Nonlinear Dynamics of Wave Mode Transition in a Hydrogen-Fueled Rotating Detonation Engine

We present a nonlinear dynamical analysis of wave mode transition in a hydrogen-fueled rotating detonation engine (RDE) combustor based on high-fidelity simulations validated against experiments from the Air Force Research Laboratory. The simulations capture the transition from a sustained single detonation wave to a sustained double co-rotating wave structure when the fuel and oxidizer mass flow rates are varied while maintaining a global equivalence ratio near unity. The predicted detonation wave frequencies are in close agreement with experimental data: 3.95 kHz (CFD) vs. 3.69 kHz (experiment) for single-wave mode, and 7.73 kHz vs. 7.37 kHz for the double-wave mode, with errors under 7%. To characterize the nonlinear dynamics during this mode transition, we analyze pressure time series extracted from several numerical probes placed along axial and azimuthal directions within the combustor. Using time-delay embedding, we reconstruct the phase-space dynamics and compute nonlinear invariants such as Poincaré sections, correlation dimension, and Lyapunov exponents. Preliminary results indicate an apparent transition from periodic to quasi-periodic or low-dimensional chaotic behavior as the second detonation wave is established within the combustor, suggesting that detonation mode bifurcation is governed by nonlinear interactions between pressure waves, fuel-air mixing, heat release, and combustion dynamics. These insights can inform the design of more stable and efficient RDEs by enabling control over wave mode transitions and improving combustor operability.