Stability evaluation of a free-piston Stirling engine using linear dimensionless models and stability curves

Abstract

A free-piston Stirling engine (FPSE) is a dynamic type of Stirling engine that uses springs to drive the piston and displacer. FPSEs differ from traditional Stirling engines in that the phase, stroke, and operating frequency of the piston and displacer cannot be directly determined by its driving mechanism. Therefore, determining the operation criterion of FPSEs is critical. This study investigated the operation criterion of FPSEs by using a theoretical model. The displacement of the piston and displacer was predicted using equations of motion. The pressure forces exerted on the piston and displacer from the working fluid were established using Schmidt’s assumption. The proposed model was simplified by introducing 13 dimensionless design parameters. The equations of motion were linearized, and their eigenvalues were obtained and used to identify the operation criterion and operating frequency. The stability curve and operating frequency were plotted in the temperature ratio–pressure force ratio domain. The operation region of FPSEs was then determined and evaluated under various amounts of spring stiffness and various damping coefficients. A prototype FPSE was developed and tested in parallel to validate the model. The results revealed a suitable charged pressure region for starting the FPSE. The FPSE could operate under a minimum heating temperature when the charged pressure was at an optimum value. Both the pressure force and spring force exerted on the displacer were in the same order. The operating frequency was close to the natural frequency of the displacer, with a difference of ± 8 %. The experimental results indicate that the proposed FPSE can start at a heating temperature of 125 ℃ with a charged pressure of 3 bar. By using the stability curve, the stability of FPSEs could be analyzed systematically. The proposed method can be used to design other FPSEs.