Four-Objective Optimization of an Irreversible Stirling Heat Engine with Linear Phenomenological Heat-Transfer Law
Abstract
:1. Introduction
2. Model of SHE Cycle and OOs
3. Multi-Objective Optimizations
4. Conclusions
- From the expressions derived of the four OOs under linear phenomenological HTL it was found that , , and were obviously different from those in reference [69], which indicates that the change of HTL also fundamentally changes the performance indicators of the heat engine;
- The deviation indexes calculated by TOPSIS and LINMAP decision-making strategies are both 0.1683 when MOO is performed on , which are smaller and the optimization results are better than the results using the Shannon Entropy strategy. Compared with the deviation indexes (0.1978, 0.8624, 0.3319, and 0.3032) calculated by single-objective optimization at maximum , , , and conditions, the deviation indexes of MOO are smaller and their results are better;
- When the genetic algorithm approaches convergence, which happens at the 331st generation for optimization, the genetic algorithm ends immediately. The average distance and spread gradually decrease from the beginning to the 25th generation, after which they remain stable until the end of the calculation. The average distance is mainly between 0.5~1.5, and the average spread keeps to nearly zero after the 25th generation, which suggests that the optimization process is nearly stable;
- When performing triple-objective optimizations, the MOO results of are better than the other combinations. The average distance mainly ranges from 0 to 0.5, and the average spread keeps to nearly zero after the 15th generation. When performing double-objective optimizations, the MOO results of are better than the other combinations. The average distance mainly ranges from 0.2 to 0.4, and the average spread keeps to nearly zero after the 20th generation;
- Compared with single-objective optimization, MOO can better take different OOs into account by choosing appropriate decision-making strategies. For the results of different objective combinations, appropriate schemes can be selected according to the actual design and operation to meet the requirements under different working conditions;
- FTT and MOO are effective tools to guide performance improvement and optimization for SHE cycles. The consideration of different HTLs is also necessary.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Buffer space | |
Heat-leakage coefficient, | |
Molar constant volume specific heat capacity, | |
Mechanism effectiveness | |
Flywheel | |
Mechanical device | |
Mole number, | |
Regenerator | |
Universal gas constant, | |
Temperature, | |
Time duration of the process, | |
Volume, | |
Compression work, J | |
Expansion work, J | |
Positive piston work, J | |
Negative piston work, J | |
Greek symbol | |
, | Heat-transfer coefficient, |
Volume–compression ratio | |
Efficiency of the regenerator | |
Cycle period, | |
Entropy-generation rate, | |
Subscripts | |
Optimal | |
Superscripts | |
Dimensionless | |
EP | Efficient power |
FTT | Finite time thermodynamics |
HT | Heat transfer |
HTL | Heat-transfer law |
MOO | Multi-objective optimization |
OO | Optimization objective |
PD | Power density |
SHE | Stirling heat engine |
WF | Working fluid |
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Parameters | Values |
---|---|
Generations | 700 |
Population size | 300 |
Pareto fraction | 0.5 |
Crossover fraction | 0.8 |
Optimization Methods | Decision- Making Strategies | Optimization Variables | Optimization Objectives | Deviation Index | ||||
---|---|---|---|---|---|---|---|---|
Four-objective optimization ) | LINMAP | 0.5815 | 1.5301 | 0.9608 | 0.2601 | 0.8905 | 0.8721 | 0.1683 |
TOPSIS | 0.5815 | 1.5301 | 0.9608 | 0.2601 | 0.8905 | 0.8721 | 0.1683 | |
Shannon Entropy | 0.6610 | 1.2684 | 0.9128 | 0.1877 | 0.6103 | 1.0000 | 0.3018 | |
Three-objective optimization ) | LINMAP | 0.5462 | 2.2788 | 0.9178 | 0.3056 | 0.9995 | 0.5597 | 0.3455 |
TOPSIS | 0.5475 | 2.2032 | 0.9226 | 0.3042 | 1.0000 | 0.5819 | 0.3306 | |
Shannon Entropy | 0.5475 | 2.2032 | 0.9226 | 0.3042 | 1.0000 | 0.5819 | 0.3306 | |
Three-objective optimization ) | LINMAP | 0.5885 | 1.5360 | 0.9670 | 0.2576 | 0.8903 | 0.8775 | 0.1648 |
TOPSIS | 0.5968 | 1.4652 | 0.9658 | 0.2462 | 0.8475 | 0.9161 | 0.1735 | |
Shannon Entropy | 0.6611 | 1.2679 | 0.9124 | 0.1875 | 0.6095 | 1.0000 | 0.3022 | |
Three-objective optimization ) | LINMAP | 0.6030 | 1.5375 | 0.9835 | 0.2512 | 0.8802 | 0.8889 | 0.1641 |
TOPSIS | 0.6030 | 1.5375 | 0.9835 | 0.2512 | 0.8802 | 0.8889 | 0.1641 | |
Shannon Entropy | 0.6610 | 1.2686 | 0.9129 | 0.1877 | 0.6106 | 1.0000 | 0.3016 | |
Three-objective optimization ) | LINMAP | 0.5718 | 1.2686 | 0.9502 | 0.2663 | 0.9017 | 0.8509 | 0.1756 |
TOPSIS | 0.5852 | 1.5303 | 0.9653 | 0.2584 | 0.8890 | 0.8766 | 0.1663 | |
Shannon Entropy | 0.6610 | 1.2686 | 0.9129 | 0.1877 | 0.6106 | 1.0000 | 0.3016 | |
Two-objective optimization ) | LINMAP | 0.5407 | 2.1898 | 0.9095 | 0.3082 | 0.9988 | 0.5771 | 0.3367 |
TOPSIS | 0.5531 | 2.2047 | 0.9325 | 0.3008 | 0.9992 | 0.5877 | 0.3250 | |
Shannon Entropy | 0.4208 | 3.6089 | 0.3745 | 0.3718 | 0.4962 | 0.1442 | 0.8630 | |
Two-objective optimization ) | LINMAP | 0.5793 | 1.9746 | 0.9740 | 0.2820 | 0.9786 | 0.6855 | 0.2580 |
TOPSIS | 0.5783 | 1.9812 | 0.9728 | 0.2827 | 0.9799 | 0.6824 | 0.2600 | |
Shannon Entropy | 0.5476 | 2.2031 | 0.9227 | 0.3042 | 1.0000 | 0.5820 | 0.3305 | |
Two-objective optimization ) | LINMAP | 0.6459 | 1.3747 | 0.9647 | 0.2141 | 0.7360 | 0.9752 | 0.2286 |
TOPSIS | 0.6468 | 1.3629 | 0.9608 | 0.2120 | 0.7257 | 0.9796 | 0.2345 | |
Shannon Entropy | 0.6610 | 1.2686 | 0.9129 | 0.1877 | 0.6107 | 1.0000 | 0.3016 | |
Two-objective optimization ) | LINMAP | 0.5026 | 2.6195 | 0.7965 | 0.3341 | 0.9482 | 0.4226 | 0.4700 |
TOPSIS | 0.5079 | 2.5508 | 0.8154 | 0.3306 | 0.9605 | 0.4442 | 0.4491 | |
Shannon Entropy | 0.5475 | 2.2033 | 0.9226 | 0.3042 | 1.0000 | 0.5819 | 0.3306 | |
Two-objective optimization ) | LINMAP | 0.5709 | 1.5216 | 0.9439 | 0.2835 | 0.8861 | 0.8620 | 0.1782 |
TOPSIS | 0.5898 | 1.4515 | 0.9551 | 0.2471 | 0.8410 | 0.9144 | 0.1792 | |
Shannon Entropy | 0.6614 | 1.2682 | 0.9126 | 0.1875 | 0.6098 | 1.0000 | 0.3021 | |
Two-objective optimization ) | LINMAP | 0.5989 | 1.5332 | 0.9797 | 0.2527 | 0.8821 | 0.8879 | 0.1636 |
TOPSIS | 0.5984 | 1.5217 | 0.9777 | 0.2518 | 0.8772 | 0.8928 | 0.1642 | |
Shannon Entropy | 0.6610 | 1.2686 | 0.9129 | 0.1877 | 0.6106 | 1.0000 | 0.3016 | |
- | 0.6229 | 1.7047 | 1.0000 | 0.2501 | 0.8909 | 0.8152 | 0.1978 | |
- | 0.4213 | 3.6042 | 0.3777 | 0.3718 | 0.5003 | 0.1456 | 0.8624 | |
- | 0.5469 | 2.2063 | 0.9213 | 0.3046 | 1.0000 | 0.5803 | 0.3319 | |
- | 0.6626 | 1.2676 | 0.9121 | 0.1870 | 0.6078 | 1.0000 | 0.3032 | |
Positive ideal point | - | - | 1.0000 | 0.3718 | 1.0000 | 1.0000 | - | |
Negative ideal point | - | - | 0.3745 | 0.1854 | 0.4962 | 0.1442 | - |
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Xu, H.; Chen, L.; Ge, Y.; Feng, H. Four-Objective Optimization of an Irreversible Stirling Heat Engine with Linear Phenomenological Heat-Transfer Law. Entropy 2022, 24, 1491. https://doi.org/10.3390/e24101491
Xu H, Chen L, Ge Y, Feng H. Four-Objective Optimization of an Irreversible Stirling Heat Engine with Linear Phenomenological Heat-Transfer Law. Entropy. 2022; 24(10):1491. https://doi.org/10.3390/e24101491
Chicago/Turabian StyleXu, Haoran, Lingen Chen, Yanlin Ge, and Huijun Feng. 2022. "Four-Objective Optimization of an Irreversible Stirling Heat Engine with Linear Phenomenological Heat-Transfer Law" Entropy 24, no. 10: 1491. https://doi.org/10.3390/e24101491
APA StyleXu, H., Chen, L., Ge, Y., & Feng, H. (2022). Four-Objective Optimization of an Irreversible Stirling Heat Engine with Linear Phenomenological Heat-Transfer Law. Entropy, 24(10), 1491. https://doi.org/10.3390/e24101491