Applying perturbation technique to analysis of a free piston Stirling engine possessing nonlinear springs

• Published in: Applied energy 2016-12, Vol.183, p.526-541
• Main Authors: Tavakolpour-Saleh, A.R., Zare, Sh, Omidvar, A.
• Format: Article
• Language: English
• Subjects: Free piston Stirling engine; Nonlinear spring; Perturbation technique
• ISSN: 0306-2619; 1872-9118
• DOI: 10.1016/j.apenergy.2016.09.009

•Multi-scale perturbation method is applied to analyze a nonlinear free piston Stirling engine.•A systematic analytical scheme is presented to estimate the gas temperature in hot and cold spaces.•Unique relationships are proposed to predict frequency, phase, pistons strokes, power and efficiency of the FPSEs.•Validity of the proposed analytical scheme is shown experimentally. This paper describes a novel design approach of the free piston Stirling engines (FPSEs) based on multiple-scale perturbation method. First, a comprehensive mathematical model for an FPSE possessing nonlinear springs is presented. Then, the method of multiple scales is used to obtain the steady-state response of the engine system. Thus, some useful analytical relationships to predict frequency, strokes of pistons, and phase angle, as well as output power and efficiency of the nonlinear FPSE, are presented. Furthermore, a systematic mathematical approach for estimating the gas temperatures within expansion and compression spaces of the FPSE is proposed based on the perturbation technique. Next, a simulation study is carried out to investigate how much the engine frequency, strokes of pistons, and phase angle of the FPSE are sensitive to the variation of gas temperature. Besides, the effect of changes in the engine design parameters such as mass and stiffness of the pistons on the output power of the FPSE is studied using simulation. Finally, a test engine is developed and experimented to verify the proposed design technique. It is found that the experimental results are in a good agreement with the simulation outcomes of the analytical model through which validity of the proposed design scheme is clearly demonstrated.