Forced Synchronization of Thermoacoustic Instability: Quasi-Periodicity Versus Intermittency Routes to Lock-In

To investigate the effectiveness of open-loop control in mitigating thermoacoustic instability in a model high-pressure, turbulent rocket combustor, this paper presents different synchronization routes to lock-in at two external sinusoidal forcing frequencies under dynamic systems theory. To achieve this, a full-scale three-dimensional detached eddy simulation is conducted with periodic forcing applied at a constant propellant mass flow rate to explore interactions between thermoacoustic instability (oscillating at [Formula: see text]) and external sinusoidal forcing (oscillating at [Formula: see text]). Additionally, a forced nonlinear universal oscillator based on the Duffing–Van der Pol (DVDP) model is developed to characterize synchronization dynamics. Results show that as the amplitude of the external forcing gradually increases ([Formula: see text]), at [Formula: see text], a quasi-periodic route to lock-in emerges; at [Formula: see text], an intermittency route to lock-in appears, with the amplitude reaching a minimum, indicating an optimal open-loop control strategy. The DVDP model qualitatively reproduces the quasi-periodic route to lock-in but fails to capture intermittency due to turbulence-induced stochasticity. Phase-locking and frequency-locking between acoustic pressure and heat release oscillations—driven by partially premixed combustion modes including premixed and diffusion flames—are identified as the key physical mechanisms underlying the bifurcation process under the open-loop control framework of thermoacoustic instability.