Effect of damping coefficients on a free-piston Stirling engine under a constant power condition based on a thermodynamic-dynamic coupled model

The Free Piston Stirling Engine (FPSE) is a complex system, in which the transient behaviors of its thermal and dynamic characteristics are coupled. To examine the strong coupling system under constant heating power and evaluate the effect of damping coefficients on engine performance, prediction of the aforementioned characteristics is essential. To this end, this study develops an FPSE system model based on quasi-static thermodynamics and piston dynamics to determine the thermal performance of the working fluid and the dynamic behavior of the displacer and piston, and the model is validated on the Re-1000. Then, the model is applied to examine the influence of the damping coefficients of two pistons on reactor core heater temperature, power, efficiency, amplitude, frequency, and phase angle under constant power condition. The results indicate that the model can well capture the transient behaviors of thermal and dynamic characteristics at Re-1000. After 0.7 s, the engine reaches a steady-state operation. Under the constant heating power of 3000 W, the displacer and piston damping significantly affect the engine's performance. Four displacement damping coefficient points are specified, and the piston damping coefficient changes in the range of Cp = 500 similar to 1600Ns/m. As a result, the heater's stable working-point temperature changes from 590 K to 1060 K leading to an increase in indicated power from 1000 W to approximately 1500 W. The displacer and piston amplitudes show an increasing and decreasing trend respectively, with a decreasing trend in frequency and phase angle, but enhanced heat transfer performance. The dynamic-thermodynamic coupling model provides an opportunity to instantly calculate the open-loop response of the FPSE, which is a reference for future FPSE power-load matching designs.