{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:43:01Z","timestamp":1777646581823,"version":"3.51.4"},"reference-count":51,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T00:00:00Z","timestamp":1760745600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51976235"],"award-info":[{"award-number":["51976235"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51606218"],"award-info":[{"award-number":["51606218"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Hubei Province, China","award":["2018CFB708"],"award-info":[{"award-number":["2018CFB708"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>To address low energy utilization efficiency and severe exergy destruction from direct discharge of high-temperature turbine exhaust, this study proposes a supercritical CO2 Brayton cogeneration system with a series-connected hot water heat exchanger for stepwise waste heat recovery. Based on finite-time thermodynamics, a physical model that provides a more realistic framework by incorporating finite temperature difference heat transfer, irreversible compression, and expansion losses is established. Aiming to maximize exergy output rate under the constraint of fixed total thermal conductance, the decision variables, including working fluid mass flow rate, pressure ratio, and thermal conductance distribution ratio, are optimized. Optimization yields a 16.06% increase in exergy output rate compared with the baseline design. The optimal parameter combination is a mass flow rate of 79 kg\/s and a pressure ratio of 5.64, with thermal conductance allocation increased for the regenerator and cooler, while decreased for the heater. The obtained results could provide theoretical guidance for enhancing energy efficiency and sustainability in S-CO2 cogeneration systems, with potential applications in industrial waste heat recovery and power generation.<\/jats:p>","DOI":"10.3390\/e27101078","type":"journal-article","created":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T08:18:54Z","timestamp":1760948334000},"page":"1078","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimization of Exergy Output Rate in a Supercritical CO2 Brayton Cogeneration System"],"prefix":"10.3390","volume":"27","author":[{"given":"Jiachi","family":"Shan","sequence":"first","affiliation":[{"name":"College of Power Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaojun","family":"Xia","sequence":"additional","affiliation":[{"name":"College of Power Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinglong","family":"Jin","sequence":"additional","affiliation":[{"name":"Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau Taipa, Macau, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"118820","DOI":"10.1016\/j.fuel.2020.118820","article-title":"Large Eddy simulations of turbulent combustion of kerosene-air in a dual swirl gas turbine model combustor at high pressures","volume":"282","author":"Huang","year":"2020","journal-title":"Fuel"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"122103","DOI":"10.1016\/j.ijheatmasstransfer.2021.122103","article-title":"Dual-effect evaluation of heat transfer deterioration of supercritical carbon dioxide in variable cross-section horizontal tubes under heating conditions","volume":"183","author":"Li","year":"2022","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_3","first-page":"3","article-title":"Utilization status and progress of carbon dioxide at home and abroad","volume":"4","author":"Wei","year":"1997","journal-title":"Low Temp. Spec. Gases"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1016\/j.net.2015.06.009","article-title":"Review of supercritical CO2 power cycle technology and current status of research and development","volume":"47","author":"Ahn","year":"2015","journal-title":"Nucl. Eng. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.13182\/NT06-A3742","article-title":"Hydrogen production using high-temperature steam electrolysis supported by advanced gas reactor with supercritical CO2 cycles","volume":"155","author":"Yildiz","year":"2006","journal-title":"Nucl. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"081602","DOI":"10.1115\/1.4032666","article-title":"Thermodynamic and economic analysis and multi-objective optimization of supercritical CO2 Brayton cycles","volume":"138","author":"Zhao","year":"2016","journal-title":"J. Eng. Gas Turbines Power"},{"key":"ref_7","first-page":"71","article-title":"Thermodynamic analysis of supercritical CO2\/Organic flash cycle for waste heat recovery in marine gas turbine","volume":"53","author":"Wang","year":"2019","journal-title":"J. Xi\u2019an Jiaotong Univ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2086","DOI":"10.1103\/PhysRevA.15.2086","article-title":"Thermodynamics in finite time. I. The step-Carnot cycle","volume":"15","author":"Andresen","year":"1977","journal-title":"Phys. Rev. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2094","DOI":"10.1103\/PhysRevA.15.2094","article-title":"Thermodynamics in finite time. II. Potentials for finite-time processes","volume":"15","author":"Salamon","year":"1977","journal-title":"Phys. Rev. A"},{"key":"ref_10","unstructured":"Andresen, B. (1983). Finite-Time Thermodynamics, University of Copenhagen."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1021\/ar00104a001","article-title":"Thermodynamics for processes in finite time","volume":"17","author":"Andresen","year":"1984","journal-title":"Acc. Chem. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1063\/1.2916405","article-title":"Thermodynamics in finite time","volume":"37","author":"Andresen","year":"1984","journal-title":"Phys. Today"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2690","DOI":"10.1002\/anie.201001411","article-title":"Current trends in finite-time thermodynamics","volume":"50","author":"Andresen","year":"2011","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Berry, R.S., Salamon, P., and Andresen, B. (2020). How it all began. Entropy, 22.","DOI":"10.3390\/e22080908"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Andresen, B., and Salamon, P. (2022). Future perspectives of finite-time thermodynamics. Entropy, 24.","DOI":"10.3390\/e24050690"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1115\/1.3450705","article-title":"The concept of irreversibility in heat exchanger design: Counter-flow heat exchangers for gas-to-gas applications","volume":"99","author":"Bejan","year":"1977","journal-title":"Trans. ASME J. Heat Transf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1016\/0017-9310(78)90064-9","article-title":"General criterion for rating heat-exchanger performance","volume":"21","author":"Bejan","year":"1978","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_18","unstructured":"Bejan, A. (1982). Entropy Generation Through Heat and Fluid Flow, Wiley."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1063\/1.362674","article-title":"Entropy generation minimization: The new thermodynamics of finite-size devices and finite-time processes","volume":"79","author":"Bejan","year":"1996","journal-title":"J. Appl. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1002\/er.804","article-title":"Fundamentals of exergy analysis, entropy generation minimization, and the generation of flow architecture","volume":"26","author":"Bejan","year":"2002","journal-title":"Int. J. Energy Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s13369-012-0444-6","article-title":"Entropy generation minimization, exergy analysis, and the constructal law","volume":"38","author":"Bejan","year":"2013","journal-title":"Ara. J. Sci. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1515\/JNETDY.1999.020","article-title":"Finite time thermodynamic optimization or entropy generation minimization of energy systems","volume":"24","author":"Chen","year":"1999","journal-title":"J. Non-Equilibrium Thermodyn."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1007\/s11431-015-5970-5","article-title":"Thermodynamic analyses and optimization for thermoelectric devices: The state of the arts","volume":"59","author":"Chen","year":"2016","journal-title":"Sci. China Technol. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Ge, Y.L., Chen, L.G., and Sun, F.R. (2016). Progress in finite time thermodynamic studies for internal combustion engine cycles. Entropy, 18.","DOI":"10.3390\/e18040139"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1016\/0017-9310(88)90064-6","article-title":"Theory of heat transfer-irreversible power plants","volume":"31","author":"Bejan","year":"1988","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_26","first-page":"2","article-title":"Performance analysis of an irreversible Brayton heat engine","volume":"70","author":"Chen","year":"1997","journal-title":"J. Inst. Energy"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2242","DOI":"10.1016\/j.apm.2009.10.033","article-title":"Optimal paths for minimizing entransy dissipation during heat transfer processes with generalized radiative heat transfer law","volume":"34","author":"Xia","year":"2010","journal-title":"Appl. Math. Model."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Lanzetta, F. (2025). Compressor power and efficiency optimization: A finite-time thermodynamics approach. Entropy, 27.","DOI":"10.3390\/e27080842"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1016\/S0035-3159(96)80063-8","article-title":"Optimisation d\u2019un cycle de Brayton moteur en contact avec des capacites thermiques finies","volume":"35","author":"Feidt","year":"1996","journal-title":"Rev. Gen. Therm."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1080\/01430750.1999.9675324","article-title":"Performance analysis for a real closed regenerated Brayton cycle via methods of finite-time thermodynamics","volume":"20","author":"Chen","year":"1999","journal-title":"Int. J. Ambient Energy"},{"key":"ref_31","first-page":"141","article-title":"Effect of heat resistance on performance of closed gas turbine regenerative cycle","volume":"19","author":"Chen","year":"1999","journal-title":"Int. J. Power Energy Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"115189","DOI":"10.1016\/j.apenergy.2020.115189","article-title":"Multi-objective optimization of combined cooling, heating, and power systems with supercritical CO2 recompression Brayton Cycle","volume":"271","author":"Yang","year":"2020","journal-title":"Appl. Energy"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"071601","DOI":"10.1115\/1.4039446","article-title":"Optimization of supercritical CO2 Brayton cycle for simple cycle gas turbines exhaust heat recovery using genetic algorithm","volume":"140","author":"Khadse","year":"2018","journal-title":"J. Energy Resour. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"120601","DOI":"10.1016\/j.applthermaleng.2023.120601","article-title":"Multi-objective optimization of recompression S-CO2 cycle for gas turbine waste heat recovery","volume":"229","author":"Jin","year":"2023","journal-title":"Appl. Therm. Eng."},{"key":"ref_35","first-page":"100203","article-title":"Multi-objective performance optimization of regenerative S-CO2 Brayton cycle based on neural network prediction","volume":"14","author":"Jin","year":"2022","journal-title":"Energy Convers. Manag. X"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Jin, Q.L., Xia, S.J., and Xie, T.C. (2022). Ecological function analysis and optimization of a recompression S-CO2 cycle for gas turbine waste heat recovery. Entropy, 24.","DOI":"10.3390\/e24050732"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Chen, J.L., Jin, Q.L., and Huang, J.L. (2024, January 20\u201322). Ecological function and exergy efficiency of split-heating split-expansion S-CO2 Brayton cycle. Proceedings of the 2023 9th International Conference on Advances in Energy Resources and Environment Engineering, Shanghai, China.","DOI":"10.2991\/978-94-6463-415-0_71"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"117592","DOI":"10.1016\/j.enconman.2023.117592","article-title":"Thermodynamic and exergoeconomic optimization of a new combined cooling and power system based on supercritical CO2 recompression Brayton cycle","volume":"295","author":"Yousef","year":"2023","journal-title":"Energy Convers. Manag."},{"key":"ref_39","first-page":"101098","article-title":"Enhancing energy efficiency and cost-effectiveness of a solar-driven supercritical CO2 Brayton cycle through multi-objective optimization","volume":"27","author":"Fashtali","year":"2025","journal-title":"Energy Convers. Manag. X"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.tsep.2018.06.003","article-title":"Power and efficiency performance analyses for a closed endoreversible binary Brayton cycle with two isothermal processes","volume":"7","author":"Qi","year":"2018","journal-title":"Therm. Sci. Eng. Prog."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"112002","DOI":"10.1016\/j.enconman.2019.112002","article-title":"Optimal allocation of heat exchangers in a supercritical carbon dioxide power cycle for waste heat recovery","volume":"199","author":"Na","year":"2019","journal-title":"Energy Convers. Manag."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2713","DOI":"10.1016\/S0196-8904(03)00046-3","article-title":"Performance analysis for an irreversible closed variable-temperature heat reservoir intercooled regenerated Brayton cycle","volume":"44","author":"Wang","year":"2003","journal-title":"Energy Convers. Manag."},{"key":"ref_43","first-page":"1072","article-title":"Exergy efficiency analysis and optimization of a preheated S-CO2 Brayton cycle","volume":"43","author":"Jin","year":"2023","journal-title":"Proc. CSEE"},{"key":"ref_44","first-page":"111","article-title":"Exergy efficiency analysis and optimization of a recuperated S-CO2 Brayton cycle","volume":"55","author":"Xia","year":"2022","journal-title":"J. South China Univ. Technol. (Nat. Sci. Ed.)"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1016\/S0196-8904(96)00090-8","article-title":"Theoretical analysis of the performance of a regenerative closed Brayton cycle with internal irreversibilities","volume":"38","author":"Chen","year":"1997","journal-title":"Energy Convers. Manag."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1179\/174602207X187221","article-title":"Power density optimization of endoreversible closed intercooled regenerated Brayton cycle","volume":"80","author":"Chen","year":"2007","journal-title":"J. Energy Ins."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1080\/01430750.2009.9675086","article-title":"Power density optimization of an irreversible variable-temperature heat reservoir closed intercooled regenerated Brayton cycle","volume":"30","author":"Chen","year":"2009","journal-title":"Int. J. Ambient Energy"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2393","DOI":"10.1016\/S0196-8904(03)00008-6","article-title":"Power, power density and efficiency optimization for a closed cycle helium turbine nuclear power plant","volume":"44","author":"Chen","year":"2003","journal-title":"Energy Convers. Manag."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1080\/01971520500198783","article-title":"Optimum heat conductance distribution for power optimization of a regenerated closed Brayton cycle","volume":"2","author":"Chen","year":"2005","journal-title":"Int. J. Green Energy"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"114757","DOI":"10.1016\/j.applthermaleng.2019.114757","article-title":"Design and performance analysis of a supercritical CO2 radial inflow turbine","volume":"167","author":"Zhou","year":"2019","journal-title":"J. Appl. Thermal Eng."},{"key":"ref_51","first-page":"223","article-title":"Pitfalls of exergy analysis","volume":"42","author":"Johannsen","year":"2017","journal-title":"J. Non-Equilibrium Thermodyn."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/10\/1078\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T08:27:43Z","timestamp":1760948863000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/10\/1078"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,18]]},"references-count":51,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["e27101078"],"URL":"https:\/\/doi.org\/10.3390\/e27101078","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,18]]}}}