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Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method

Author

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  • Chin-Hsiang Cheng

    (Department of Aeronautics and Astronautics, National Cheng Kung University, No.1, University Road, Tainan 70101, Taiwan)

  • Duc-Thuan Phung

    (Department of Aeronautics and Astronautics, National Cheng Kung University, No.1, University Road, Tainan 70101, Taiwan)

Abstract

This study focuses on optimizing a 100-W-class β-Type Stirling engine by combining the modified thermodynamic model and the variable-step simplified conjugate gradient (VSCGM) method. For the modified thermodynamic model, non-uniform pressure is directly introduced into the energy equation, so the indicated power and heat transfer rates can reach energy balance while the VSCGM is an updated version of the simplified conjugate gradient method (SCGM) with adaptive increments and step lengths to the optimization process; thus, it requires fewer iterations to reach the optimal solution than the SCGM. For the baseline case, the indicated power progressively raises from 88.2 to 210.2 W and the thermal efficiency increases from 34.8 to 46.4% before and after optimization, respectively. The study shows the VSCGM possesses robust property. All optimal results from the VSCGM are well-matched with those of the computational fluid dynamics (CFD) model. Heating temperature and rotation speed have positive effects on optimal engine performance. The optimal indicated power rises linearly with the charged pressure, whereas the optimal thermal efficiency tends to decrease. The study also points out that results of the modified thermodynamic model with fixed values of unknowns agree well with the CFD results at points far from the baseline case.

Suggested Citation

  • Chin-Hsiang Cheng & Duc-Thuan Phung, 2021. "Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method," Energies, MDPI, vol. 14(23), pages 1-14, November.
  • Handle: RePEc:gam:jeners:v:14:y:2021:i:23:p:7835-:d:685495
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    References listed on IDEAS

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    1. Patel, Vivek & Savsani, Vimal, 2016. "Multi-objective optimization of a Stirling heat engine using TS-TLBO (tutorial training and self learning inspired teaching-learning based optimization) algorithm," Energy, Elsevier, vol. 95(C), pages 528-541.
    2. Chin-Hsiang Cheng & Yu-Ting Lin, 2020. "Optimization of a Stirling Engine by Variable-Step Simplified Conjugate-Gradient Method and Neural Network Training Algorithm," Energies, MDPI, vol. 13(19), pages 1-18, October.
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    7. Chin-Hsiang Cheng & Yi-Han Tan, 2020. "Numerical Optimization of a Four-Cylinder Double-Acting Stirling Engine Based on Non-Ideal Adiabatic Thermodynamic Model and SCGM Method," Energies, MDPI, vol. 13(8), pages 1-19, April.
    8. Cheng, Chin-Hsiang & Yu, Ying-Ju, 2010. "Numerical model for predicting thermodynamic cycle and thermal efficiency of a beta-type Stirling engine with rhombic-drive mechanism," Renewable Energy, Elsevier, vol. 35(11), pages 2590-2601.
    9. Cheng, Chin-Hsiang & Yu, Ying-Ju, 2011. "Dynamic simulation of a beta-type Stirling engine with cam-drive mechanism via the combination of the thermodynamic and dynamic models," Renewable Energy, Elsevier, vol. 36(2), pages 714-725.
    10. Cheng, Chin-Hsiang & Yang, Hang-Suin & Keong, Lam, 2013. "Theoretical and experimental study of a 300-W beta-type Stirling engine," Energy, Elsevier, vol. 59(C), pages 590-599.
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    Cited by:

    1. George-Rafael Domenikos & Irene Koronaki & Theodoros Papingiotis & Panagiotis Bitsikas, 2023. "Parametric Numerical Analysis of β -Type Stirling Engine," Energies, MDPI, vol. 16(18), pages 1-14, September.
    2. Chin-Hsiang Cheng & Duc-Thuan Phung, 2022. "Modeling of Thermal-Lag Engine with Validation by Experimental Data," Energies, MDPI, vol. 15(20), pages 1-17, October.

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