Using Frame Transformation to Enhance Analysis of Quasi-Periodic Rotating Detonation Rocket Engine Behavior*

Rotating detonation rocket engines (RDRE) often have quasi-periodic longtime behavior, which is significantly more difficult to analyze than periodic behavior because not all pairs of frequencies present are rationally related.  For certain classes of quasi-periodic spatio-temporal waves, we have previously shown (Phys. Rev. E 106, 024607, 2022) that the frequency content is dependent, in predictable ways, on the frame in which the behavior is observed.  We show that noisy pressure fields from RDRE simulations exhibit this behavior, and obtain the relationships between the frequency content of the pressure field and the angular velocity of the rotating frame.  Using these relationships, we show how rotating frames can be used to better extract the frequencies, by increasing the separation between very close frequency peaks.  Increasing this separation reduces spectral leakage, which is particularly desirable when the time series available are not long.  We are also able to identify rotating frame velocities in which the pressure field is temporally periodic.  This reduced complexity offers several benefits, one of which is that the behavior can now be fully captured in finite time, which is not possible for quasi-periodic behavior.