Stability analysis of thermal-lag Stirling engines

This paper is the first paper clarifying the causes and physical insight of the thermal-lag phenomena by presenting analytical solutions. The theoretical solutions presented are able to answer critical questions about the thermal-lag engine which have not been answered since it was proposed roughly thirty years ago. We find the criteria for onset of the thermal-lag oscillation in the engine. We confirm Tailer's postulation that a thermal lag can be created to a certain extent by the imperfect heat transfer. We find that the thermal lag angles can be altered by artificially adjusting the geometrical and physical parameters. Finally, the influence of thermal lag on the indicated work output of the engine can be evaluated. In the present study, a nonlinear instability analysis is performed and theoretical solutions are carried out by perturbation method. In parallel, a prototype engine is developed and tested to partially verify the present theory. Experiments are conducted by measuring the displacement of piston under various heating temperatures and design parameters. Close agreement between the experimental data and the theoretical predictions, particularly in the steady oscillation regime, has been observed.