## 4 Discussion  
### SETAI Behavior under Asymmetric Supply Structure  
Previous investigations have shown that \(L_{\text{P}}\) and \(\varphi\) collectively influence the interaction between sound pressure oscillation and heat release oscillation, determining whether SETAI can be encouraged [9; 25]. Specifically, when \(L_{\text{P}}/\lambda_{\text{P}}\) complies with Equation (5), the mode shape within the premixed chamber corresponds to a quarter to a half wave. In this scenario, a pressure node will exist upstream of the flame stabilizer, as the far end (inlet) of the premixed chamber acts as a pressure antinode due to its near-closed acoustic boundary condition. It should be noted that there is a potential error regarding the far end of the premixed duct not completely adhering to a closed boundary condition. Thus, when  
Figure 6: Oscillation variation with changing length of one side of premixed chamber in comparison to both changing equally (\(L_{2}=1.65\) m, \(\varphi_{1}=\varphi_{2}=0.9\)). Figure 7: The pressure oscillation under asymmetric combustion condition. the instantaneous pressure at the flame stabilizer exceeds its average value, the pressure will increase in the flow direction. This pressure difference between the two sides of the flame stabilizer will reduce the mixture flow rate, causing a flow rate oscillation that is phase-led by 90\({}^{\circ}\) relative to the pressure oscillation. In contrast, the flow rate oscillation will be phase-lagged by 90\({}^{\circ}\) relative to the pressure oscillation when Equation (6) is satisfied. For combustion with \(\varphi\) = 0.9, \(\tau\) satisfies Equation (7) (where \(T_{\text{M}}\) is the oscillation period). This indicates that the phase lag of heat release oscillation is less than 180\({}^{\circ}\) relative to the flow rate oscillation. In this case, the phase difference between sound pressure oscillation and heat release oscillation would be less than 90\({}^{\circ}\), promoting the oscillation as long as Equation (5) is also satisfied. When Equations (6) and (7) are simultaneously satisfied, however, the sound pressure oscillation and heat release oscillation are out of phase, resulting in a negative Rayleigh criterion that suppresses oscillation. In the combustion of \(\varphi\) = 0.7, however, Equation (8) is satisfied, and therefore the condition of \(L_{\text{P}}/\lambda_{\text{P}}\) satisfying Equation (6) can result in an oscillation promotion, while Equation (5) results in oscillation suppression. In a symmetric supply structure, both sides have the same effect of either promoting or suppressing oscillation. In an asymmetric supply system, a different \(L_{\text{P}}\) value may lead to the interaction between heat release oscillation and sound pressure oscillation promoting each other on one side but suppressing each other on the other side. \[\frac{2n+1}{4}<\frac{L_{\text{P}}}{\lambda_{\text{P}}}<\frac{2n+2}{4} \tag{5}\]  
\[\frac{2n}{4}<\frac{L_{\text{P}}}{\lambda_{\text{P}}}<\frac{2n+1}{4} \tag{6}\]  
\[\frac{2 mT_{\text{M}}}{2}<\tau<\frac{(2m+1)T_{\text{M}}}{2} \tag{7}\]  
\[\frac{(2m+1)T_{\text{M}}}{2}<\tau<\frac{(2m+2)T_{\text{M}}}{2} \tag{8}\]  
The ratio of \(L_{\text{P}}\) to \(\lambda_{\text{P}}\) was calculated on each side to analyze the mechanism of encouraging or suppressing oscillation under an asymmetric supply structure, combining the results with those obtained from measuring \(P_{\text{RMS}}\), as shown in Tables 2-4. In asymmetric supply systems, the heat release oscillation is probably in a different phase between the two sides, generating two sources (OS\({}_{1}\) and OS\({}_{2}\), respectively) with different effects on pressure oscillation. Taking the results in Table 2 as an example, in the symmetric supply system with \(L_{1}\) = \(L_{2}\) = 2.06 m, \(L_{\text{P}}/\lambda_{\text{P}}\) is 0.439. Under this condition, both OS\({}_{1}\) and OS\({}_{2}\) promote oscillation, resulting in a strong oscillation with \(P_{\text{RMS}}\) as high as 4108 Pa.