Parametric Optimization Analysis of a Free-Piston Stirling Engine

This paper presents an analysis to characterize the Free-Piston Stirling Engine (FPSE).The mathematical model of the thermodynamic processes of the FPSE, along with its mechanical dynamics, was proposed.Schmidt's assumptions, which include the thermodynamic behavior of an ideal gas, were used to develop the pressure equation and work per engine cycle.The pressure equation of the working fluid driving the engine was linearized before being incorporated into the system's equations of motion.The thermodynamic-dynamic model was arranged in state differential equation form.The effects of six parameters in the system's equations of motion-including the power piston mass, displacer mass, power piston spring stiffness, displacer spring stiffness, damping coefficient of a linear alternator, and hot-end temperature-on engine stability were studied and optimized.The optimum and stable operation of FPSE leads to quiet, smooth, and high efficiency.To investigate the optimal operation parameter, The eigenvalues of the state differential equation matrix were used along with geometric constraints and analysis of the piston stroke.The stability of dynamic components was computed through the eigenvalues and optimum strokes of both the power piston and displacer.The optimal stroke will allow the engine to achieve the highest work per cycle.The stable behavior of the FPSE prototype with ambient pressure was discussed.All six parameters were varied within their possible ranges to investigate the optimal parameter set for achieving maximum power.The maximum power of the engine at 0.125W is achieved at a power piston mass of 0.8 kg, displacer mass of 0.15 kg, power piston spring stiffness of 725 N/m, displacer spring stiffness of 850 N/m, alternator damping of 8.8 Ns/m and Th=850 K.