## 3 Results
### Effects of the Gas Temperature  
Figure 7a-e show the variation tendency of sound pressure amplitude in the combustion chamber while the gas temperature ranged from 0 to 100 \({}^{\circ}\)C. This study selected five gas temperatures, each increasing by 25 \({}^{\circ}\)C. In this part, the combustor length and thermal power remain constant. It can be inferred from Figure 7 that the sound pressure amplitude gradually declined as the gas temperature increased from o to 100 \({}^{\circ}\)C. Different from the changes in combustor length shown in Figure 4, the oscillation curve showed a linear change. The trend of oscillation frequency change is also different from that in Figure 4; the oscillation frequency experienced a slowly increasing trend as the gas temperature rose. The triggering time of thermoacoustic oscillation varied obviously when the inlet gas temperature changed. In Figure 7a, at the temperature point of 0 \({}^{\circ}\)C, thermoacoustic oscillation emerged within 0.3 s; however, at the temperature point of 100 \({}^{\circ}\)C, Figure 7e illustrates that thermoacoustic oscillation emerged after 1.1 s.  
The detailed values of the sound pressure amplitude and triggering time under different gas temperatures are displayed in Figure 8. It can be seen that the amplitude of thermoacoustic oscillation decreased but the triggering time was prolonged. As the inlet  
Figure 6: Effects of different combustor lengths on the thermoacoustic oscillation climb rate; the combustor length ranged from 1.2 to 6.0 m.  
Figure 7: Effects of different gas temperatures on the sound pressure amplitude in the combustion chamber; the gas temperature ranged from 0 to 100 \({}^{\circ}\)C. (**a**) 0 \({}^{\circ}\)C. (**b**) 25 \({}^{\circ}\)C. (**c**) 50 \({}^{\circ}\)C. (**d**) 75 \({}^{\circ}\)C. (**e**) 100 \({}^{\circ}\)C.  
premixed gas temperature increased from 0 to 100 \({}^{\circ}\)C, the thermoacoustic oscillation triggering time increased from 0.26 s to 1.13 s, while the sound pressure amplitude decreased from 3.44 \(\times\) 10\({}^{5}\) Pa to 2.4 \(\times\) 10\({}^{5}\) Pa. The sound pressure amplitude experienced a linear descent while the gas temperature increased from 0 to 100 \({}^{\circ}\)C. This is because the triggering of thermoacoustic oscillations is related to the Rayleigh criterion. The oscillation frequency f slowly improved as the inlet gas temperature increased, and the phase difference between the flame heat-release rate and sound wave changed to \(\Delta p=\omega t+\varphi\), where \(\omega\) denotes the circular frequency, and the relationship is \(\omega=2\pi\textit{f}\). The symbol \(\varphi\) stands for the initial phase value. As the thermoacoustic oscillation frequency f gradually increases, the circular frequency \(\omega\) also starts to rise; this leads to an increase in the phase difference, causing a decrease in the oscillation amplitude. Figure 9 shows the climb rate of thermoacoustic oscillations as the gas temperature increased from 0 to 100 \({}^{\circ}\)C. Consistent with the amplitude variation trend of thermoacoustic oscillation, the climb rate dropped from 24.01 \(\times\) 10\({}^{5}\) Pa/s to 11.06 \(\times\) 10\({}^{5}\) Pa/s as the temperature rose. This means that the thermodynamic characteristics of the working fluid at the burner inlet were closely related to the excitation speed of thermoacoustic oscillations. Compared with the results in Figure 8, where, as the temperature increased, the slope of the curve for the triggering time of the thermoacoustic oscillation increased, the climb rate in Figure 9 declined. For lean-premixed combustors, the duration of the thermoacoustic oscillation triggering time and the climb rate are contradictory indexes. Therefore, it is necessary to optimize the parameter settings to obtain a reasonable thermoacoustic oscillation triggering time and climb rate, thereby improving the stability and safety of the system [39].