Interaction between acoustics and flame dynamics in a multi-element liquid rocket engine: Mode switching via quasi-periodic oscillation

This study presents the first numerical evidence of mode switching via quasi-periodic oscillations in a self-excited thermoacoustic system—model multi-element liquid rocket combustor burning methane and hydrogen peroxide—by varying the global equivalence ratio (1.7 ≤ ϕ ≤ 0.3). We employed a full-scale, three-dimensional compressible Detached Eddy Simulation in OpenFOAM, coupled with the partially stirred reactor turbulent combustion model, and modeled chemical reactions with a global two-step reaction mechanism to account for finite-rate chemistry. The methane mass flow rate is systematically reduced to explore three main aspects: (1) dynamical bifurcations in the thermoacoustic system, (2) the coupling between pressure and the combustion fields, and (3) the evolution of flame dynamics, including mixing and combustion modes. Results reveal multiple bifurcations and mode switching. For 1.7 ≤ ϕ ≤ 0.5, the system shows simple period-1 limit cycle oscillations dominated by the first longitudinal (1L) acoustic mode. As ϕ decreases to 0.3, the system transitions to a low-amplitude limit cycle state dominated by the second transverse (2T) acoustic mode. At ϕ = 0.4, interactions between multiple acoustic modes (1L, 2T) and non-acoustic mode induce a quasi-periodic state with three periods. Frequency-locking is identified as the mechanism driving mode switching, and the spatial distribution of premixed and diffusion flames, analyzed through the Flame Index, is shown to be critical in this process.