A new thermal model based on polytropic numerical simulation of Stirling engines

• A new numerical polytropic model was presented for Stirling engine simulation.
• A methodology was given for determining the average polytropic indexes.
• Various power and heat losses were integrated in the numerical model.
• The new model predicted thermal performance of the engine with higher accuracy.
• Effect of the engine parameters on polytropic indexes was surveyed.

The new numerical thermal model based on polytropic expansion/compression processes was developed for predicting thermal performance of Stirling engines. In this regard, differential governing equations of early adiabatic model of Stirling engines were modified to consider polytropic heat transfers of the working fluid to the surrounding through expansion/compression cylinder walls. Therefore, adiabatic expansion/compression processes of the early adiabatic model were substituted with polytropic expansion/compression processes in the new thermal model. In order to increase accuracy of the thermal model, various loss mechanisms including effect of mass leakage from working to buffer spaces and heat leakage from expansion to compression spaces, due to thermal conductivity (shuttle heat transfer effect) of the displacer, were implemented in basic differential equations of polytropic analysis. In addition, in a similar manner to the early simple analysis, effect of non-ideal heat recovery of the regenerator and hydraulic pressure drop were considered in heater, cooler and regenerator. Also, magnitude of the piston back pressure was corrected in terms of piston velocity using the principle of finite speed thermodynamics (FST) and mechanical friction between piston and cylinder was taken into account in the new thermal model. On the other hand, longitudinal heat conduction between the heater and cooler through the regenerator wall was modeled as an additional loss mechanism. Finally, the new model called polytropic analysis of Stirling engine with various losses (PSVL) mechanisms was applied to a prototype Stirling engine, namely GPU-3 Stirling engine, and the obtained results were evaluated through comparison with previous thermal models and experimental results. Based on the new PSVL model, the output power and thermal efficiency of the GPU-3 engine were predicted with +14.34% and +3.14% (as a difference), respectively.