Characteristics of combustion instability mode transition under transient switching operations in a coaxial staged combustor

To address the unclear mechanisms underlying the mode transition of combustion instability induced by variations in fuel staging ratios, transient numerical simulations of the dynamic fuel switching process in a natural gas coaxial staged combustor were conducted using Wall-Modeled Large Eddy Simulation coupled with the partially premixed Flamelet Generated Manifold approach. Combining the Synchrosqueezing Wavelet Transform and delay-coordinate phase-space reconstruction, the temporal evolution and trajectory morphology of the combustion response were analyzed. The time-frequency evolution characteristics of the heat release rate (HRR) alongside temperature and velocity flow fields were comprehensively tracked. The results demonstrate that the combustion response depends strongly on the initial operating condition and switching path. Identical target fuel-staging ratios may exhibit distinct combustion responses owing to different switching histories, demonstrating path dependence. The variation in HRR induced by changing the fuel staging ratio was closely associated with the mode transition. Specifically, during the S4 → U1 switch, a transient decrease followed by an increase in HRR was observed during the early switching stage. This variation was associated with changes in the shear-layer dynamics and vortex evolution, which contributed to the subsequent transition of the combustion mode. Spectral and correlation analyses showed coincident dominant pressure and global-HRR frequencies of 300–450 Hz with high magnitude-squared coherence in seven cases, whereas S5 → U2 exhibited frequency mismatch and a substantially lower zero-lag Pearson correlation coefficient. Moreover, delay-coordinate phase portraits further revealed distinct trajectory morphologies among the switching paths, supporting the path dependence identified from the time-domain analysis.