Investigating limit cycle in a free piston Stirling engine using describing function technique and genetic algorithm

Abstract

This paper focuses on evaluating a free piston Stirling engine (FPSE) using describing function method along with a genetic algorithm (GA). In this regard, first, the nonlinear terms of the free piston Stirling engine are investigated by describing function technique and then, the stability of system oscillation is demonstrated using the proposed novel method. Indeed, the mentioned idea is characterized via a graphical representation incorporating genetic algorithm. Afterwards, the free piston Stirling engine parameters including the amplitudes of power and displacer pistons, operating frequency, and phase difference between the pistons motions are estimated via this novel strategy. In the sequel, the generating work and output power of FPSE are calculated taking into account the acquired parameters. Subsequently, the simulation results are verified using the practical data of a prototype engine (i.e. SUTech-SR-1). It is found that the simulation outcomes are in a good agreement with the experimental results, through which the validity of proposed method is affirmed. Indeed, this technique not only assures the stable oscillation (i.e. the sufficient condition) of the free piston Stirling engines but also can predict the engine performance including the generated work and output power as well as the values of design parameters. Furthermore, this technique can easily be applied to design problem of other new converters such as thermos-acoustic engines as well.