Predicting performance and onset criteria of a three-stage double-acting thermoacoustic Stirling oscillator: Analysis and experiment

In this paper, a novel analytical approach is proposed to predict the performance and onset criteria of a three-stage double-acting thermoacoustic Stirling oscillator (TDTASO). First, a coupled dynamic-thermodynamic model justifying the behavior of TDTASO is presented, taking into account Schmidt's theory assumptions. Subsequently, the manipulation of the obtained governing equations reveals that the considered Stirling oscillator is a physical regulator system. Thus, the onset criteria, which are the necessary conditions for designing such oscillators, are assessed based on a new analytical method resulting from a regulator-like model. Accordingly, the onset temperature difference is predicted corresponding to different dimensions of the resonator section in the TDTASO. Next, the sensitivity of the TDTASO to the inconsistency of resonators' dimensions is investigated. The results show that increasing the length of the mismatched water column results in a higher frequency. Finally, a prototype TDTASO is constructed and experimentally evaluated. Accordingly, the oscillator frequency is measured 3.14 Hz corresponding to the onset temperature of 163 C and the resonator length of 0.52 m. The experimental data demonstrate the effectiveness of the proposed analytical scheme in predicting the necessary conditions for designing the TDTASO.