## 3 Results and Discussion
### Effect of FMRF on Flame
Figure 7 displays the phase-averaged CH\({}_{2}\)O- and SO\({}_{2}\)-PLIF measurements from flames with 80% FMRRF at a mean fuel mass flow rate of 0.142 g/s. Ten phases during one acoustic period are displayed with an interval of 36\({}^{\circ}\), corresponding to a 250 \(\upmu\)s separation. Phase 0\({}^{\circ}\) is the time when the fuel is injected into the combustion chamber. A bulge of CH\({}_{2}\)O-PLIF signal was formed at the chamber entrance and spread downstream periodically. The area and intensity of the bulge both increased as the phase increased. The phase-average distribution of the SO\({}_{2}\)-PLIF signal remained basically unchanged, with tiny alterations along the central axis, which was far from the heat release zone denoted by OH\({}^{*}\)-CL distribution demonstrated in Figure 5, indicating that the influence of FMRRF was local and did not alter the global flame directly. Until phase 252\({}^{\circ}\), the boundary of the CH\({}_{2}\)O bulge perfectly complemented the SO\({}_{2}\)-PLIF signal. After that, these two signal distributions overlapped in the downstream area because the SO\({}_{2}\)-PLIF distribution was broader than the reaction zone [51,64]. The CH\({}_{2}\)O- and SO\({}_{2}\)-PLIF signal intensities were visible near the fuel outlet axially and radially, indicating a quick temperature rise. Figure 8 displays some typical instantaneous CH\({}_{2}\)O- and SO\({}_{2}\)-PLIF images taken in the unforced and forced cases with 80% FMRRF at a mean fuel mass flow rate of 0.142 g/s. For unforced cases, as shown in Figure 8a,b, the Reynolds number of flames at the burner exit is about 4000. The small-scale turbulent structures are observed in the shear layer between fuel and air. CH\({}_{2}\)O is a product of thermal decomposition and early oxidation of fuel, and it is typically located on the fuel-rich side of the reaction zone. SO\({}_{2}\)-PLIF, representing  
Figure 7: Phase-averaged CH\({}_{2}\)O- (**every left**) and SO\({}_{2}\)-PLIF (**every right**) images from flames at a mean fuel mass flow rate of 0.142 g/s and air velocity of 17.1 m/s with 80% FMRRF, and the phase is marked in every subgraph. the high-temperature region, surrounds the fuel region in a stable, non-premixed flame (refer to Figure 8b and Refs. [18; 19; 20; 21]). The instantaneous flame structures are similar to the piloted turbulent jet flame reported in Ref. [64], in which the fuel jet enters the combustion chamber and is surrounded by hot recirculating products, and the non-premixed flame is formed in the shear layer where the fuel and hot product mix. Local extinction events are identified based on the following considerations. A discontinuity in the CH\({}_{2}\)O-PLIF signal (marked by red arrows in Figure 8a) indicates a disruption in the fuel decomposition process. The absence of the SO\({}_{2}\)-PLIF signal (denoted by red arrows in Figure 8b) suggests a local temperature drop. These discontinuities in the unforced flame demonstrate that local extinction occurs due to the high scalar dissipation rate in the shear layer, where a continuous stoichiometric surface exists [65; 66]. The fuel accelerates into the combustion chamber in the first three phases until 158\({}^{\circ}\) for the forced cases with 80% FMFRF, as displayed in Figure 8c,d. A large-scale vortex pair is periodically generated in the shear layer between the fuel jet and the recirculating product, which stretches the flame surface. The CH\({}_{2}\)O-PLIF signal forms a pair of bulges and is enhanced in the strong vortex (highlighted by the red rectangle). It is attributed to the preheating effect of surrounding hot, exhausted gases, which is helpful to the CH\({}_{2}\)O formation.