Evolution dynamics and instability mechanisms of four-wave collisions in rotating detonation engines

Abstract

This study presents the first systematic investigation of instability mechanisms in four-wave collision regimes of rotating detonation engines (RDEs), within a methane/oxygen-enriched air ($30\text{\%}{O}_2$, $50\text{\%}{O}_2$) annular combustor. Compared to two-wave collisions, four-wave collisions exhibit inherently unstable wave symmetry and heightened sensitivity to inflow variations: elevated oxygen enrichment, equivalence ratio, and mass flow rate induce detonation strength imbalance, driving progressive transitions from symmetric four-wave collisions with stationary collision points to inducing collision-point migration (CPM), asynchronous behaviors (Async 4CR), and eventual single-wave dominance. The Async 4CR regime is uniquely characterized by subharmonic components at half the dominant frequency, originating from temporal offsets between successive wave collisions. Its unstable transitions to single-wave modes involve amplified upstream pressure feedback and elevated wall temperature growth rates. To quantify these instabilities, an analytical framework combining pressure peak-interval calculation and auto-correlation was developed to correlate periodic peak bifurcation and CPM dynamics. A linear model linking pressure peak-interval to angular CPM deviations was established based on near-constant CPM velocities, enabling single-sensor tracking of time-resolved CPM trajectories. The nonlinear and stochastic nature of CPM was revealed, featuring arbitrary migration directions, diverse maximal deviation angles (20–45°), and irregular periods (5–39 ms). The model remains valid under temporally oscillating fuel inflow, capturing transiently amplified CPM angles and reduced detonation stability during fuel flow rise. These findings reveal the complex instabilities and mode evolution patterns of four-wave collision regimes in RDEs, critical for advancing mode control and evaluating RDE performance.

Novelty and significance

(1) This study resolved typical CPM patterns during mode evolutions associated with four-wave collision instabilities. Unstable asynchronous collision regimes unique to four-wave collision systems were identified for the first time. (2) The developed linear model enables quantitative reconstruction of time-resolved CPM trajectories through peak bifurcation analysis of easily-accessible single-sensor pressure, offering direct extensibility to two-wave collisions and other high-frequency signals. (3) The stochastic nature of CPM driven by nonlinear detonation dynamics was underscored, while providing the experimental evidence on the destabilizing effects of time-varying oscillating inflow.