Underlying physics of limit-cycle, beating and quasi-periodic oscillations in thermoacoustic devices

Abstract

Under certain circumstances, self-excited acoustic oscillations inside thermoacoustic systems exhibit beating and quasi-periodic patterns, in contrast to constant-amplitude limit-cycle oscillations regularly studied in the literature. This paper explores the underlying physics of limit cycles, beating and quasi-periodicity in thermoacoustic devices from acoustic/vibrational and thermodynamic/hydrodynamic perspectives. Firstly, the acousto-mechanical coupling between the thermoacoustic engine and external load is investigated using a lumped element model, which is verified against a distributed parameter model. The effect of external load on the natural frequencies and mode shapes of intrinsic oscillation modes is inspected. Secondly, the thermo-acoustic coupling between the temperature and acoustic fields is analysed using a reduced-order network model based on the linear thermoacoustic theory. The effect of thermoacoustic core on stability of oscillation modes is studied. Finally, the steady-state behaviour of the device is examined by considering the unsteady linear decay/growth and nonlinear saturation processes. This study demonstrates that the linear mode selection decides whether the steady state is static (quiescent) or dynamic. Apart from linear mode selection, the dynamic steady-state responses are also affected by nonlinear mode competition during the saturation process. Simultaneous excitement of oscillation modes at different external loads may lead to distinctively different steady-state waveforms including beating and quasi-periodicity. Discussions on the steady-state energy transition/conversion indicate that, to improve the performance of the thermoacoustic device, excitation of the oscillation mode whose frequency is close to that of the external load is encouraged. It is suggested that ultra-compliant transducers should be employed for better acoustic power extraction.