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Scaling laws for free piston Stirling engine design: Benefits and challenges of miniaturization

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  • Formosa, Fabien
  • Fréchette, Luc G.

Abstract

This work explores the scaling effects for FPSE (free piston Stirling engines), which are known for their simple architecture and potentially high thermodynamic performances. Scaling laws are given and their potential for miniaturization is highlighted. A simple model which allows the design of the geometrical parameters of the heat exchangers, the regenerator and the masses of the pistons is proposed. It is based on the definition of six characteristic dimensionless groups. They are derived from the physics underlying the behavior of the free piston Stirling machine and their relevancy is backed up by comparisons between documented Stirling engines from the literature. Keeping constant values for each group throughout the scaling range theoretically ensures constant performance. The main losses of Stirling engine (heat conduction loss, reheat loss in the regenerator, pressure drop and gas-spring hysteresis) can be expressed as a function of the geometrical and operating parameters. Additionally, the consequences of leakage due to the manufacturing precision of pistons architectures are underlined. From the proposed scaling laws, potential power and efficiency of Stirling cycle engines at a millimeter scale can be anticipated. It appears that the power density increases with miniaturization. It is also shown that the dynamic masses related to the engine size are increased when scaling down and that the gap leakage presents the highest detrimental effects on the efficiency. These results call for dedicated architectures for micro-engines.

Suggested Citation

  • Formosa, Fabien & Fréchette, Luc G., 2013. "Scaling laws for free piston Stirling engine design: Benefits and challenges of miniaturization," Energy, Elsevier, vol. 57(C), pages 796-808.
    • Handle: RePEc:eee:energy:v:57:y:2013:i:c:p:796-808
    DOI: 10.1016/j.energy.2013.05.009
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    1. 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.
    2. 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.
    3. Preetham, B.S. & Weiss, L., 2016. "Investigations of a new free piston expander engine cycle," Energy, Elsevier, vol. 106(C), pages 535-545.
    4. Wang, Qian & Wu, Fan & Zhao, Yan & Bai, Jin & Huang, Rong, 2019. "Study on combustion characteristics and ignition limits extending of micro free-piston engines," Energy, Elsevier, vol. 179(C), pages 805-814.
    5. Burugupally, Sindhu Preetham & Weiss, Leland, 2019. "Design and performance of a miniature free piston expander," Energy, Elsevier, vol. 170(C), pages 611-618.
    6. Ayodeji Sowale & Athanasios J. Kolios, 2018. "Thermodynamic Performance of Heat Exchangers in a Free Piston Stirling Engine," Energies, MDPI, vol. 11(3), pages 1-20, February.
    7. 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).
    8. Mou, Jian & Hong, Guotong, 2017. "Startup mechanism and power distribution of free piston Stirling engine," Energy, Elsevier, vol. 123(C), pages 655-663.
    9. Cheng, Chin-Hsiang & Yang, Hang-Suin, 2014. "Optimization of rhombic drive mechanism used in beta-type Stirling engine based on dimensionless analysis," Energy, Elsevier, vol. 64(C), pages 970-978.
    10. Xu, Yonghong & Tong, Liang & Zhang, Hongguang & Hou, Xiaochen & Yang, Fubin & Yu, Fei & Yang, Yuxin & Liu, Rong & Tian, Yaming & Zhao, Tenglong, 2018. "Experimental and simulation study of a free piston expander–linear generator for small-scale organic Rankine cycle," Energy, Elsevier, vol. 161(C), pages 776-791.
    11. Bert, Juliette & Chrenko, Daniela & Sophy, Tonino & Le Moyne, Luis & Sirot, Frédéric, 2014. "Simulation, experimental validation and kinematic optimization of a Stirling engine using air and helium," Energy, Elsevier, vol. 78(C), pages 701-712.
    12. Sindhu Preetham Burugupally & Leland Weiss, 2018. "Power Generation via Small Length Scale Thermo-Mechanical Systems: Current Status and Challenges, a Review," Energies, MDPI, vol. 11(9), pages 1-22, August.
    13. 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.
    14. Ayodeji Sowale & Edward J. Anthony & Athanasios John Kolios, 2018. "Optimisation of a Quasi-Steady Model of a Free-Piston Stirling Engine," Energies, MDPI, vol. 12(1), pages 1-17, December.
    15. 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.

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