Investigation on the hysteresis behavior of a quarter-wavelength standing-wave thermoacoustic engine

Like many nonlinear dynamical systems, thermoacoustic engines (TAEs) exhibit hysteresis behavior in the amplitude of self-excited acoustic oscillations when the temperature gradient implemented across the porous material is first increased and then decreased gradually. This research studies the hysteresis of a quarter-wavelength standing-wave TAE that relies on a parallel plate stack to realize thermal-acoustic energy conversion. Computational fluid dynamics (CFD) is first employed to investigate the influence of stack parameters, such as stack gap and position, on the hysteresis behavior of the TAE. Following this, in analogy with the modeling of Rijke tubes, a simplified mathematical model of the TAE is developed to provide a qualitative interpretation of the hysteresis curves obtained from the CFD simulations. Finally, experimental tests are conducted to validate the presence of hysteresis in the TAE. Results show that in the bistable zone, the dynamic behavior of the TAE can be either linearly stable fixed points or limit cycles. An external pressure disturbance or energy sink can be applied to alter the dynamics of the TAE. There exist optimal values for the stack gap and position at which the lower and upper critical temperatures, as well as their difference, are minimized. At the optimal stack gap, the pressure amplitude reaches its minimum. However, as the stack is shifted toward the open end, the pressure amplitude gradually decreases, highlighting a trade-off between reducing the onset temperature difference and improving acoustic power generation. The present study gives deeper insights into the hysteresis phenomena reported in previous experimental studies, providing useful guidelines for reducing the critical temperature gradients for the excitation of acoustic oscillations in TAEs.