## 2 Experimental Setup and Measurements  
The experimental setup consisted of a bluff body diffusion burner equipped with an acoustic forcing system, and diagnostics for the flow, acoustic and flame dynamics as shown in Figure 1. The burner was designed with a plate bluff body and four radial methane nozzles with a diameter of 3 mm. The bottom of the test rig was fitted with a loudspeaker cavity, housing a 140 mm diameter speaker that was powered by a power amplifier (YAMAHA, PX8). The acoustic signal was modulated by a RIGOL DG1022 z signal generator, which controlled the frequency of the sin-wave signal. Both the power amplifier and the signal generator modulated the amplitude of the forced power. The air supply was provided by an air compressor. A Thorlabs PMM01 photomultiplier tube (PMT) equipped with a narrow bandpass filter (Thorlabs FB430-10) at a wavelength of 430 nm \(\pm\) 10 nm was used to monitor the overall flame CH* chemiluminescence release, with the PMT signal proportional to the heat release. Two GRAS 46 BE flush-mounted microphones were installed at the burner inlet to calculate the velocity fluctuation amplitude and phase using the two-microphone method [44], based on the collected signals from the two microphones. The distance between the two microphones was 125 mm. [PERSON] et al. [45] reported good agreement between the excited velocity fluctuation amplitude and phase measured by the hot wire and two-microphone method in the frequency range of 20-500 Hz. The PMT and microphone signals were simultaneously recorded at a frequency of 5 kHz using a data acquisition system (NI-cDAQ-9174, NI9239, NI9234). A high-speed camera (HSC) (AgileDevice M220) integrated with an image intensifier (EyeiTS S-HQB-F) and a narrow bandpass filter at a wavelength of 430 nm \(\pm\) 10 nm were employed to capture the CH radicals release of the flame at a sampling frequency of 2000 fps, with an exposure time of 0.45 ms for each image. The amplification factor of the image intensifier was set to the same value under different experimental conditions. A Z-type schlieren photography system was established to observe the structure of the flame's hot gas response. This consists of a pair of parabolic mirrors (250 mm in diameter and 2.5 m focal length), a point light source, a knife edge, and a high-speed camera (AgileDevice, M220). The time-resolved schlieren flame images were captured with a frame rate of 2000 fps, exposure time of 0.05 ms, and image size of 1080\(\times\)920 pixels. While the schlieren system and the CH* chemiluminescence images were not synchronized, the schlieren system was synchronized with microphone signal acquisition. The methane used in the experiment was obtained from a natural gas pipeline, with a low heat value of 34.5 MJ/Nm\({}^{3}\) and a methane volume fraction of 94.4%. The natural gas flow rate was maintained at 0.42 Nm\({}^{3}\)/h, while the air flow rate was set to 4.67 Nm\({}^{3}\)/h, resulting in an overall equivalence ratio of 0.86, which represents the normal operating condition of an industrial boiler. The mean air velocity before the nozzle was \(\bar{u}\) = 1.41 m/s, and the natural gas velocity at the gas nozzle was 4.14 m/s. The air jet flow velocity at the ring of the nozzle was \(u_{0}\) = 3.52 m/s. The velocity excitation frequency ranged from 10 Hz to 120 Hz, with a 5 Hz interval in the low-frequency range of 10 Hz to 50 Hz, and a 10 Hz interval in the excitation frequency range of 50 Hz to 100 Hz. The relative velocity excitation amplitude ranged from 0.10 to 0.50. The operating conditions are shown in Table 1.