Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method
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 i...
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MDPI AG
2021-11-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/14/23/7835 |
| _version_ | 1797507940069933056 |
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| author | Chin-Hsiang Cheng Duc-Thuan Phung |
| author_facet | Chin-Hsiang Cheng Duc-Thuan Phung |
| author_sort | Chin-Hsiang Cheng |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T04:55:34Z |
| format | Article |
| id | doaj.art-b3d61746dd714574aa550e394c6f390b |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-10T04:55:34Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-b3d61746dd714574aa550e394c6f390b2023-11-23T02:18:26ZengMDPI AGEnergies1996-10732021-11-011423783510.3390/en14237835Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient MethodChin-Hsiang Cheng0Duc-Thuan Phung1Department of Aeronautics and Astronautics, National Cheng Kung University, No.1, University Road, Tainan 70101, TaiwanDepartment of Aeronautics and Astronautics, National Cheng Kung University, No.1, University Road, Tainan 70101, TaiwanThis 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.https://www.mdpi.com/1996-1073/14/23/7835VSCGMCFD modelmodified thermodynamic model100-W-class β-type Stirling engineoptimization |
| spellingShingle | Chin-Hsiang Cheng Duc-Thuan Phung Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method Energies VSCGM CFD model modified thermodynamic model 100-W-class β-type Stirling engine optimization |
| title | Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method |
| title_full | Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method |
| title_fullStr | Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method |
| title_full_unstemmed | Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method |
| title_short | Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method |
| title_sort | numerical optimization of the β type stirling engine performance using the variable step simplified conjugate gradient method |
| topic | VSCGM CFD model modified thermodynamic model 100-W-class β-type Stirling engine optimization |
| url | https://www.mdpi.com/1996-1073/14/23/7835 |
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