Free piston Stirling engine response to the change in displacer’s spring stiffness value

This study aims to deduce the effect of the displacer spring’s stiffness on the free piston Stirling engine (FPSE) performance. A combined dynamics and thermal model is developed and numerically solved without the need for linearisation using MATLAB SimulinkTM. The model takes into consideration the damping losses, pressure differences between the hot and cold spaces, collisions at stroke limits, losses due to flow in the annular clearance between the displacer and the cylinder’s wall, fluid mixing and the effect of dead volumes. The proposed model estimates the operating frequencies, strokes of displacer and piston, dead volume, average output power, compression ratio, and total conversion efficiency. It was found that the displacer’s spring stiffness has a significant effect on the engine’s performance. For a given engine there is an optimum range for the displacer’s spring stiffness that should be considered. Through the study, the stiffness value was changed gradually, and the engine’s performance and cycle were observed. The maximum effect obtained was increasing the output average power by about 132.4% when changing the displacer’s spring stiffness by 44.4% till the optimum value and then the average output power dropped afterwards. The output cycles and results are illustrated and discussed.