## 1 Introduction
The effects of the Strouhal number, the Peclet number, and convective velocity on hot spot propagation were also discussed, which were related to the entropy wave. Some experimental work was also conducted to obtain the HRR response of the jet diffusion flame. [PERSON] et al. [31] studied the forced reacting plumes of a jet non-premixed flame and discussed the interaction of the buoyancy-driven instability and the convective instability. The flame pinch-off was observed with strong low-frequency perturbations and the flame exhibited a low-pass filter characteristic. The dynamics of the jet diffusion flame in a standing wave were studied [32; 33; 34; 35; 36]. The low-pass characteristic of the response of the jet diffusion flame was also observed in this geometry. The effects of the excitation frequency and amplitude, the position of the fuel nozzle, and the fuel type on the flame dynamics were discussed in these papers. [PERSON] et al. [37] measured the FDF of a coaxial jet diffusion flame with an excitation frequency ranging from 80 Hz to 200 Hz. The gain of the FDF was independent of the forced amplitude. However, the phase-lag decreased with increasing forced amplitude. In past research, the non-premixed flame was usually treated as an active control method of combustion instability in premixed flame. However, in recent studies, the self-excited combustion instability of non-premixed flame has also been observed and discussed [38; 39]. For the industrial burner, the air and fuel were usually organized in cross-flow jets to enhance the mixing process. In order to anchor the flame, the bluff body was used as the flame stabilization structure. The stabilization mechanism of such bluff body non-premixed flames has been studied [40]. [PERSON] and [PERSON] [41] investigated the effects of the excitation frequency and the amplitude on the flame lift-off height and the reattachment, as well as the combustion efficiency and emissions of a radial injector non-premixed flame. However, the characteristics of the heat release response to acoustic excitation have not been clearly studied. Another factor affecting combustion stability is the acoustic characteristics of the combustion chamber cavity, which is mainly determined by its geometric dimensions and the flow field parameters. The natural oscillation mode is presented as a low frequency in practical industrial combustion equipment determined by the geometry parameters of the large cavity [42; 43]. Therefore, the response to low-frequency excitation is significant. In summary, many attempts have been made to understand the response mechanism of the non-premixed flame with different geometries. However, much less data are available for systematic studies of the FTF and FDF of non-premixed flames under acoustic perturbations, especially in experiments. The effects of the excitation frequency and amplitude on the phase-lag and gain of the FTF and FDF of the non-premixed flame are not yet clear. The objective of the present work is to investigate the characteristics of the response of a methane-air bluff body non-premixed flame to low-frequency forced acoustic excitation in the air flow. The FDF of the flame was measured. The spatial heat release response of the flame was analyzed with the CH* chemiluminescence images and schlieren images. The research results aim to broaden the scope of the mechanisms of the interaction of the forced flow perturbations and unsteady combustion and provide a foundation for the prediction of combustion instability of the non-premixed flame. The results may provide instructions for designing stable combustion in industrial burners.