## 2 Experimental Approach  
### Burner Assembly  
The experimental apparatus used in this work was modified based on the bluff-body swirl burner described in Ref. [57], equipped with a loudspeaker offering an external acoustic forcing. A schematic of the burner is shown in Figure 1a, consisting of two concentric parts. The outer circular duct was 350 mm long with an inner diameter \(D=37\) mm, with the inside fitted with a solid conical bluff body of diameter \(d=25\) mm, giving a passage blockage ratio of 50%. The air entered from the annulus between the outer duct wall and the bluff body. For the non-premixed flames, there was a central hollow pipe with a diameter of 4 mm in the center of the bluff body to feed the methane. The outlet was open to the atmosphere, and the temperature of the inlet gases was the same as the ambient. A swirler with a 60\({}^{\circ}\) vane angle to the central axis was located 41.6 mm upstream of the outlet plane, creating a circumferential component of the inlet air velocity. According to [PERSON] and [PERSON], the swirl number was calculated as 1.23 [58]. The swirler was anti-clockwise when looking along the flow direction of the inlet air. A square UV-fused silica quartz enclosure (95 mm in width and 150 mm in length) was placed on the top of the burner to provide optical access for measuring the flame and prevent air entrainment from the surroundings. In addition, better stability could be achieved since a square enclosure can offer a larger combustion chamber than an inscribed circular one. The typical flow field of such a burner is shown in Figure 1b, which was measured using LDV [59; 60]. The main structure of the flow field can be distinguished in Figure 1b,  
Figure 1: (**a**) Schematic of the burner and (**b**) flame structure of non-premixed swirling flame [59; 60]. including the central recirculation zone (CRZ), the outer recirculation zone, and the shear layer formed between the air flow and RZs. The CRZ brings hot combustion products back to the nozzle, which is essential for flame stability. Fuel injection is in the center of the flow field, and the inner shear layer is formed between the fuel jet and the CRZ in the downstream regions, where the mixing of the fresh fuel and the hot recirculated gases is enhanced. Consequently, the flame is of a non-premixed type. When an external acoustic forcing was applied to the fuel flow, the averaged flow rate could not reflect the instantaneous radial velocity distribution, and the fuel penetrated the RZ to create a jet-like flame with a periodic bulging base. Additionally, no evidence showed a precessing vortex core occurring in the flame. The air and fuel mass flow rate was controlled by mass flow controllers (MKS, Andover, MA, USA & Sevenstar, Beijing, China). Methane was pumped and sinusoidally modulated by a 90 mm diameter loudspeaker (HiVi, Zhuhai, China) controlled by an amplified sine-wave signal from a function generator (Yamaha, Iwata, Japan & RIGOL, Suzhou, China). As shown in Figure 1b, the loudspeaker was mounted coaxially in a plenum upstream of the central fuel injection tube to create the forced fuel mass flow rate fluctuation (FMRFF) on the non-premixed flame and induce heat release fluctuations. The loudspeaker worked at 400 Hz because it was the primary resonant frequency of the plenum and burner assembly. Table 1 shows detailed experimental conditions. A 2% volume fraction of SO\({}_{2}\) was added into methane in the case of SO\({}_{2}\)-PLIF measurements. The flame structure was recorded starting from a stable condition till approaching the blowoff. The amplitude of the flow rate fluctuation was determined by the forcing strength controlled by the voltage applied to the loudspeaker, which varied from 0 to 2 V. To quantify the FMRF of the inlet fuel flow, the relationship between fuel mass flow rate and the loudspeaker voltage was investigated.