{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:50:16Z","timestamp":1760244616360,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,18]],"date-time":"2022-12-18T00:00:00Z","timestamp":1671321600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["51806235"],"award-info":[{"award-number":["51806235"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, for a highly coupled two-stage ejector-based cooling cycle, the optimization of primary nozzle length and angle of the second-stage ejector under varied primary nozzle diameters of the second stage was conducted first. Next, the evaluation for the influence of variable back pressure on ER of the two-stage ejector was performed. Last, the identification of the effect of the variable back pressure on the key geometries of the two-stage ejector was carried out. The results revealed that: (1) with the increase of the nozzle diameter at the second stage, the ER of both stages decreased with the increases of the length and angle of the converging section of the second-stage primary nozzle; (2) the pressure lift ratio range of the second-stage ejector in the critical mode gradually increased with the increase of the nozzle diameter of the second-stage; (3) when the pressure lift ratio increased from 102% to 106%, the peak ER of the second-stage decreased, and the influence of the area ratio and nozzle exit position of the second-stage ejector on its ER was reduced; (4) with the increase of nozzle diameter of the second-stage, the influence of area ratio and nozzle exit position of the second-stage on the second-stage performance decreased; and (5) the optimal AR of the second stage decreased but the optimal nozzle exit position of the second stage kept constant with the pressure lift ratio of the two-stage ejector.<\/jats:p>","DOI":"10.3390\/e24121847","type":"journal-article","created":{"date-parts":[[2022,12,19]],"date-time":"2022-12-19T05:55:43Z","timestamp":1671429343000},"page":"1847","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Effect of Back Pressure on Performances and Key Geometries of the Second Stage in a Highly Coupled Two-Stage Ejector"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7674-176X","authenticated-orcid":false,"given":"Jia","family":"Yan","sequence":"first","affiliation":[{"name":"School of Civil Engineering and Architecture, Southwest University of Science and Technology, Mianyang 621010, China"}]},{"given":"Yuetong","family":"Shu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering and Architecture, Southwest University of Science and Technology, Mianyang 621010, China"}]},{"given":"Chen","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Control Science and Engineering, Shandong University, Jinan 250061, China"},{"name":"Department of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester M13 9PL, UK"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"125101","DOI":"10.1016\/j.energy.2022.125101","article-title":"An improved hydraulic model of gathering pipeline network integrating pressure-exchange ejector","volume":"260","author":"Hong","year":"2022","journal-title":"Energy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.ijrefrig.2022.09.011","article-title":"Thermodynamic analysis of a modified vapor-injection heat pump cycle using an ejector","volume":"145","author":"Zhao","year":"2023","journal-title":"Int. J. Refrig."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"104412","DOI":"10.1016\/j.pnucene.2022.104412","article-title":"Optimization of an ejector to mitigate cavitation phenomena with coupled CFD\/BP neural network and particle swarm optimization algorithm","volume":"153","author":"Zhang","year":"2022","journal-title":"Prog. Nucl. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"119228","DOI":"10.1016\/j.applthermaleng.2022.119228","article-title":"One-dimensional mathematical modeling of two-phase ejectors: Extension to mixtures and mapping of the local exergy destruction","volume":"217","author":"Wilhelmsen","year":"2022","journal-title":"Appl. Therm. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/j.matpr.2022.09.141","article-title":"A comprehensive study on solar ejector cooling system: A review","volume":"69","author":"Kulkarni","year":"2022","journal-title":"Mater. Today Proc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/j.matpr.2022.09.258","article-title":"A comprehensive studies on constant area mixing (CAM) and constant pressure mixing (CPM) Ejectors: A review","volume":"69","author":"Kumar","year":"2022","journal-title":"Mater. Today Proc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1016\/j.ijheatmasstransfer.2016.05.129","article-title":"Optimization study of a two-stage ejector\u2013diffuser system","volume":"101","author":"Kong","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.ijheatmasstransfer.2015.01.117","article-title":"Analytical and computational studies on the performance of a two-stage ejector\u2013diffuser system","volume":"85","author":"Kong","year":"2015","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.ijrefrig.2020.08.002","article-title":"Theoretical analysis on a novel two-stage compression transcritical CO2 dual-evaporator refrigeration cycle with an ejector","volume":"119","author":"Liu","year":"2020","journal-title":"Int. J. Refrig."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"113761","DOI":"10.1016\/j.enconman.2020.113761","article-title":"Thermal performance of an absorption-assisted two-stage ejector air-to-water heat pump","volume":"230","author":"Wang","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"116094","DOI":"10.1016\/j.enconman.2022.116094","article-title":"Analysis of a modified transcritical CO2 two-stage ejector-compression cycle for domestic hot water production","volume":"269","author":"Liu","year":"2022","journal-title":"Energy Convers. Manag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.enconman.2018.08.110","article-title":"Optimization on ejector key geometries of a two-stage ejector-based mul-ti-evaporator refrigeration system","volume":"175","author":"Yan","year":"2018","journal-title":"Energ. Convers. Manag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.ijrefrig.2021.09.012","article-title":"Hybrid two\u2013stage CO2 transcritical mechanical compression\u2013ejector cooling cycle: Thermodynamic analysis and optimization","volume":"132","author":"Ierin","year":"2021","journal-title":"Int. J. Refrig."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"113541","DOI":"10.1016\/j.enconman.2020.113541","article-title":"Continuous production of cryogenic energy at low-temperature using two-stage ejector cooling system, Kalina power cycle, cold energy storage unit, and photovoltaic system","volume":"227","author":"Ghorbani","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"118005","DOI":"10.1016\/j.applthermaleng.2021.118005","article-title":"Performance analysis of an ejector-assisted two-stage evaporation single-stage va-por-compression cycle","volume":"205","author":"Cao","year":"2022","journal-title":"Appl. Therm. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"118730","DOI":"10.1016\/j.applthermaleng.2022.118730","article-title":"Numerical analysis of two-stage vacuum ejector performance considering the influence of phase transition and non-condensable gases","volume":"213","author":"Sun","year":"2022","journal-title":"Appl. Therm. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1016\/j.jngse.2016.07.031","article-title":"Numerical assessment on the performance of two-stage ejector to boost the low-pressure natural gas","volume":"34","author":"Chen","year":"2016","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2700","DOI":"10.1016\/j.matpr.2020.08.483","article-title":"Computational analysis of a supersonic two-stage ejector","volume":"38","author":"Yadav","year":"2021","journal-title":"Mater. Today Proc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"8546","DOI":"10.1016\/j.egyr.2022.06.066","article-title":"Exergy destruction characteristics of a transcritical carbon dioxide two-stage compres-sion\/ejector refrigeration system for low-temperature cold storage","volume":"8","author":"Yang","year":"2022","journal-title":"Energy Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"12944","DOI":"10.1016\/j.egyr.2022.09.108","article-title":"Evaluation of the ejector two-stage compression refrigeration cycle with work perfor-mance from energy, conventional exergy and advanced exergy perspectives","volume":"8","author":"Yang","year":"2022","journal-title":"Energy Rep."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"101158","DOI":"10.1016\/j.tsep.2021.101158","article-title":"An ejector based Transcritical Regenerative Series Two-Stage Organic Rankine Cycle for du-al\/multi-source heat recovery applications","volume":"27","author":"Surendran","year":"2022","journal-title":"Therm. Sci. Eng. Prog."},{"key":"ref_22","first-page":"101658","article-title":"A novel ejectors integration with two-stages adsorption desalination: Away to scavenge the ambient energy","volume":"48","author":"Ali","year":"2021","journal-title":"Sustain. Energy Technol. Assess."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1016\/j.applthermaleng.2016.07.104","article-title":"Numerical study and design of a two-stage ejector for subzero refrigeration","volume":"108","author":"Ding","year":"2016","journal-title":"Appl. Therm. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1016\/j.applthermaleng.2019.03.083","article-title":"Performance of a new two-stage transcritical CO2 refrigeration cycle with two ejectors","volume":"156","author":"Cheraghi","year":"2019","journal-title":"Appl. Therm. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"114713","DOI":"10.1016\/j.applthermaleng.2019.114713","article-title":"Design and investigation of a two-stage vacuum ejector for MED-TVC system","volume":"167","author":"Xue","year":"2020","journal-title":"Appl. Therm. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"116284","DOI":"10.1016\/j.applthermaleng.2020.116284","article-title":"Thermodynamic analysis of the optimal operating conditions for a two-stage CO2 refrigeration unit in warm climates with and without ejector","volume":"185","year":"2021","journal-title":"Appl. Therm. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"116565","DOI":"10.1016\/j.applthermaleng.2021.116565","article-title":"Optimal design of two-stage ejector for subzero refrigeration system on fishing vessel","volume":"187","author":"Wang","year":"2021","journal-title":"Appl. Therm. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Viscito, L., Lillo, G., Napoli, G., and Mauro, A.W. (2021). Waste Heat Driven Multi-Ejector Cooling Systems: Optimization of Design at Partial Load; Seasonal Performance and Cost Evaluation. Energies, 14.","DOI":"10.3390\/en14185663"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Lillo, G., Mastrullo, R., Mauro, A.W., Trinchieri, R., and Viscito, L. (2020). Thermo-Economic Analysis of a Hybrid Ejector Refrigerating System Based on a Low Grade Heat Source. Energies, 13.","DOI":"10.3390\/en13030562"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Li, H., Wang, X., Huang, H., Ning, J., and Tu, J. (2021). A Numerical Analysis of the Influence of Nozzle Geometric Structure on Spontaneous Steam Condensation and Irreversibility in the Steam Ejector Nozzle. Appl. Sci., 11.","DOI":"10.3390\/app112411954"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1016\/j.applthermaleng.2019.01.028","article-title":"Effects of operating conditions and cooling loads on two-stage ejector perfor-mances","volume":"150","author":"Wen","year":"2019","journal-title":"Appl Therm. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"117362","DOI":"10.1016\/j.applthermaleng.2021.117362","article-title":"Optimization on key geometries of a highly coupled two-stage ejector","volume":"197","author":"Yan","year":"2021","journal-title":"Appl. Therm. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.ijrefrig.2013.07.027","article-title":"A CFD analysis of the flow structure inside a steam ejector to identify the suitable experi-mental operating conditions for a solardriven refrigeration system","volume":"39","author":"Allouche","year":"2014","journal-title":"Int. J. Refrig."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1760","DOI":"10.1016\/j.rser.2008.09.032","article-title":"Progress of mathematical modeling on ejectors","volume":"13","author":"He","year":"2009","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"116845","DOI":"10.1016\/j.applthermaleng.2021.116845","article-title":"Influence of liquid volume fraction on ejector performance: A numerical study","volume":"190","author":"Wen","year":"2021","journal-title":"Appl. Therm. Eng."},{"key":"ref_36","unstructured":"NIST Chemistry WebBook (2010, February 01). NIST Standard Reference Database Number 69, Available online: http:\/\/webbook.nist.gov\/chemistry."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1847\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:43:42Z","timestamp":1760147022000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1847"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,18]]},"references-count":36,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["e24121847"],"URL":"https:\/\/doi.org\/10.3390\/e24121847","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,12,18]]}}}