Amplitude death in ring-coupled network with asymmetric thermoacoustic oscillators and nonlocal time-delay interactions

This numerical study examines the pressure amplitude distribution, focusing on amplitude death, in a ring-coupled network of nonlocally coupled asymmetric thermoacoustic oscillators. Each decoupled self-excited thermoacoustic oscillator is modeled using the classical Rijke tube model. We investigate three configurations with asymmetric thermoacoustic oscillators: localized asymmetry, side-by-side asymmetry, and alternating asymmetry. Asymmetries are introduced through frequency detuning and heater power mismatching. Our study reveals that the configuration with alternating asymmetry induces the largest region of amplitude death compared to the other two configurations, where all originally self-excited oscillators become quenched in the network. The remaining energy of oscillations often concentrates at the two ends of the axis of symmetry. The region of amplitude death generally increases with the number of thermoacoustic oscillators and remains unchanged when the number of oscillators is sufficiently large (n = 8). The variation of the global average pressure amplitude predicted by the proposed model qualitatively agrees with previous experimental observations. In summary, we conclude: (1) reduced-order models developed from a dynamical system approach can provide a qualitative prediction of the system's pressure amplitude distribution, potentially offering useful information for avoiding operating parameters that lead to high-amplitude thermoacoustic oscillations in multi-combustor systems; and (2) introducing asymmetries into a ring-coupled network can potentially be leveraged to weaken self-excited oscillations in multi-combustor systems globally.