A new non-ideal second order thermal model with additional loss effects for simulating beta Stirling engines

In this paper, comprehensive governing differential equations of Stirling engines have been developed by coupling the effect of gas leakage through the displacer gap, gas leakage into the crank case and the shuttle heat loss into the traditional model. Instantaneous pressures and temperatures of the working fluid in the engine were evaluated at same time step. The present model was deployed for the thermal simulation of the GPU-3 Stirling engine and the obtained results were robustly compared to experimental data as well as results from previous numerical models. Then, parametric studies were conducted to assess the impact of geometrical and operating parameters on the performance of Stirling engines working with helium or hydrogen. Results suggest that the modifications made in this model led to better accuracy and consistency in predicting the experimental data of the prototype engine at all speeds, compared with most previous models. It was found that there exists a minimum dimensionless gap number, for every engine pressure below which mass leakage into the compression volume may not impact the brake power and energetic efficiency of the engine. In addition, an optimum mean effective pressure was found for maximum energetic efficiency of the engine. This optimum value is higher for helium gas than for hydrogen gas. Further results indicated that the brake power and energetic efficiency of the prototype Stirling engine can be significantly improved by 30% and 18%, respectively, provided that the heater temperature is raised to 850 °C while the cooler temperature is reduced to 0 °C