## 4 Discussion
### SETAI Behavior under Asymmetric Supply Structure
However, when \(L_{2}\) is changed, OS\({}_{2}\) may suppress the oscillation, as observed in cases 29, 30, 31, and 38, resulting in an overall weak oscillation. Furthermore, it is notable that although OS\({}_{1}\) still has a strong promotion effect in cases 28, 36, and 37, these conditions only exhibit combustion noise without obvious oscillation. The results in Tables 3 and 4 also demonstrate the same regularity, where most cases show that the whole system can only be pushed into a strong oscillation when OS\({}_{2}\) has a promotion effect. An exceptional circumstance occurs in cases 58 and 59, where both OS\({}_{1}\) and OS\({}_{2}\) have a promotion effect, but the whole system does not exhibit oscillation. This may be because the sound pressure antinode is too close to the stabilizer [24], resulting in a relatively weak flow rate oscillation and muting the thermo-acoustic interaction. These observations indicate that, for an asymmetric supply structure, a necessary but not sufficient condition for strong oscillation is that both \(L_{1}\) and \(L_{2}\) satisfy oscillation promotion. Table 5 lists the phase of sound pressure oscillation at seven measurement points under various cases. These data clearly demonstrate that the sound pressure differs within the two premixed chambers in an asymmetric supply structure. In particular, the pressure oscillation phase at the close end (P\({}_{2}\) and P\({}_{3}\)) is very close in the symmetric supply structure but differs significantly in some asymmetric supply structure cases. This difference in pressure oscillation phase between P\({}_{2}\) and P\({}_{3}\) implies the asynchronized heat release oscillation between two inlets of the combustion chamber. In the symmetric supply system, the flow rate oscillation at the combustion chamber inlet is almost synchronous between the two sides, resulting in synchronous heat release oscillation. Therefore, the coupling between pressure and heat release oscillation is also the same between the two sides, and OS\({}_{1}\) and OS\({}_{2}\) have the same effect on the system's SETAI. For asymmetric supply systems, it is important to note that although OS\({}_{1}\) and OS\({}_{2}\) still experience the same pressure oscillation within the combustion chamber, their heat release oscillation may not be synchronized. Specifically, during certain periods within an oscillation cycle, the heat release oscillation may increase sound pressure on one side but have a reducing effect on the other side. In this case, there is a possibility that either OS\({}_{1}\) or OS\({}_{2}\) may individually encourage SETAI, but their promotional effects may partly cancel each other out. Consequently, the oscillation in an asymmetric supply system is generally weaker than in the two corresponding symmetric systems, as reflected in Tables 2-4 and Figures 4-6. The non-synchronous sound pressure oscillation between the two premixed chambers is the reason for the reduced oscillation under the asymmetric supply structure, and thus the system SETAI could potentially be controlled simply by altering the length of one premixed chamber. Figure 8 compares the sound pressure oscillation in case 64 with the two corresponding symmetric systems. The oscillation condition in case 64 (\(L_{1}\)= 1.65 m and \(L_{2}\) = 3.87 m) is almost the same as in the two symmetric supply structures, in terms of both frequency and amplitude. This is unlike the phenomenon observed in Figure 2 or Figure 3. Case 64 was specially designed such that one premixed chamber is longer than the other by half \(\lambda_{\rm P}\). This implies that the pressure mode shape at the upstream position of the flame stabilizer is the same between the two sides, despite having different \(L_{\rm P}\). Under the same combustion conditions, a synchronous heat release oscillation was obtained between OS1 and OS2, resulting in pressure oscillation behavior that is as strong as that in the corresponding symmetric system.