Theoretical solutions for power output of thermal-lag Stirling engine

•First study presenting theoretical solutions for power output of thermal-lag Stirling engine.•Instability analysis of the thermal-lag phenomenon is performed under various loading and friction conditions.•Amplitude and frequency shift under various loading have been derived. This study is attempted to present theoretical solutions for power output of thermal-lag Stirling engine. In this study, a dimensionless nonlinear dynamic model is built. Equation of motion of piston and energy equations for working gases in cold and hot sides are developed and solved by perturbation method. Emphasis of the study is focused on the instability of the thermal-lag phenomenon under various loading and friction damping conditions. Thus, dynamic behavior of the engine with or without friction damping is investigated. The critical curves that separate the stable and unstable zones are plotted. The onset of the thermal-lag oscillation under different loading conditions takes place only when the operating condition is located in the stable zone. The power output of the engine is then evaluated based on the theoretical solutions, and dependence of the power output on influential parameters is investigated. Furthermore, an amplitude equation and a frequency shift equation are presented, and the dynamic characteristics of the engine and the frequency shift can be determined by solving these two equations.