基于热动电全耦合分析的自由活塞斯特林发电机三阶动态模型研究

[Background] The Free-Piston Stirling Generator (FPSG) is regarded as a key enabling technology for deep space exploration, owing to its high efficiency, extended lifespan, and superior reliability. However, owing to the absence of rigid mechanical constraints, the FPSG operates as a self-excited oscillation system governed by intricate non-linear interactions among gas dynamics, mechanical inertia, and electromagnetic forces. Consequently, numerical simulation of its performance is complicated, where a trade-off between computational efficiency and the precision required to resolve transient coupling effects is rarely achieved by existing methods. [Purpose] This study aims to develop a high-fidelity analytical framework for FPSGs to resolve existing deficiencies in transient performance prediction and clarify the thermal-dynamic-electric coupling mechanism. [Methods] Firstly, governing equations based on quasi-one-dimensional unsteady flow assumptions were utilized to resolve mass, momentum, and energy conservation within the thermodynamic cycle. Then, mechanical dynamics were derived via rigid body kinetics, while the electromagnetic subsystem was modeled incorporating non-linear parameters. Subsequently, solution of this stiff, high-dimensional system was executed using a high-order Runge-Kutta-Fehlberg (RK45) numerical integration algorithm. Finally, model validity was substantiated through comparison with a 100 W-class prototype to obtain P-V (Pressure-Volume) indicator diagram and output power. [Results] Simulation and verification results indicate the agreement between the calculated P-V indicator diagrams and reference data was indicated by the simulation results. Specifically, an indicated power of 142.42 W is reported against a reference of 132.48 W, representing a relative deviation of approximately 7.5%. With the system frequency maintained at 29.4 Hz, a phase angle of 77.3° is observed between the displacer and power piston. Additionally, complex cyclic behaviors, including working fluid compressibility, transient pressure wave propagation, and non-linear electromagnetic damping, are effectively captured. [Conclusions] The complex transient response and energy conversion characteristics of the FPSG are effectively predicted by the developed third-order dynamic model proposed in this study. Through the rigorous resolution of multi-physics coupling, a robust theoretical framework is provided for the design, performance prediction, and optimization of nuclear power conversion systems intended for deep space exploration.