Cross-variable amplitude frequency coupling in complex turbulent thermoacoustic systems

The acoustic field dynamics (p′) in combustors with turbulent reacting flow transitions from low-amplitude chaos to high-amplitude self-excited periodic oscillations with increase in Reynolds number. This transition occurs via intermittency, characterized by bursts of high-amplitude periodic oscillations amidst epochs of low-amplitude chaotic fluctuations. Such a transition in the dynamics is due to the interactions between the hydrodynamics, acoustics, and combustion subsystems. We observe that high-amplitude bursts in p′ are accompanied by frequency modulation in heat release rate fluctuations (q̇′) during intermittency, and this interaction is substantial in the outer shear layer region of the combustor. We identify such regions of strong amplitude-frequency coupling using natural visibility graphs based on the time series of q̇′ at several locations in the flow field. Natural visibility graphs are efficient in capturing frequency modulations, and measures estimated from these graphs by conditional time-averaging during epochs of high- and low-amplitude p′ fluctuations quantify these modulations. Identifying such critical regions in the flow domain is essential to undertake smart passive control strategies for suppressing flow instabilities.