Using Rotating Reference Frames to Manipulate Rotating Detonation Rocket Engine Frequency Spectra, Including Transformation of Temporal Quasi-Periodicity to Strict Periodicity

Rotating detonation rocket engines (RDREs) can exhibit a behavior known as galloping, in which spatial gaps between consecutive denotation waves vary over time. This can result in quasi-periodic long-time behavior, which is significantly more difficult to analyze than periodic behavior. We use the fact that, for certain classes of quasi-periodic spatio-temporal waves, the frequency content depends in predictable ways on the frame in which the behavior is observed. We analyze slightly noisy pressure fields computed in three-dimensional RDRE simulations and show that they exhibit this behavior. Relationships between the frequency content of the pressure field and the angular velocity of rotating frames in which the field could be analyzed are obtained, and these relationships are used to show how rotating frames of analysis can be selected and used to render the pressure field time-periodic and to better extract frequency information. The data can then be analyzed in rotating reference frames for which separation between close frequency peaks is significantly increased, which reduces uncertainty (e.g., due to spectral leakage) in determining peak frequencies. We also identify rotating-frame angular velocities in which the pressure field is temporally periodic. This reduced complexity offers several advantages, one being that the behavior can now be fully captured in finite time, which is not possible for quasi-periodic behavior. A countably infinite number of such rotating reference frames exist, and we discuss the potential advantages to be considered in selecting from among them.