As a continuation of earlier work on phase-wise flow-field dynamics in a disk-shaped rotating detonation rocket engine (disk-RDRE) Nejaamtheen et al., “Combined experimental and numerical analysis of flow-field evolution and wave number formulation in disk-shaped rotating detonation rocket engines,” Combust. Flame 282, 114515 (2025), this study applies spectral-modal analysis to clarify the underlying instability modes. High-fidelity, time-resolved pressure fields from a three-dimensional (3D) simulation are analyzed to track how detonation-driven structures evolve from ignition to a quasi-steady regime. The focus is on the onset of instability, the development of detonative tangential instability and the formation of a non-purely tangential limit cycle. Fast Fourier transform, short-time Fourier transform (STFT), dynamic mode decomposition (DMD), and proper orthogonal decomposition (POD) are combined to resolve frequency content, temporal evolution, and spatial mode shapes. STFT shows how discrete bands in the 7–50 kHz range are activated, broadened, and then settled into sustained oscillations. DMD provides growth rates and coherence, identifying weakly growing or near-neutral modes between about 12 and 30 kHz during the transition to instability. POD extracts the most energetic structures and shows how the flow shifts from mainly transverse patterns to mixed radial-tangential modes. In the later phases, both DMD and POD indicate a dual-modal state dominated by a first tangential-first radial (1T-1R) hybrid mode with nearly fixed phase offsets and stable frequency content near the detonation rotation frequency. This hybrid 1T-1R behavior is consistent with separate propane-nitrous-oxide disk-RDRE experiments on the same geometry, which report similar 11–13 kHz bands and wall-anchored detonation fronts. Overall, the results link modal dynamics with frequency signatures and provide a clearer physical basis for assessing and controlling detonation stability in disk-RDRE configurations.
Nejaamtheen et al. (Sun,) studied this question.