Justifying performance of thermo-acoustic Stirling engines based on a novel lumped mechanical model

This paper presents a novel lumped mechanical model incorporating modern control theory to investigate performance and startup condition of thermo-acoustic Stirling engines (TASEs). Although different well-defined mathematical approaches have been devised to design free piston Stirling engines (FPSEs), however, such important analytical methods cannot be directly applied to the TASEs as they are complex fluid systems. Accordingly, a purely mechanical analogous model of TASEs is first presented and then, the similarity of TASEs to FPSEs is revealed. Additionally, manipulating the extracted dynamic equations of the new mechanical analogous model shows that the TASEs are physical regulators from the viewpoint of modern control theory. Indeed, the mentioned idea is a significant outcome of this work and thus, the powerful design techniques of control engineering can be effectively used to simplify the design procedure of the TASEs. Next, the influence of design parameters such as resonator length, inertance length, pulse tube length, hot and cold gas temperatures, mean pressure, connecting tube, and compliance on the real and imaginary parts of the dominant poles of the physical closed-loop system is investigated based on the control principles. Besides, a quality index is introduced to evaluate resonance phenomenon in the TASEs. Finally, validity of the proposed mathematical model incorporating the control-based design technique is affirmed using practical data of three prototype engines.