, the horizontal movement direction of the unburned fuel was opposite to the flame, and it should be emphasized that in this process, the observed fuel was constantly updated. Thus, the unburned fuel oscillation phase should be approximately consistent with that of the flame oscillation acceleration \(a\), which was confirmed in Figure 9b.