## 3 Results and Discussion
### Ignition Process Visualization  
Based on the high speed flame/schlieren images, the ignition process under different acoustic excitation frequencies was visualized and quantitatively analyzed. The ignition initiation is defined as the moment when the ignition device generates sparks. The transient ignition process of a similar methane diffusion flame has been introduced for experimental validation. The selected case is a coflow diffusion methane flame, with the Reynolds number of methane at 55 and the surrounding air 1710, in reference [35]. As shown in Table 1, the Reynolds number of methane and surrounding air in the current study is 480 and 1110, respectively. Figure 6 shows the change of flame height in the ignition process for the selected case in [35] and the case without acoustic perturbation in the present study. It can be seen that the flame heights in both cases are both increasing with time in almost linear trends. The flame propagations in two cases are with similar time and length scales. The flame height of the current study is higher, which is mainly due to the larger Reynolds number of methane. The experiment repeatability is also checked by the flame height for repeating the same case five times, while the flame height variation is within \(\pm\)5%. Figure 7 shows the flame/schlieren images and the velocity contours of the five selected cases, with a time interval at 3.5 ms. In the case without acoustic excitation, as can be seen from the schlieren images in Figure 7a, an initial flame kernel is formed after ignition, which then propagates both upward and downward. The flame attaches to the nozzle exit around 10 ms. It can be seen from the color and schlieren images that the flame then mainly propagates downstream and reaches a distance about 100 mm at 28 ms, which indicates that a stable flame is established. With schlieren velocimetry, the velocities of the flame front and the turbulent structure inside the flame are both resolved using schlieren images. The motion of the flame front is caused by the propagation of flame in the unignited gas, while the turbulent hot gas is mainly affected by inertia force and buoyancy force. It can be seen from Figure 7a that the absolute velocity at the front of the flame increases rapidly after ignition, reaching a maximum of about 3 m/s, and decreases slightly during the upward propagation process. The velocity of the turbulent structure inside the flame is lower than the flame front, which is below 2 m/s. During the whole process, the center of the flame front protrudes towards unburned gas, which is called a mushroom flame [36]. As shown in Figure 7b, for the case with 10 Hz acoustic excitation, the flame kernel formation and propagation are similar to the case without external perturbation. A stable flame is established around 28 ms. However, a large-scale vortex structure can be observed to develop from upstream to downstream, as indicated by the white dotted line in the schlieren image. This structure is due to the superposition of the comprehensive buoyancy effect of acoustic excitation. The vortex structure interacts with the flame, which will affect  
Figure 6: The comparison of experimental data with similar test conditions [35]. the subsequent flame development. The maximum absolute velocity of the flame front reaches about 3 m/s and decreases gradually during the upward propagation. However, the flame no longer keeps the standard mushroom flame and the center of the flame front protrudes toward the ignition gas, which is called a tulip flame [36]. In the cases of 30 Hz and 50 Hz, similar large-scale vortex structures can be observed in the schlieren images. As can be seen from the flame images in Figure 7c,d, the shape of the flame changes dramatically during the ignition process compared with the case without external acoustic excitation. However, the flame heights at 28 ms for the two cases are lower than the 10 Hz and 0 Hz cases. The flame front still shows high velocities, which is around 2 m/s and smaller than the cases of 10 Hz and 0 Hz.