Study on the delayed response characteristics of a rotating detonation wave under continuous inlet adjustment

The response of rotating detonation waves (RDWs) to continuous geometric adjustment is key to achieving controllable operation of a rotating detonation engine (RDE). Existing research lacks understanding of the dynamic response during continuous geometric modulation. Accordingly, this paper conducted a study on the delayed response characteristics of the RDW in the configuration with continuous adjustment of the inlet throat area (A_3.1). A continuously adjustable inlet system, combined with an optical signal-based algorithm for extracting instantaneous RDW characteristics, enabled accurate measurement of the RDW velocity. The study elucidated two types of delayed response of the RDW to changes in the exit area/inlet throat area (A₈/A_3.1): actuation hysteresis and amplitude hysteresis. It defined the initial response delay (Δt₁), the total adjustment delay (Δt₂), and the velocity deficit (Δv). Their underlying mechanisms were characterized. Through cold flow/detonation state comparative experiments and nonlinear dynamic analysis, it was revealed that the delayed response is physically a serially coupled multiphysics process dominated by system stiffness. Further investigation revealed that the delayed response behavior is jointly determined by the equivalence ratio (Φ), the adjustment direction, and the initial state. Φ dominates the system stiffness by influencing the RDW strength. The adjustment direction introduces asymmetry in the delayed response: the path with increasing A₈/A_3.1 results in a larger Δv, whereas the path with decreasing A₈/A_3.1 leads to longer Δt₁ and Δt₂. Adjustments initiated from a high-intensity state exhibit a stronger tendency to maintain homeostasis. The delayed response patterns and quantification methods elucidated in this study provide a critical foundation and essential data support for the design of RDE control laws.