Black-Box Modeling of Rotating Detonation Combustors and Their Injector Plena Coupling

The phenomenon of onset time after ignition in atmospheric and backpressurized rotating detonation combustors is dealt with in the current Paper. By altering the airflow and fuel flow rates, plenum supply pressures, and the backpressure, the rotating-detonation-combustor/plenum coupling is modeled as a black-box system by training a single-input/single-output (combustor pressure dynamics and plenum oscillations, respectively) autoregressive output and exogeneous input model with 0.2 s of experimental data and validating it with the next 0.15 s of measured values. The simulated data are seen to match the experimentally observed pressure oscillations to a reasonable degree within a 95% confidence interval in magnitude and also capture the main detonation frequencies accurately across multiple operating modes. The air plenum is found to be a lower-order system that can be predicted well using three poles and two zeros, whereas preliminary analysis carried out here suggests that the fuel plenum is of a much higher order requiring at least 80 poles and 30 zeros. The onset time for the studied backpressurized operation is found to be dictated by the settling time of the air plenum obtained from its impulse response, whereas such a congruence does not exist for atmospheric rotating detonation combustors. For the latter, the onset time seems to be correlated to decreasing fuel supply pressures. Frequency response plots of the air and fuel plenum when subjected to the detonation propagation in the combustor shows the air plenum to behave like a bandpass filter allowing the detonation frequency to pass through with the highest amplitude. The fuel-plenum/combustor coupling, on the other hand, is seen to behave like a comb filter, alternatively damping and strengthening certain phases, for the single test modeled. This is attributed to the fuel plenum behaving like a reverberation chamber that always retains the memory of the initial detonation impulse.