Higher order modeling of a free‑piston Stirling engine: analysis and experiment

This paper focuses on higher order modeling and design of the free-piston Stirling engine (FPSE) based on Ant Colony Optimization (ACO). First, the governing thermodynamics and dynamical equations of the engine have been derived. Then, the design parameters of the engine are selected taking into account the finite heat transfer coefficient (resulting in a fifth-order model) and pressure drop (resulting in a sixth-order model) in the dynamical system and the corresponding differential equations are derived in detail. In the following, the mentioned methods and their performance in modeling the FPSE dynamics are investigated. The simulated results show that the effect of the pressure drop on the places of the closed-loop poles of the system is not significant, while the heat transfer coefficient has a considerable effect on the engine dynamics. Accordingly, a fifth-order model along with ACO algorithm is proposed to justify the FPSE behavior. To validate the presented modeling scheme, the prototype engine SUTECH-SR-1 was experimented. It is found that the values of parameters obtained from the proposed design method are close to those of the experiment. Besides, the presented higher order model predicts the engine behavior with an acceptable accuracy through which the validity of the design technique is affirmed.