Abstract
This research predicts the onset conditions of the free piston Stirling engines using analytical solution of the governing equations and averaging-based Lyapunov technique. In this regard, firstly, the linear dynamic equations of the free piston Stirling engines are extracted. Then, the analytical solutions of the motion equations of the displacer and the power pistons are obtained. Afterwards, these analytical solutions are put into the mean value of the time derivative of Lyapunov function to obtain a convenient relation which provides meaningful information regarding the onset condition of free piston Stirling engines. The mentioned procedure has been verified by the results of multiple numerical simulations and the experimental data (B10-B and SUTech-SR-1). In addition, the results of this method have been validated by the outcomes obtained from the state-space technique. Lastly, by comparing the results of the simulation works and the experiments, it has been confirmed that this method is capable of precisely predicting the onset condition of free piston Stirling engines. Besides, the proposed approach could be used as a powerful tool to predict the behavior of various free piston Stirling engines regardless of whether they meet the onset condition or not.
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