Reflections on Free-Piston Stirling Engines. Part 1. Cyclic Steady Operation

In spite of the conceptual simplicity, the design of the free-piston Stirling engines (FPSEs) is made difficult by the necessity to accurately foresee the effect of the various geometric, dynamic, and thermodynamic variables on their behavior. This paper describes a fully developed mathematical model able to characterize these machines taking into account all of the relevant physical aspects involved, including the casing motion. A closed-form solution of the governing equations is used, together with a theorem developed by the authors to derive a basic criterion for the FPSE cyclic steady operation. Because this criterion is expressed in an analytical form as a function of the different variables involved, it is possible to choose the engine design parameters to ensure a steady periodic state. The developed model may be used not only for design purposes but also to simulate theoretically the dynamic behavior of a built engine.