In this study, we present the first numerical evidence of multiple bifurcation processes occurring in a multi-element model liquid rocket engine before and after the longitudinal thermoacoustic instability regime, as we vary the oxidizer inlet temperature within the range of 400–1400 K. To accurately capture the non-premixed turbulent combustion process, a comprehensive three-dimensional compressible detached eddy algorithm was employed, incorporating a two-step methane/oxygen chemical reaction kinetic mechanism based on OpenFOAM. After validating the numerical framework and achieving grid independence, we focus on (1) investigating the transition routes of system dynamics and (2) analyzing the spatiotemporal evolution of multiple jet combustion flow fields during the multi-bifurcation process. Our results indicate that the system dynamics undergoes two successive bifurcating processes. During the first bifurcation (400 K ≤ T ≤ 800 K), the system dynamics transitions into a full period-1 oscillation through intermittency. In the second bifurcation (1200 K ≤ T ≤ 1400 K), the system shifts from a limit cycle state back to a combustion noise state. The complex coupling mechanism between injectors is further elucidated through frequency spectrum results of radial velocity and temperature near the initial shear layer in the wakes of different injectors, especially the symmetry-breaking response between different injector jets. The analysis of snapshots and flame index also reveals the spatiotemporal evolution of combustion flow fields, specifically highlighting vortex dynamics, heat release, and combustion modes that potentially contribute to thermoacoustic instability.

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