Enhanced Analysis of Quasi-Periodic Rotating Detonation Rocket Engine Frequency Behavior by Means of Transformation to Rotating Frames

Rotating detonation rocket engines (RDREs) can exhibit a behavior known as galloping, in which spacing between consecutive denotation waves varies over time. This can result in quasi-periodic long-time behavior, which is significantly more difficult to analyze than periodic behavior. For certain classes of quasi-periodic spatio-temporal waves, we previously showed (Phys. Rev. E 106, 024607, 2022) that the frequency content depends in predictable ways on the frame in which the behavior is observed. Here, we analyze slightly noisy pressure fields from three-dimensional RDRE simulations and show that they exhibit this behavior. We obtain the relationships between the frequency content of the pressure field and the angular velocity of rotating frames in which the field could be analyzed, and use these relationships to show how rotating frames can be used to better extract frequencies. The data can then be analyzed in 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 benefits, 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 frames exist, and we discuss the potential advantages to be considered in selecting from among them.