Assessment of frequency and stroke in three-stage liquid-piston thermoacoustic Stirling engines via a new approach: Analysis and experiment

This article introduces a new approach to assess the frequency and oscillation amplitude of three-stage liquid-piston thermoacoustic Stirling engines (TLTASEs). Such oscillators exhibit complex behavior due to their highly nonlinear dynamics and large oscillation amplitude. Thus, accurate prediction of the key parameters such as frequency and stroke is crucial for their performance optimization and stable operation. First, a new dynamic-thermodynamic lumped model justifying the system performance is presented and then, a novel analytical method is proposed to predict limit cycle characteristics. It is shown that the proposed analytical method simplifies the limit cycle analysis in TLTASEs and provides a general tool for understanding the complex dynamics of nonlinear harmonic coupled oscillators provided that the coupled oscillators are identical. The simulation results reveal that the proposed analytical method predicts the piston stroke with an error of 4.4 % while accurately estimating the frequency. Finally, to verify the mathematical model and analytical method, a prototype TLTASE is preliminarily tested. The piston stroke, gas pressure amplitude, and frequency are respectively measured as 0.08 m, 7 kPa, and 14.92 rad/s which are close to the analytical values of 0.09 m, 7.61 kPa, and 14.45 rad/s respectively. Consequently, the effectiveness of the proposed method is reaffirmed.