Bistability and triggering in a thermoacoustic engine: A numerical study

Abstract

Although bistability and triggering in a thermoacoustic engine have been observed experimentally in the literature, the underlying physics behind these nonlinear phenomena is not well understood. In this paper, computational fluid dynamics (CFD) simulations of the bistability and triggering phenomena inside a quarter-wavelength standing-wave thermoacoustic engine (TAE) are presented. First, the dynamic/acoustic and heat transfer/hydrodynamic characteristics of the TAE are examined through simulations. Numerical results are validated against theoretical predictions based on linear thermoacoustic theory. Secondly, we focus on the bistable/two-valued zone (so-called “hysteresis loop”) and thermoacoustic triggering in the TAE. CFD results demonstrate that there are two critical temperatures which determine the stability of a thermoacoustic system. Self-sustained acoustic oscillations cannot occur at a hot-end temperature less than the lower critical temperature (so-called “damping temperature”) and must occur at temperatures above the upper critical temperature (so-called “onset temperature”). In between, the system may either be in the quiescent state or in limit-cycle oscillations, and an external acoustic pressure disturbance may induce the oscillations to commence. The smaller the hot-end temperature, the larger is the external disturbance required to initiate instability. Bistability and triggering, which cannot be explained by linear theory, are further interpreted from both nonlinear dynamics and energy balance viewpoints by conducting bifurcation/phase space analyzes and examining the simulated temperature fields. The research work in this study provides useful guidelines for reducing the temperature difference for thermoacoustic instability, and thereby the quality of low-grade heat source a TAE can utilize.