Derivation of coupling conditions of amplitude death in delay-coupled thermoacoustic oscillators

Amplitude death, meaning the stabilization of an unstable equilibrium state, appears in delay coupled oscillators even if the oscillators have the same frequency. In this study, we aim to stop thermoacoustic oscillations by the amplitude death induced by delay. Thermoacoustic oscillations in combustors of gas turbine engines cause serious damage to the engine. Development of the method for suppressing thermoacoustic oscillations is urgent necessity. Recently, the amplitude death in the thermoacoustic oscillators was demonstrated by using delay and diffusive couplings. The delay coupling was introduced by gas-filled tubes. The experimental death regions were compared with the delay-coupled van der Pol systems and qualitative agreement was achieved, but the acoustic feature of the connecting tube was not considered. For a full acoustical modeling of the coupled thermoacoustic oscillator, we modelled two thermoacoustic oscillators coupled by connecting tubes by the linear acoustic theory based on hydrodynamic equations. The amplitude death regions are described on the parametric plane of the tube length and diameter and the regions are compared with the experimental results. We report on the findings that the coupling by the two tubes with different length can achieve the amplitude death for smaller tube radius than single tube coupling.