Distinguishing harmonic behavior of longitudinal resonant combustion in a variable geometry model rocket combustor

Throughout the study of high frequency combustion instability in a single element Continuously Variable Resonance Combustor (CVRC), the excitation of the fundamental longitudinal mode is closely followed by the excitation of higher harmonic modes. In an attempt to establish a heuristic relationship between the appearances of the fundamental mode and its harmonics, several unstable fixed geometry and variable geometry tests from the CVRC are analyzed through traditional Fourier-based methods and alternative signal processing methods such as wavelet analysis and Instantaneous Frequency (IF) Analysis from PC Signal Analysis. Early results led to the conclusion that traditional Fourier-based analysis provides believable and consistent results for the first three modes. However, Fourier analysis is sensitive to effects from non-sinusoidal waveforms. Further work using manufactured signals with both sinusoidal and steepfronted waveforms established that it is unclear which parts of the calculated harmonic signals are data artifacts and which are true signal. Supplementary assessment of IF Analysis and the traditional Fourier-based analysis explored the applicability of each method, the inherent data artifacts, and distinguishing behavior between the experimental data and those data artifacts. The results obtained from the IF Analysis provide good agreement with the traditional Fourier-based analysis, though one uses FIR filters and the other uses IIR filters. The validity of the results is sensitive to the settings chosen for these filters. It is shown that harmonic modal content exists in the CVRC, but it is also shown that the current results include indistinguishable Fourier artifacts. Both methods are sensitive to the sinusoidal assumption and cannot correctly interpret steep-fronted waveforms. This supplementary assessment has shown that IF Analysis is no worse than traditional Fourier-based analysis, but it fails to provide additional useful information. Qualitative modal behavior is distinguishable from the experimental data, including the sequential excitation of modes and the increasing growth rate with increasing mode number. However, quantitative results such as the growth rate or modal amplitude have been shown to be unreliable. The acoustic wave assumption is supported by the standing wave behavior observed in CVRC, specifically the decreasing amplitude of a mode near its equivalent pressure node location and the relative phase between modal signals on either side of its equivalent pressure node. However, the shock-like wave assumption has not been completely disproved. Additional work needs to be done with wavelet analysis using steep-fronted wavelet shapes to assess the potential steep-fronted waveform