Performance Optimizations with Single-, Bi-, Tri-, and Quadru-Objective for Irreversible Atkinson Cycle with Nonlinear Variation of Working Fluid’s Specific Heat
Abstract
:1. Introduction
2. Cycle Model and Performance Parameters
3. Performance Optimization with the Maximum Power Density Criterion
4. Multi-Objective Optimization
5. Conclusions
- (1)
- There is an to maximize the . With the cycle maximum temperature ratio increases, the and corresponding to the will increase. With the increases of HTL, FL, IIL, the and corresponding to the cycle maximum will decrease.
- (2)
- Under the maximum criterion, the will be higher and the size will be smaller.
- (3)
- Compared with single-objective optimization, MOO has less contradictions and conflicts. Comparing the results of single-, bi-, tri-, and quadru-objective optimization, when the LINMAP solution is optimized with , , and as the objective functions, the contradiction is smaller and the result is more perfect.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Heat transfer loss coefficient () | |
Specific heat at constant pressure | |
Specific heat at constant volume | |
Ecological function | |
Adiabatic index (-) | |
Molar flow rate | |
Power output | |
Power density | |
Heat transfer rate | |
Gas constant (-) | |
T | Temperature |
Greek symbol | |
Compression ratio (-) | |
Thermal efficiency (-) | |
Irreversible compression efficiency (-) | |
Irreversible expansion efficiency (-) | |
Friction coefficient | |
Entropy generation rate | |
Cycle maximum temperature ratio (-) | |
Subscripts | |
Input | |
Maximum value | |
Output | |
Max power density condition | |
Max thermal efficiency condition | |
Environment | |
, , | Cycle state points |
Superscripts | |
– | Dimensionless |
Abbreviations
AC | Atkinson cycle |
FL | Friction loss |
FTT | Finite time thermodynamics |
HTL | Heat transfer loss |
IIL | Internal irreversibility loss |
MOO | Multi-objective optimization |
PC | Performance characteristics |
SH | Specific heats |
WF | Working fluid |
References
- Andresen, B.; Berry, R.S.; Ondrechen, M.J.; Salamon, P. Thermodynamics for processes in finite time. Acc. Chem. Res. 1984, 17, 266–271. [Google Scholar] [CrossRef]
- Chen, L.G.; Wu, C.; Sun, F.R. Finite Time Thermodynamic Optimization or Entropy Generation Minimization of Energy Systems. J. Non-Equilib. Thermodyn. 1999, 22, 327–359. [Google Scholar] [CrossRef]
- Andresen, B. Current Trends in Finite-Time Thermodynamics. Angew. Chem. Int. Ed. 2011, 50, 2690–2704. [Google Scholar] [CrossRef] [PubMed]
- Berry, R.S.; Salamon, P.; Andresen, B. How It All Began. Entropy 2020, 22, 908. [Google Scholar] [CrossRef] [PubMed]
- Hoffmann, K.H.; Burzler, J.; Fischer, A.; Schaller, M.; Schubert, S. Optimal Process Paths for Endoreversible Systems. J. Non-Equilib. Thermodyn. 2003, 28, 233–268. [Google Scholar] [CrossRef]
- Zaeva, M.A.; Tsirlin, A.M.; Didina, O.V. Finite Time Thermodynamics: Realizability Domain of Heat to Work Converters. J. Non-Equilib. Thermodyn. 2019, 44, 181–191. [Google Scholar] [CrossRef]
- Masser, R.; Hoffmann, K.H. Endoreversible Modeling of a Hydraulic Recuperation System. Entropy 2020, 22, 383. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Kushner, A.; Lychagin, V.; Roop, M. Optimal Thermodynamic Processes for Gases. Entropy 2020, 22, 448. [Google Scholar] [CrossRef]
- De Vos, A. Endoreversible models for the thermodynamics of computing. Entropy 2020, 22, 660. [Google Scholar] [CrossRef]
- Masser, R.; Khodja, A.; Scheunert, M.; Schwalbe, K.; Fischer, A.; Paul, R.; Hoffmann, K.H. Optimized Piston Motion for an Alpha-Type Stirling Engine. Entropy 2020, 22, 700. [Google Scholar] [CrossRef]
- Chen, L.; Ma, K.; Ge, Y.; Feng, H. Re-Optimization of Expansion Work of a Heated Working Fluid with Generalized Radiative Heat Transfer Law. Entropy 2020, 22, 720. [Google Scholar] [CrossRef]
- Tsirlin, A.; Gagarina, L. Finite-Time Thermodynamics in Economics. Entropy 2020, 22, 891. [Google Scholar] [CrossRef]
- Tsirlin, A.; Sukin, I. Averaged Optimization and Finite-Time Thermodynamics. Entropy 2020, 22, 912. [Google Scholar] [CrossRef]
- Muschik, W.; Hoffmann, K.H. Modeling, Simulation, and Reconstruction of 2-Reservoir Heat-to-Power Processes in Finite-Time Thermodynamics. Entropy 2020, 22, 997. [Google Scholar] [CrossRef]
- Insinga, A.R. The Quantum Friction and Optimal Finite-Time Performance of the Quantum Otto Cycle. Entropy 2020, 22, 1060. [Google Scholar] [CrossRef]
- Schön, J.C. Optimal Control of Hydrogen Atom-Like Systems as Thermodynamic Engines in Finite Time. Entropy 2020, 22, 1066. [Google Scholar] [CrossRef]
- Andresen, B.; Essex, C. Thermodynamics at Very Long Time and Space Scales. Entropy 2020, 22, 1090. [Google Scholar] [CrossRef]
- Chen, L.; Ma, K.; Feng, H.; Ge, Y. Optimal Configuration of a Gas Expansion Process in a Piston-Type Cylinder with Generalized Convective Heat Transfer Law. Energies 2020, 13, 3229. [Google Scholar] [CrossRef]
- Scheunert, M.; Masser, R.; Khodja, A.; Paul, R.; Schwalbe, K.; Fischer, A.; Hoffmann, K.H. Power-Optimized Sinusoidal Piston Motion and Its Performance Gain for an Alpha-Type Stirling Engine with Limited Regeneration. Energies 2020, 13, 4564. [Google Scholar] [CrossRef]
- Boykov, S.; Andresen, B.; Akhremenkov, A.A.; Tsirlin, A.M. Evaluation of Irreversibility and Optimal Organization of an Integrated Multi-Stream Heat Exchange System. J. Non-Equilib. Thermodyn. 2020, 45, 155–171. [Google Scholar] [CrossRef]
- Chen, L.G.; Feng, H.J.; Ge, Y.L. Maximum energy output chemical pump configuration with an infinite-low- and a finite-high-chemical potential mass reservoirs. Energy Convers. Manag. 2020, 223, 113261. [Google Scholar] [CrossRef]
- Hoffmann, K.H.; Burzler, J.M.; Schubert, S. Endoreversible thermodynamics. J. Non-Equilib. Thermodyn. 1997, 22, 311–355. [Google Scholar]
- Wagner, K.; Hoffmann, K.H. Endoreversible modeling of a PEM fuel cell. J. Non-Equilib. Thermodyn. 2015, 40, 283–294. [Google Scholar] [CrossRef]
- Muschik, W. Concepts of phenominological irreversible quantum thermodynamics I: Closed undecomposed Schottky systems in semi-classical description. J. Non-Equilib. Thermodyn. 2019, 44, 1–13. [Google Scholar] [CrossRef] [Green Version]
- Ponmurugan, M. Attainability of Maximum Work and the Reversible Efficiency of Minimally Nonlinear Irreversible Heat Engines. J. Non-Equilib. Thermodyn. 2019, 44, 143–153. [Google Scholar] [CrossRef] [Green Version]
- Raman, R.; Kumar, N. Performance Analysis of Diesel Cycle under Efficient Power Density Condition with Variable Specific Heat of Working Fluid. J. Non-Equilib. Thermodyn. 2019, 44, 405–416. [Google Scholar] [CrossRef]
- Schwalbe, K.; Hoffmann, K.H. Stochastic Novikov Engine with Fourier Heat Transport. J. Non-Equilib. Thermodyn. 2019, 44, 417–424. [Google Scholar] [CrossRef]
- Morisaki, T.; Ikegami, Y. Maximum power of a multistage Rankine cycle in low-grade thermal energy conversion. Appl. Therm. Eng. 2014, 69, 78–85. [Google Scholar] [CrossRef]
- Yasunaga, T.; Ikegami, Y. Application of Finite-time Thermodynamics for Evaluation Method of Heat Engines. Energy Procedia 2017, 129, 995–1001. [Google Scholar] [CrossRef]
- Yasunaga, T.; Fontaine, K.; Morisaki, T.; Ikegami, Y. Performance evaluation of heat exchangers for application to ocean thermal energy conversion system. Ocean Therm. Energy Convers. 2017, 22, 65–75. [Google Scholar]
- Yasunaga, T.; Koyama, N.; Noguchi, T.; Morisaki, T.; Ikegami, Y. Thermodynamical optimum heat source mean velocity in heat exchangers on OTEC. In Proceedings of the Grand Renewable Energy 2018, Yokohama, Japan, 17–22 June 2018. [Google Scholar]
- Yasunaga, T.; Noguchi, T.; Morisaki, T.; Ikegami, Y. Basic Heat Exchanger Performance Evaluation Method on OTEC. J. Mar. Sci. Eng. 2018, 6, 32. [Google Scholar] [CrossRef] [Green Version]
- Fontaine, K.; Yasunaga, T.; Ikegami, Y. OTEC Maximum Net Power Output Using Carnot Cycle and Application to Simplify Heat Exchanger Selection. Entropy 2019, 21, 1143. [Google Scholar] [CrossRef] [Green Version]
- Yasunaga, T.; Ikegami, Y. Finite-Time Thermodynamic Model for Evaluating Heat Engines in Ocean Thermal Energy Conversion. Entropy 2020, 22, 211. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Yasunaga, T.; Ikegami, Y. Fundamental characteristics in power generation by heat engines on ocean thermal energy conversion (Construction of finite-time thermodynamic model and effect of heat source flow rate). Trans. JSME 2020, 86. [Google Scholar] [CrossRef]
- Feidt, M. Carnot Cycle and Heat Engine: Fundamentals and Applications. Entropy 2020, 22, 348. [Google Scholar] [CrossRef] [Green Version]
- Feidt, M.; Costea, M. Effect of machine entropy production on the optimal performance of a refrigerator. Entropy 2020, 22, 913. [Google Scholar] [CrossRef]
- Ma, Y.-H. Effect of Finite-Size Heat Source’s Heat Capacity on the Efficiency of Heat Engine. Entropy 2020, 22, 1002. [Google Scholar] [CrossRef]
- Rogolino, P.; Cimmelli, V.A. Thermoelectric efficiency of Silicon–Germanium alloys in finite-time thermodynamics. Entropy 2020, 22, 1116. [Google Scholar] [CrossRef]
- Essex, C.; Das, I. Radiative Transfer and Generalized Wind. Entropy 2020, 22, 1153. [Google Scholar] [CrossRef]
- Dann, R.; Kosloff, R.; Salamon, P. Quantum Finite-Time Thermodynamics: Insight from a Single Qubit Engine. Entropy 2020, 22, 1255. [Google Scholar] [CrossRef]
- Chen, L.; Feng, H.; Ge, Y. Power and Efficiency Optimization for Open Combined Regenerative Brayton and Inverse Brayton Cycles with Regeneration before the Inverse Cycle. Entropy 2020, 22, 677. [Google Scholar] [CrossRef]
- Tang, C.; Chen, L.; Feng, H.; Wang, W.; Ge, Y. Power Optimization of a Modified Closed Binary Brayton Cycle with Two Isothermal Heating Processes and Coupled to Variable-Temperature Reservoirs. Energies 2020, 13, 3212. [Google Scholar] [CrossRef]
- Chen, L.; Shen, J.; Ge, Y.; Wu, Z.; Wang, W.; Zhu, F.; Feng, H. Power and efficiency optimization of open Maisotsenko-Brayton cycle and performance comparison with traditional open regenerated Brayton cycle. Energy Convers. Manag. 2020, 217, 113001. [Google Scholar] [CrossRef]
- Chen, L.; Yang, B.; Feng, H.; Ge, Y.; Xia, S. Performance optimization of an open simple-cycle gas turbine combined cooling, heating and power plant driven by basic oxygen furnace gas in China’s steelmaking plants. Energy 2020, 203, 117791. [Google Scholar] [CrossRef]
- Feng, H.; Chen, W.; Chen, L.; Tang, W. Power and efficiency optimizations of an irreversible regenerative organic Rankine cycle. Energy Convers. Manag. 2020, 220, 113079. [Google Scholar] [CrossRef]
- Feng, H.; Wu, Z.; Chen, L.; Ge, Y. Constructal thermodynamic optimization for dual-pressure organic Rankine cycle in waste heat utilization system. Energy Convers. Manag. 2021, 227, 113585. [Google Scholar] [CrossRef]
- Wu, Z.; Feng, H.; Chen, L.; Tang, W.; Shi, J.; Ge, Y. Constructal thermodynamic optimization for ocean thermal energy conversion system with dual-pressure organic Rankine cycle. Energy Convers. Manag. 2020, 210, 112727. [Google Scholar] [CrossRef]
- Feng, H.; Qin, W.; Chen, L.; Cai, C.; Ge, Y.; Xia, S. Power output, thermal efficiency and exergy-based ecological performance optimizations of an irreversible KCS-34 coupled to variable temperature heat reservoirs. Energy Convers. Manag. 2020, 205, 112424. [Google Scholar] [CrossRef]
- Qiu, S.; Ding, Z.; Chen, L. Performance evaluation and parametric optimum design of irreversible thermionic generators based on van der Waals heterostructures. Energy Convers. Manag. 2020, 225, 113360. [Google Scholar] [CrossRef]
- Chen, L.; Meng, F.; Ge, Y.; Feng, H.; Xia, S. Performance optimization of a class of combined thermoelectric heating devices. Sci. China Ser. E Technol. Sci. 2020, 63, 2640–2648. [Google Scholar] [CrossRef]
- Chen, L.G.; Ge, Y.L.; Liu, C.; Feng, H.J.; Lorenzini, G. Performance of universal reciprocating heat-engine cycle with variable specific heats ratio of working fluid. Entropy 2020, 22, 397. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Wu, H.; Ge, Y.; Chen, L.; Feng, H. Power, efficiency, ecological function and ecological coefficient of performance optimizations of irreversible Diesel cycle based on finite piston speed. Energy 2021, 216, 119235. [Google Scholar] [CrossRef]
- Ge, Y.; Chen, L.; Sun, F. Progress in Finite Time Thermodynamic Studies for Internal Combustion Engine Cycles. Entropy 2016, 18, 139. [Google Scholar] [CrossRef] [Green Version]
- Chen, L.; Lin, J.; Sun, F.; Wu, C. Efficiency of an Atkinson engine at maximum power density. Energy Convers. Manag. 1998, 39, 337–341. [Google Scholar] [CrossRef]
- Rashidi, M.M.; Hajipour, A. Comparison of performance of air-standard Atkinson, Diesel and Otto cycles with constant specific heats. Int. J. Adv. Des. Manuf. Technol. 2013, 6, 57–62. [Google Scholar]
- Hou, S.-S. Comparison of performances of air standard Atkinson and Otto cycles with heat transfer considerations. Energy Convers. Manag. 2007, 48, 1683–1690. [Google Scholar] [CrossRef]
- Qin, X.; Chen, L.; Sun, F.; Wu, C. The universal power and efficiency characteristics for irreversible reciprocating heat engine cycles. Eur. J. Phys. 2003, 24, 359–366. [Google Scholar] [CrossRef]
- Ge, Y.; Chen, L.; Sun, F.; Wu, C. Reciprocating heat-engine cycles. Appl. Energy 2005, 81, 397–408. [Google Scholar] [CrossRef]
- Zhao, Y.; Chen, J. Performance analysis and parametric optimum criteria of an irreversible Atkinson heat-engine. Appl. Energy 2006, 83, 789–800. [Google Scholar] [CrossRef]
- Ust, Y. A Comparative Performance Analysis and Optimization of the Irreversible Atkinson Cycle under Maximum Power Density and Maximum Power Conditions. Int. J. Thermophys. 2009, 30, 1001–1013. [Google Scholar] [CrossRef]
- Shi, S.; Ge, Y.; Chen, L.; Feng, H. Four-Objective Optimization of Irreversible Atkinson Cycle Based on NSGA-II. Entropy 2020, 22, 1150. [Google Scholar] [CrossRef]
- Al-Sarkhi, A.; Akash, B.; Abu-Nada, E.; Alhinti, I. Efficiency of Atkinson engine at maximum power density using temperature dependent specific heats. Jordan J. Mech. Ind. Eng. 2008, 2, 71–75. [Google Scholar]
- Patodi, K.; Maheshwari, G. Performance analysis of an Atkinson cycle with variable specific heats of the working fluid under maximum efficient power conditions. Int. J. Low-Carbon Technol. 2012, 8, 289–294. [Google Scholar] [CrossRef]
- Ge, Y.L.; Chen, L.G.; Sun, F.R.; Wu, C. Performance of endoreversible Atkinson cycle. J. Energy Inst. 2007, 80, 52–54. [Google Scholar] [CrossRef]
- Ge, Y.; Chen, L.; Sun, F.; Wu, C. Performance of an Atkinson cycle with heat transfer, friction and variable specific-heats of the working fluid. Appl. Energy 2006, 83, 1210–1221. [Google Scholar] [CrossRef]
- Lin, J.-C.; Hou, S.-S. Influence of heat loss on the performance of an air-standard Atkinson cycle. Appl. Energy 2007, 84, 904–920. [Google Scholar] [CrossRef]
- Hajipour, A.; Rashidi, M.M.; Ali, M.; Yang, Z.; Bég, O.A. Thermodynamic Analysis and Comparison of the Air-Standard Atkinson and Dual-Atkinson Cycles with Heat Loss, Friction and Variable Specific Heats of Working Fluid. Arab. J. Sci. Eng. 2016, 41, 1635–1645. [Google Scholar] [CrossRef]
- Shi, S.S.; Chen, L.G.; Ge, Y.L.; Wu, Z.X. Power density characteristics of irreversible Atkinson cycle with variable specific heats of the working fluid changing linearly with its temperature. Energy Conserv. 2020, 39, 114–119. (In Chinese) [Google Scholar]
- Ge, Y.; Chen, L.; Sun, F. Finite time thermodynamic modeling and analysis for an irreversible Atkinson cycle. Therm. Sci. 2010, 14, 887–896. [Google Scholar] [CrossRef]
- Ebrahimi, R. Performance analysis of irreversible Atkinson cycle with considerations of stroke length and volumetric efficiency. J. Energy Inst. 2011, 84, 38–43. [Google Scholar] [CrossRef]
- Zhao, J.; Li, Y.; Xu, F. The effects of the engine design and operation parameters on the performance of an Atkinson engine considering heat-transfer, friction, combustion efficiency and variable specific-heat. Energy Convers. Manag. 2017, 151, 11–22. [Google Scholar] [CrossRef]
- Gonca, G. Performance Analysis of an Atkinson Cycle Engine under Effective Power and Effective Power Density Conditions. Acta Phys. Pol. A 2017, 132, 1306–1313. [Google Scholar] [CrossRef]
- Ebrahimi, R. Effect of Volume Ratio of Heat Rejection Process on Performance of an Atkinson Cycle. Acta Phys. Pol. A 2018, 133, 201–205. [Google Scholar] [CrossRef]
- Zhao, J.X.; Xu, F.C. Finite-time thermodynamic modeling and a comparative performance analysis for irreversible Otto, Miller and Atkinson Cycles. Entropy 2018, 20, 75. [Google Scholar] [CrossRef] [Green Version]
- Ahmadi, M.H.; Pourkiaei, S.M.; Ghazvini, M.; Pourfayaz, F. Thermodynamic assessment and optimization of performance of irreversible Atkinson cycle. Iran. J. Chem. Chem. Eng. 2020, 39, 267–280. [Google Scholar]
- Ahmadi, M.H.; Dehghani, S.; Mohammadi, A.H.; Feidt, M.; Barranco-Jiménez, M.A. Optimal design of a solar driven heat engine based on thermal and thermo-economic criteria. Energy Convers. Manag. 2013, 75, 635–642. [Google Scholar] [CrossRef]
- Ahmadi, M.H.; Mohammadi, A.H.; Dehghani, S.; Barranco-Jiménez, M.A. Multi-objective thermodynamic-based optimization of output power of Solar Dish-Stirling engine by implementing an evolutionary algorithm. Energy Convers. Manag. 2013, 75, 438–445. [Google Scholar] [CrossRef]
- Ahmadi, M.H.; Mohammadi, A.H.; Feidt, M.; Pourkiaei, S.M. Multi-objective optimization of an irreversible Stirling cryogenic refrigerator cycle. Energy Convers. Manag. 2014, 82, 351–360. [Google Scholar] [CrossRef]
- Ahmadi, M.H. Thermodynamic analysis and optimization of an irreversible Ericsson cryogenic refrigerator cycle. Energy Convers. Manag. 2015, 89, 147–155. [Google Scholar] [CrossRef]
- Ahmadi, M.H.; Jokar, M.A.; Ming, T.; Feidt, M.; Pourfayaz, F.; Astaraei, F.R. Multi-objective performance optimization of irreversible molten carbonate fuel cell–Braysson heat engine and thermodynamic analysis with ecological objective approach. Energy 2018, 144, 707–722. [Google Scholar] [CrossRef]
- Jokar, M.A.; Ahmadi, M.H.; Sharifpur, M.; Meyer, J.P.; Pourfayaz, F.; Ming, T. Thermodynamic evaluation and multi-objective optimization of molten carbonate fuel cell-supercritical CO 2 Brayton cycle hybrid system. Energy Convers. Manag. 2017, 153, 538–556. [Google Scholar] [CrossRef]
- Ghasemkhani, A.; Farahat, S.; Naserian, M.M. Multi-objective optimization and decision making of endoreversible combined cycles with consideration of different heat exchangers by finite time thermodynamics. Energy Convers. Manag. 2018, 171, 1052–1062. [Google Scholar] [CrossRef]
- Han, Z.; Mei, Z.; Li, P. Multi-objective optimization and sensitivity analysis of an organic Rankine cycle coupled with a one-dimensional radial-inflow turbine efficiency prediction model. Energy Convers. Manag. 2018, 166, 37–47. [Google Scholar] [CrossRef]
- Wang, M.; Jing, R.; Zhang, H.; Meng, C.; Li, N.; Zhao, Y. An innovative Organic Rankine Cycle (ORC) based Ocean Thermal Energy Conversion (OTEC) system with performance simulation and multi-objective optimization. Appl. Therm. Eng. 2018, 145, 743–754. [Google Scholar] [CrossRef]
- Hu, S.; Li, J.; Yang, F.; Yang, Z.; Duan, Y. Multi-objective optimization of organic Rankine cycle using hydrofluorolefins (HFOs) based on different target preferences. Energy 2020, 203, 117848. [Google Scholar] [CrossRef]
- Hu, S.; Li, J.; Yang, F.; Yang, Z.; Duan, Y. How to design organic Rankine cycle system under fluctuating ambient temperature: A multi-objective approach. Energy Convers. Manag. 2020, 224, 113331. [Google Scholar] [CrossRef]
- Tang, C.; Feng, H.; Chen, L.; Wang, W. Power density analysis and multi-objective optimization for a modified endoreversible simple closed Brayton cycle with one isothermal heating process. Energy Rep. 2020, 6, 1648–1657. [Google Scholar] [CrossRef]
- Chen, L.; Tang, C.; Feng, H.; Ge, Y. Power, Efficiency, Power Density and Ecological Function Optimization for an Irreversible Modified Closed Variable-Temperature Reservoir Regenerative Brayton Cycle with One Isothermal Heating Process. Energies 2020, 13, 5133. [Google Scholar] [CrossRef]
- Zhang, L.; Chen, L.; Xia, S.; Ge, Y.; Wang, C.; Feng, H. Multi-objective optimization for helium-heated reverse water gas shift reactor by using NSGA-II. Int. J. Heat Mass Transf. 2020, 148, 119025. [Google Scholar] [CrossRef]
- Sun, M.; Xia, S.; Chen, L.; Wang, C.; Tang, C. Minimum Entropy Generation Rate and Maximum Yield Optimization of Sulfuric Acid Decomposition Process Using NSGA-II. Entropy 2020, 22, 1065. [Google Scholar] [CrossRef]
- Sadeghi, S.; Ghandehariun, S.; Naterer, G.F. Exergoeconomic and multi-objective optimization of a solar thermochemical hydrogen production plant with heat recovery. Energy Convers. Manag. 2020, 225, 113441. [Google Scholar] [CrossRef]
- Wu, Z.; Feng, H.; Chen, L.; Ge, Y. Performance Optimization of a Condenser in Ocean Thermal Energy Conversion (OTEC) System Based on Constructal Theory and a Multi-Objective Genetic Algorithm. Entropy 2020, 22, 641. [Google Scholar] [CrossRef]
- Ghorani, M.M.; Haghighi, M.H.S.; Riasi, A. Entropy generation minimization of a pump running in reverse mode based on surrogate models and NSGA-II. Int. Commun. Heat Mass Transf. 2020, 118, 104898. [Google Scholar] [CrossRef]
- Shi, S.; Chen, L.; Ge, Y.; Feng, H. Performance Optimizations with Single-, Bi-, Tri-, and Quadru-Objective for Irreversible Diesel Cycle. Entropy 2021, 23, 826. [Google Scholar] [CrossRef]
- Angulo-Brown, F. An ecological optimization criterion for finite-time heat engines. J. Appl. Phys. 1991, 69, 7465–7469. [Google Scholar] [CrossRef]
- Yan, Z.J. Comment on ecological optimization criterion for finite-time heat engines. J. Appl. Phys. 1993, 73, 3583. [Google Scholar]
- Chen, L.G.; Sun, F.R.; Chen, W.Z. The ecological quality factor for thermodynamic cycles. J. Eng. Therm. Energy Power 1994, 9, 374–376. (In Chinese) [Google Scholar]
Optimization Methods | Decision Methods | Optimization Variable | Optimization Objectives | Deviation Index | |||
---|---|---|---|---|---|---|---|
Quadru-objective optimization (, , and ) | LINMAP | 7.5172 | 0.9865 | 0.4450 | 0.9997 | 0.9890 | 0.1250 |
TOPSIS | 7.5172 | 0.9865 | 0.4450 | 0.9997 | 0.9890 | 0.1250 | |
Shannon Entropy | 9.1311 | 0.9564 | 0.4459 | 0.9345 | 0.9999 | 0.5266 | |
Tri-objective optimization (, and ) | LINMAP | 7.1952 | 0.9907 | 0.4438 | 0.9958 | 0.9839 | 0.1395 |
TOPSIS | 7.2939 | 0.9895 | 0.4442 | 0.9978 | 0.9856 | 0.1307 | |
Shannon Entropy | 7.5582 | 0.9859 | 0.4451 | 0.9998 | 0.9896 | 0.1253 | |
Tri-objective optimization (, and ) | LINMAP | 7.5054 | 0.9866 | 0.4449 | 0.9999 | 0.9888 | 0.1247 |
TOPSIS | 7.5485 | 0.9860 | 0.4451 | 0.9999 | 0.9894 | 0.1252 | |
Shannon Entropy | 9.1297 | 0.9564 | 0.4459 | 0.9349 | 0.9999 | 0.5247 | |
Tri-objective optimization (, and ) | LINMAP | 7.4763 | 0.9871 | 0.4449 | 0.9996 | 0.9883 | 0.1249 |
TOPSIS | 7.4763 | 0.9871 | 0.4449 | 0.9996 | 0.9883 | 0.1249 | |
Shannon Entropy | 9.1314 | 0.9564 | 0.4459 | 0.9345 | 0.9999 | 0.5279 | |
Tri-objective optimization (, and ) | LINMAP | 7.8916 | 0.9808 | 0.4459 | 0.9966 | 0.9936 | 0.1457 |
TOPSIS | 7.8817 | 0.9809 | 0.4459 | 0.9968 | 0.9935 | 0.1450 | |
Shannon Entropy | 9.1320 | 0.4459 | 0.9344 | 0.9345 | 0.9999 | 0.5269 | |
Bi-objective optimization ( and ) | LINMAP | 7.0477 | 0.9924 | 0.4431 | 0.9920 | 0.9812 | 0.1609 |
TOPSIS | 7.0330 | 0.9926 | 0.4431 | 0.9915 | 0.9809 | 0.1639 | |
Shannon Entropy | 8.4845 | 0.9700 | 0.4465 | 0.9764 | 0.9983 | 0.2074 | |
Bi-objective optimization ( and ) | LINMAP | 7.1705 | 0.9910 | 0.4437 | 0.9952 | 0.9835 | 0.1423 |
TOPSIS | 7.1705 | 0.9910 | 0.4437 | 0.9952 | 0.9835 | 0.1423 | |
Shannon Entropy | 7.5573 | 0.9859 | 0.4451 | 0.9998 | 0.9896 | 0.1252 | |
Bi-objective optimization ( and ) | LINMAP | 7.4628 | 0.9872 | 0.4448 | 0.9980 | 0.9882 | 0.1248 |
TOPSIS | 7.5003 | 0.9867 | 0.4450 | 0.9999 | 0.9887 | 0.1248 | |
Shannon Entropy | 9.1277 | 0.9564 | 0.4459 | 0.9350 | 0.9999 | 0.5241 | |
Bi-objective optimization ( and ) | LINMAP | 7.7359 | 0.9832 | 0.4456 | 0.9989 | 0.9919 | 0.1328 |
TOPSIS | 7.7259 | 0.9834 | 0.4456 | 0.9990 | 0.9918 | 0.1318 | |
Shannon Entropy | 7.5597 | 0.9859 | 0.4451 | 0.9998 | 0.9896 | 0.1252 | |
Bi-objective optimization ( and ) | LINMAP | 8.8286 | 0.9630 | 0.4463 | 0.9566 | 0.9996 | 0.3968 |
TOPSIS | 8.8388 | 0.9628 | 0.4463 | 0.9559 | 0.9996 | 0.4011 | |
Shannon Entropy | 9.1297 | 0.9564 | 0.4459 | 0.9349 | 0.9999 | 0.5247 | |
Bi-objective optimization ( and ) | LINMAP | 7.8949 | 0.9807 | 0.4460 | 0.9965 | 0.9936 | 0.1463 |
TOPSIS | 7.8857 | 0.9813 | 0.4459 | 0.9967 | 0.9935 | 0.1427 | |
Shannon Entropy | 9.1334 | 0.9563 | 0.4459 | 0.9999 | 0.9999 | 0.5276 | |
Maximum of | —— | 5.8100 | 0.9999 | 0.4338 | 0.8928 | 0.9478 | 0.7326 |
Maximum of | —— | 8.5000 | 0.9697 | 0.4465 | 0.9756 | 0.9984 | 0.2752 |
Maximum of | —— | 7.5900 | 0.9853 | 0.4453 | 0.9998 | 0.9902 | 0.1260 |
Maximum of | —— | 9.1300 | 0.9571 | 0.4459 | 0.9372 | 0.9999 | 0.5120 |
Positive ideal point | —— | 0.9999 | 0.4465 | 0.9998 | 0.9999 | —— | |
Negative ideal point | —— | 0.9564 | 0.4335 | 0.8895 | 0.9470 | —— |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Shi, S.; Ge, Y.; Chen, L.; Feng, H. Performance Optimizations with Single-, Bi-, Tri-, and Quadru-Objective for Irreversible Atkinson Cycle with Nonlinear Variation of Working Fluid’s Specific Heat. Energies 2021, 14, 4175. https://doi.org/10.3390/en14144175
Shi S, Ge Y, Chen L, Feng H. Performance Optimizations with Single-, Bi-, Tri-, and Quadru-Objective for Irreversible Atkinson Cycle with Nonlinear Variation of Working Fluid’s Specific Heat. Energies. 2021; 14(14):4175. https://doi.org/10.3390/en14144175
Chicago/Turabian StyleShi, Shuangshuang, Yanlin Ge, Lingen Chen, and Huijun Feng. 2021. "Performance Optimizations with Single-, Bi-, Tri-, and Quadru-Objective for Irreversible Atkinson Cycle with Nonlinear Variation of Working Fluid’s Specific Heat" Energies 14, no. 14: 4175. https://doi.org/10.3390/en14144175