Equivalence ratio independence and dependence ranges of system responses for a nonlinear thermoacoustic oscillation in a Rijke tube

Thermoacoustic instabilities in a combustion system remains a challengeable problem in industry over decades. It usually involves with the nonlinear interaction between unsteady heat release and pressure fluctuations. The nonlinear oscillation excited by this interaction can be intense enough to result in combustion problems even severe damage of the engine. Therefore, it is important to understand the system response to various parameters. In this study, the system nonlinearity to equivalence ratio change was mainly focused on. A Rijke tube system with a premixed methane-air laminar flame was utilised to trigger the self-excited oscillations with varied equivalence ratios (Φ). The time-domain analysis methods including phase difference, Recurrence Plot (RP) and Recurrence quantification analysis (RQA) were applied to obtain the characteristics of system nonlinearities. Both Φ-independence and Φ-dependence ranges of system frequency responses have been discovered. The results of phase difference and recurrence analysis have also validated the finding of both ranges. The corresponding characteristics of system nonlinearity in both ranges have been investigated. The similarity among the systems in the Φ-independence range under the same burner position and methane flowrate can be highlighted from the system frequency response, phase difference and system dynamics. It is found that the phase difference analysis, RP and RQA utilised in this study are capable of investigating the nonlinearities of the self-excited thermoacoustic oscillation.