Optimization of geometrical parameters for Stirling engines based on theoretical analysis

► Optimization of phase angle and swept volume ratio of Stirling engine. ► Explain why β type engine produces highest shaft work and γ type the lowest. ► Explain why γ-type engine is capable of operating with low temperature difference. ► First attempt to optimize Stirling engine in terms of shaft work. This study is aimed at theoretical analysis of the effects of the geometrical parameters on the shaft work of the Stirling engines. The optimal combination of the phase angle and the swept volume ratio, that leads to maximization of the shaft work of the engine, is obtained under different specified conditions. Effects of the effectiveness of mechanism, the dead volume ratio, and the temperature ratio on the maximum shaft work of the engine as well as the optimal combination of the phase angle and the swept volume ration are evaluated. Theoretical analysis of the performance of three types of Stirling engines, α-, β-, and γ-type, has also been carried out, and a comparison in relative performance among these three types of engines is attempted. Results show that for the particular cases considered in this study, the β-type Stirling engine produces highest shaft work and the γ-type engine the lowest. In general, the γ-type engine must be very mechanism effective so as to deliver sufficient shaft work. However, among the three types of engines, the γ-type engine is most capable of operating with low temperature difference. On the contrary, the α-type engine is particularly not suitable for the applications with low temperature difference since its dimensionless shaft work is found to gradually vanish as the temperature ratio is increased.