In longitudinal combustion instability, spatial-temporal coupling between unsteady heat release and resonant acoustic modes of the chamber leads to rapidly growing pressure oscillations at frequencies corresponding to chamber acoustic modes. Growth to limit cycle amplitude is rapid and multiple harmonic modes are seen within 5 to 15 ms, creating the need for a method to reliably and repeatably calculate growth rates and relative onset times of the multiple modes that are observed. Experimental data from the Continuously Varying Resonance Chamber (CVRC) offers the chance to investigate physical relationships between the modes of unstable combustion in a single element model rocket combustor, here using decomposed peroxide and gaseous methane at equivalence ratio of 0.8. Several signal analysis methods are reviewed, including wavelet analysis and the oscillation decrement, with the conclusion that Fourier-based band pass filtering combined with a statistical noise threshold is the best of the reviewed methods for this application based on ease of use, time resolution, added user bias to the data, and consistency across test cases. Results confirm the sequential onset of harmonic modes once the fundamental mode is excited. Furthermore, observed growth behavior for the second and third modes is nearly indistinguishable from each other in both fixed and variable geometry tests.
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