Optimal cross-sectional area ratio between porous material and resonance tube for the onset of self-excited oscillations in standing-wave thermoacoustic engines

Thermoacoustic engines (TAEs) are heat-driven devices that rely on a temperature gradient in the porous material to initiate acoustic oscillations in the resonance tube. This study investigates the optimal cross-sectional area ratio between the porous material and resonance tube for the onset of self-excited acoustic oscillations in standing-wave TAEs. Experiments are conducted and numerical models are developed to explore the onset behavior of thermoacoustic systems. It is found that the system-level reduced-order network model can predict the onset temperature and frequency with high accuracy. There is an optimal area ratio between the porous material and resonance tube for achieving the lowest onset temperature. For the single-stage and double-stage TAEs with ambient air as the working fluid in this study, the lowest onset temperature of 79 K and 87 K are obtained with optimal area ratios being 3.5 and 5.1, and r_h/δ_k (r_h and δ_k are the hydraulic radius and thermal penetration depth) being 1.54 and 1.62, respectively. The research outcomes in this work will provide valuable guidance for the construction of low-onset-temperature thermoacoustic systems for low-grade heat recovery or energy harvesting purposes.