## 3 Results and Discussion  
### Cold Flow Pattern  
The process of fuel injection into the flow field before ignition is defined as cold flow field. In this study, the cold flow field has been visualized by the schlieren images, based on which the quantitative velocity information has been estimated using the optical flow method. It can be observed from the schlieren images that the cold flow field shows a periodic change after the addition of acoustic excitation, which corresponds well to the applied excitation frequency. Schlieren images and the resolved velocity contours with equal time intervals within a period under different excitation frequencies are shown in Figure 5. Images within 100 ms, 33 ms, 20 ms and 10 ms were chosen for the test cases, with external excitations at 10 Hz, 30 Hz, 50 Hz and 100 Hz, respectively. For comparison, images with a time interval of 3.5 ms are displayed for the case without external excitation.  
As can be seen from Figure 5a, when there is no external acoustic excitation, the cold flow field has no obvious change in time sequence. The region near the nozzle exit has shown a laminar pattern, while a turbulent structure can be observed in the downstream, as shown in the dashed white box in Figure 5a. The flow in the laminar region develops steadily downstream and the fluid trajectory presents a regular smooth curve, which is caused by the small holes on the ring structure, as shown in Figure 1b. However, the flow in the turbulent region is relatively random, chaotic and has no obvious regularity. The velocity of the main stream area is about 1 m/s, which also shows little change at different time instants.  
The acoustic excitation has great influences on the flow field, resulting in an uneven velocity distribution both in time and space. For the case of 10 Hz, the velocity field has shown cyclic variation with time, as shown by Figure 5b. The maximum velocity can reach to 2 m/s at certain time instants, while at 56 ms the velocity is no more than 0.5 m/s. The dramatic change indicates the 10 Hz perturbation has influenced a large-scale area with a distance up to 80-120 mm further to the nozzle exit. For the cases with 30 Hz and 50 Hz perturbations, as shown in Figure 5c,d, the regular formation of a periodical vortex structure can be observed, which accordingly corresponds to the acoustic frequency. The area with strong variation is confined below 80 mm in the downstream, which is smaller than the 10 Hz case. It can be observed clearly from the velocity contours that some high-speed zones are near the nozzle exit, as indicated by the white box, showing velocity around 2 m/s. The discontinuity between the high-speed zone and the surrounding area means the existence of a large velocity gradient in the local area. For the case of 100 Hz,  
Figure 4: Comparison between (**a**) the original flame image and (**b**) the enhanced image through the spatial filter method.  
the acoustic perturbation effect is confined to a smaller region, which is not beyond 40 mm downstream. Some local areas also show a high velocity around 2 m/s, while the velocity discontinuity can be observed. However, the perturbation is not able to resolve large-scale cyclic variation, while the region further downstream is similar to the case without acoustic excitation.  
Figure 5: Schlieren and velocity contours of cold flow field under different conditions: (**a**) no acoustic excitation; (**b**) 10 Hz excitation; (**c**) 30 Hz excitation; (**d**) 50 Hz excitation; (**e**) 100 Hz excitation.