Multi-objective optimization of a four-cylinder free-piston Stirling engine for deep-sea nuclear power systems based on energy and exergy analysis

Double-acting free-piston Stirling engine (DAFPSE) presents a potential solution for deep-sea nuclear energy conversions, with its closed-cycle configuration, low vibration, and minimal maintenance. However, studies focusing on its design and multi-objective optimization remain scarce, particularly those considering the exergy efficiency and power density. In this study, a mathematical model based on energy and exergy analysis was established to design the Stirling engine, investigating the effects of structure and operating parameters on engine performance. Results revealed that the exergy efficiency decreased with larger dead volume ratios but increased with higher regenerator effectiveness, owing to enhanced heat recovery and reduced entropy generation. Specifically, exergy efficiency increased by 116.52% as the regenerator effectiveness increased from 0.2 to 0.8. Increasing hot end temperature enhanced exergy efficiency at low dead volume ratios, while excessive entropy generation at higher dead volume ratios led to a reduction. Additionally, elevated engine speed and pressure increased entropy generation as a result of larger temperature differences and flow resistance. A multi-objective optimization based on parameter sensitivity analysis was carried out to optimize power density, thermal efficiency, and exergy efficiency. The optimal solution achieved a Stirling engine with a power density of 8.85 MW/m 3 , exergy efficiency of 33.71%, and thermal efficiency of 22.04%. This optimized design, which balances high power density with thermodynamic efficiency, provides a practical and valuable reference for the development of compact, high-performance energy conversion systems suitable for the stringent space and weight constraints of deep-sea nuclear power applications.