Experimental investigation of nonstationary phenomena in a hollow rotating detonation combustor using wavelet analysis techniques

Rotating detonation engines (RDEs) potentially offer an increase in total pressure across the combustor and significantly increased combustion speed. Advanced analysis tools are needed to comprehensively evaluate the complex, unsteady operation associated with RDE combustion behavior. One of the current analysis challenges of unstable modes is nonstationarity. Many traditional techniques rely on the assumption of a stationary signal such as the Fourier transform, spectral proper-orthogonal decomposition, etc. These techniques work well for stable cases exhibiting stationarity; however, they begin to unravel and introduce ambiguity for nonstationary signals. It stands to reason that analysis of nonstationary signals should be analyzed as such. The continuous wavelet transform (CWT) is effective for extracting a wide range of frequencies from nonstationary signals and has been successfully applied to the fields of geophysics, medicine, turbulence, combustion, and others. Two signals may be cross-compared with the cross wavelet transform (XWT) to ascertain phase angle and common power. A working summary of wavelets and affiliated analysis techniques is presented, then applied to experimental data of a hollow rotating detonation combustor (H-RDC). The results of these methods demonstrate high spectral–temporal resolution for characterizing nonstationary phenomena, including the evolution of two thermoacoustic modes corresponding to the first and second tangential acoustic modes, during the deflagration-to-detonation transition (DDT). Using wavelet analysis techniques, in conjunction with classical methods, an amplitude-modulated and frequency-fluctuating behavior is revealed from pressure data and correlates with a phase shift in acoustic pressure between the air plenum and combustion chamber. Novelty and significance statement Like traditional deflagrative combustors, understanding nonstationary modes of operation in RDEs is crucial for development of the device. To date, wavelet analysis techniques have not been thoroughly implemented for analysis of RDEs, and further, nonstationary modes of the unconventional hollow architecture are not well understood. This work aims to broaden the understanding of nonstationary operating modes by applying wavelet-transform techniques to experimental RDE data. Power, common power, and phase lag of pressure data are all determined with wavelet techniques and shown to be insightful analysis tools for nonstationary RDE operations such as the DDT and self-suppression modes.