Relaxation Oscillation Property of Combustion Instability in a Cavity-Stabilized Supersonic Combustor

Periodic flame flashback is a prominent manifestation of combustion instability in scramjet combustors, yet its underlying dynamic mechanism remains insufficiently understood. In this study, the oscillatory behavior of flame flashback in a cavity-based supersonic combustor is investigated from the perspective of nonlinear dynamic systems. Synchronized measurements of combustor pressure and flame-front position were obtained using high-speed [Formula: see text] chemiluminescence imaging and dynamic pressure diagnostics. By reconstructing the system trajectory in a two-dimensional phase space defined by flame-front position and its temporal derivative, a stable limit cycle is identified, indicating the presence of a self-sustained periodic oscillation. Quantitative analysis reveals a pronounced separation between fast and slow temporal processes (time-scale ratio of approximately 5). The resulting phase-space trajectory exhibits an approximately rectangular geometry composed of slow evolution branches connected by rapid transitions, which is a characteristic feature of relaxation oscillations. Using singular perturbation theory as an interpretative framework, the oscillation cycle can be understood as an alternation between two quasi-steady combustion modes—jet–wake stabilization and cavity-stabilized combustion—linked by rapid flashback and blowoff events. Further comparison with the classical Lienard oscillator shows strong geometric similarity in phase-space structure, supporting the classification of the observed phenomenon as a step-type relaxation oscillation. Additional experiments at a lower equivalence ratio demonstrate that the same dynamic structure persists under different combustion intensities, indicating a degree of universality of this slow–fast dynamic mechanism in supersonic combustion instability.