## 3 Results
### Effects of Thermal Power  
Figure 10a-e show the sound pressure amplitude in the combustion chamber. When the thermal power of the combustor ranged from 0.013 to 0.065 kW, the chamber length and inlet gas temperature of the combustor remained constant. In the beginning, it can be inferred from Figure 10 that the sound pressure amplitude gradually increased when the thermal bellows were 0.052 kW. However, the sound pressure amplitude gradually decreased when the thermal power reached 0.065 kW. Additionally, the sparsity of the oscillation curve remained almost unchanged, which denotes that the oscillation frequency maintained a relatively stable value. The triggering time of thermoacoustic oscillation varies significantly when thermal power changes. In Figure 10a, at the thermal power  
Figure 8: Effects of different gas temperatures on the sound pressure amplitude and triggering time; the gas temperature ranged from o to 100 \({}^{\circ}\)C.  
of 0.013 kW, thermoacoustic oscillation emerged within 0.3 s; however, at the thermal power of 0.065 kW, Figure 10e shows that thermoacoustic oscillation emerged within 0.05 s. Figure 10 also indicates that there was a remarkable difference in the climb rate during the thermoacoustic oscillation excitation processes. The reason why the thermoacoustic oscillation amplitude did not significantly increase may be related to the intake pressure and burner heat dissipation. After the increase in thermal power, the degree of heat dissipation of the combustor increases. The oscillation frequency is almost unchanged; this may be attributed to the slight change in the acoustic wavelength in the combustion chamber. The detailed values of the sound pressure amplitude and triggering time under different thermal powers are displayed in Figure 11, and the triggering time is shortened. As the combustor thermal power increased from 0.013 to 0.065 kW, the thermoacoustic oscillation triggering time decreased from 0.26 s to 0.043 s. The triggering time of thermoacoustic oscillations is related to the Rayleigh criterion. The triggering time declined as thermal power increased, which caused the increase in the flame heat-release rate, leading to easier excitation of thermoacoustic oscillations. However, when the thermal power reached  
Figure 10: Effects of different thermal powers on the sound pressure amplitude in the combustion chamber; the thermal power ranged from 0.013 to 0.065 kW. (**a**) 0.013 kW. (**b**) 0.026 kW. (**c**) 0.039 kW. (**d**) 0.052 kW. (**e**) 0.065 kW. Figure 9: Effects of different gas temperatures on the thermoacoustic oscillation climb rate; the gas temperature ranged from 0 to 100 \({}^{\circ}\)C.  
0.052 kW, the decreasing trend of the thermoacoustic oscillation triggering time became slower. This may be because the heat dissipation effect of the combustor was greater than the influence of the flame heat-release rate. In this study, adiabatic effects were not considered; this may have resulted in a slight decrease in the thermoacoustic oscillation amplitude in the combustion chamber. Figure 12 shows the climb rate of thermoacoustic oscillations as the thermal power of the combustor increased from 0.013 to 0.065 kW. Contrary to the trend of the changes in the excitation time of thermoacoustic oscillations, the climb rate rose from 18.72 \(\times\) 10\({}^{5}\) Pa/s to 27.65 \(\times\) 10\({}^{5}\) Pa/s as the thermal power rose. However, the trend of the curve changes in both indexes was relatively consistent, ranging from significant to slow changes. Comparing this discovery with the research results in Sections 3.1 and 3.2, it can be found that it is crucial to reasonably set parameters for the effective active control of lean-premixed thermoacoustic oscillations. There are several areas that can be optimized to achieve the best thermoacoustic oscillation active control effect.