Spectral Analysis of Wave Mode Transition in a Hydrogen-Fueled Rotating Detonation Engine

Rotating detonation engines (RDEs) exhibit complex azimuthal wave dynamics whose transitions due to changes in inflow boundary conditions strongly influence combustor stability and performance. In this study, we analyze the spatio-temporal evolution of the pressure field during a wave-mode transition from a single-wave detonation front to a co-rotating two-wave detonation in a hydrogen-fueled RDE using Unsteady Reynolds-Averaged Navier-Stokes simulations with finite-rate chemistry. We examine temporally evolving pressure from azimuthally and axially distributed probes, which are decomposed using spectral analysis, azimuthal Fourier transforms, and short-time Fourier transforms. We analyzed time-resolved, band-integrated modal energies for the dominant modes corresponding to single and double wave structure to quantify modal competition during the transition. The energy ratio corresponding to the two modes reveals a temporal and downstream-propagating switching front, indicating a convective reorganization of the modal dominance. This transition coincides with a marked reduction in the intensity, peak amplitude, and skewness of the pressure fluctuations, providing statistical evidence of a shift from detonation-driven to oblique-shock-dominated dynamics. These results establish a direct quantitative link between azimuthal mode competition and axial flow transitions in RDEs.