Stabilization of thermoacoustic oscillators by delay coupling

This paper presents a numerical description of amplitude death in delay-coupled thermoacoustic oscillators. An oscillator is a gas-filled resonance tube with a temperature gradient. Delay coupling is introduced by hollow tubes that connect the oscillators. Thermoacoustic oscillators and their connecting tubes are modeled by linear acoustic equations. For them, two coupling methods are tested: single-tube and double-tube coupling. For single-tube coupling, amplitude death occurs when the connecting tube length is one-quarter or three-quarters of the wavelength of the oscillation frequency and when the tube diameter is greater than 62.5% of the resonance tube diameter. For double-tube coupling, amplitude death occurs with specific combinations of the tube lengths given by integer multiples of the half-wavelength. The required tube diameter is as small as 7.5% of the resonance tube diameter. Death regions for the double-tube coupling are verified from the experimentally obtained results. Comparison with the delay-coupled van der Pol oscillators highlights acoustic aspects of the double-tube coupling.