Working mechanism and characteristics of gas parcels in the Stirling cycle

Highlights: • A third-order model of a self-made engine with a relative error • The working mechanism of gas parcels is analyzed from the Lagrange perspective. • The thermodynamic cycle of gas parcels is quantitatively described. • A β-type prototype engine is manufactured, tested and numerically simulated. The Stirling engine is a promising device to efficiently utilize external heat sources for various purposes. The understanding of the thermodynamic cycle of the gas parcels present in the Stirling engine is vital to its design and optimization. In this paper, a one-dimensional transient numerical model for Stirling engines is developed. A system for a β-type prototype was built and investigated by using both experimental and numerical methods. The relative error between the experimental and theoretical results measures <6%. A post-processing method was further defined to track the gas parcels. Moreover, the Lagrange perspective was introduced to quantitatively describe the thermodynamic cycles, capturing the working mechanism of the gas parcels. The findings show that all the gas parcels produce periodic heat-to-work conversions despite their different thermodynamic cycles. The relay-style trend of adjacent gas parcels was observed in both the pressure-specific volume and the temperature-specific entropy diagrams. Finally, the thermodynamic processes of different volume phase angles were compared, showing that the specific work increases from 105.5 kJ/kg to 242.8 kJ/kg when the phase angle changes from 30° to 90°. This work provides a mesoscopic view to understand the working mechanism and build a solid foundation for the optimization of Stirling engines.