Nonlinear Coupled Dynamics of Pressure and Heat Release Rate During Wave Mode Transition In a Hydrogen-Fueled Rotating Detonation Engine

Abstract

In this study, we investigate the coupled dynamics of pressure and heat release during the transition from a single to a double corotating detonationwave in a hydrogen-fueled rotating detonation engine (RDE) combustor. We analyze azimuthally decomposed pressure and heat-release-rate fluctuations to characterize the nonlinear multiphysics interactions that govern instability growth and secondary wave formation. We employ high-fidelity simulation datasets validated against experiments for the present analysis. The axial distributions of statistics of fluctuating quantities show a progressive transition from coherent detonation dynamics to shock-controlled combustion. Further analysis is carried out in terms of the modal energies, time-frequency spectra, crossspectral coherence, thermoacoustic phase synchronization, and higher-order fluctuation statistics. The azimuthal modal energies of pressure and heat release reveal a clear redistribution of energy from the primary mode toward higher-order modes during the onset of wave splitting. Time-frequency analysis and modal coherence maps identify localized frequency locking and strong spatiotemporal coupling between pressure and heat-release-rate fluctuations. The time-lag analysis further shows that pressure fluctuations in the injector and annular wall regions systematically precede heat-release amplification near the detonation front, thus demonstrating a causal feedback mechanism responsible for secondary ignition and wave bifurcation. The combined modal, spectral, phase, and statistical diagnostics distinguish coherent detonation-driven turbulence from incoherent deflagration zones and provide predictive markers for the onset of wave-mode transition.