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

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  • Tavakolpour-Saleh, A.R.
  • Zare, Sh.
  • Omidvar, A.

Abstract

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.

Suggested Citation

  • Tavakolpour-Saleh, A.R. & Zare, Sh. & Omidvar, A., 2016. "Applying perturbation technique to analysis of a free piston Stirling engine possessing nonlinear springs," Applied Energy, Elsevier, vol. 183(C), pages 526-541.
    • Handle: RePEc:eee:appene:v:183:y:2016:i:c:p:526-541
    DOI: 10.1016/j.apenergy.2016.09.009
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    Cited by:

    1. Tavakolpour-Saleh, A.R., 2021. "A novel theorem on motion stability," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    2. Tavakolpour-Saleh, A.R. & Zare, SH. & Bahreman, H., 2017. "A novel active free piston Stirling engine: Modeling, development, and experiment," Applied Energy, Elsevier, vol. 199(C), pages 400-415.
    3. Carmela Perozziello & Lavinia Grosu & Bianca Maria Vaglieco, 2021. "Free-Piston Stirling Engine Technologies and Models: A Review," Energies, MDPI, vol. 14(21), pages 1-22, October.
    4. Zhu, Shunmin & Yu, Guoyao & O, Jongmin & Xu, Tao & Wu, Zhanghua & Dai, Wei & Luo, Ercang, 2018. "Modeling and experimental investigation of a free-piston Stirling engine-based micro-combined heat and power system," Applied Energy, Elsevier, vol. 226(C), pages 522-533.
    5. Zare, Shahryar & Tavakolpour-Saleh, A.R. & Binazadeh, T., 2023. "Analytical investigation of free piston Stirling engines using practical stability method," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    6. Zare, Shahryar & Tavakolpour-Saleh, Alireza & Shourangiz-Haghighi, Alireza & Binazadeh, Tahereh, 2019. "Assessment of damping coefficients ranges in design of a free piston Stirling engine: Simulation and experiment," Energy, Elsevier, vol. 185(C), pages 633-643.
    7. Hu, J.Y. & Luo, E.C. & Dai, W. & Zhang, L.M., 2017. "Parameter sensitivity analysis of duplex Stirling coolers," Applied Energy, Elsevier, vol. 190(C), pages 1039-1046.
    8. Tavakolpour-Saleh, A.R. & Zare, Shahryar, 2021. "Justifying performance of thermo-acoustic Stirling engines based on a novel lumped mechanical model," Energy, Elsevier, vol. 227(C).
    9. Zare, Shahryar & Tavakolpour-saleh, A.R. & Aghahosseini, A. & Sangdani, M.H. & Mirshekari, Reza, 2021. "Design and optimization of Stirling engines using soft computing methods: A review," Applied Energy, Elsevier, vol. 283(C).
    10. Tavakolpour-Saleh, A.R. & Zare, Shahryar, 2019. "An averaging-based Lyapunov technique to design thermal oscillators: A case study on free piston Stirling engine," Energy, Elsevier, vol. 189(C).
    11. Mou, Jian & Hong, Guotong, 2017. "Startup mechanism and power distribution of free piston Stirling engine," Energy, Elsevier, vol. 123(C), pages 655-663.
    12. Chen, Pengfan & Yang, Peng & Liu, Liu & Liu, Yingwen, 2021. "Parametric investigation of the phase characteristics of a beta-type free piston Stirling engine based on a thermodynamic-dynamic coupled model," Energy, Elsevier, vol. 219(C).
    13. Zare, Shahryar & Tavakolpour-Saleh, A.R., 2020. "Predicting onset conditions of a free piston Stirling engine," Applied Energy, Elsevier, vol. 262(C).

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