Application of the Continuous- and Cross- Wavelet Transforms to an Experimental Hollow Rotating Detonation Engine

Rotating detonation engines (RDEs) potentially offer an increase in total pressure across combustion, as well as a dramatically increased speed of combustion. These inherently unsteady devices necessitate advanced analysis tools to better understand the complex physical phenomena present throughout them. One technique is the continuous wavelet transform (CWT). The CWT was designed for extraction of 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 compared with the cross wavelet transform (XWT) where phase angle and cross wavelet power can be ascertained. A working summary of wavelets, the CWT, and the XWT is presented then applied to experimental data of a hollow rotating detonation combustor (H-RDC). The results of these methods show a high spectral-temporal resolution of nonstationary phenomena such as the deflagration-to-detonation transition (DDT).