{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,30]],"date-time":"2026-05-30T02:06:50Z","timestamp":1780106810313,"version":"3.54.0"},"reference-count":35,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,2]],"date-time":"2022-07-02T00:00:00Z","timestamp":1656720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSFC (National Natural Science Foundation of China)-Shandong Joint Fund","award":["U2006221"],"award-info":[{"award-number":["U2006221"]}]},{"name":"NSFC (National Natural Science Foundation of China)-Shandong Joint Fund","award":["ZR2021ME161"],"award-info":[{"award-number":["ZR2021ME161"]}]},{"name":"Shandong Provincial Fund","award":["U2006221"],"award-info":[{"award-number":["U2006221"]}]},{"name":"Shandong Provincial Fund","award":["ZR2021ME161"],"award-info":[{"award-number":["ZR2021ME161"]}]},{"name":"Ocean Industry Leading Talent Team","award":["U2006221"],"award-info":[{"award-number":["U2006221"]}]},{"name":"Ocean Industry Leading Talent Team","award":["ZR2021ME161"],"award-info":[{"award-number":["ZR2021ME161"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The energy loss of the multi-stage centrifugal pump was investigated by numerical analysis using the entropy generation method with the RNG k-\u03b5 turbulence model. Entropy generation due to time-averaged motion and velocity fluctuation was mainly considered. It was found that the entropy generation of guide vanes and impellers account for 71.2% and 23.3% of the total entropy generation under the designed flow condition. The guide vanes are the main hydraulic loss domains and their entropy generation is about 9 W\/K, followed by impellers. There are vortices at the tongue of the guide vane inlet as well as flow separations in the impellers, which lead to entropy generation. The fluid impacts the outer surface of the guide vanes, resulting in the increase in entropy generation. There are refluxes near the guide vane tongues which also increase the entropy generation of this part. The entropy generation distribution of the guide vanes and impellers was investigated, which found that the positive guide vane has more entropy generation compared with the reverse guide. The entropy generation of the blade suction surface is higher compared with the pressure surface. This study indicated that the entropy generation method has distinct advantages in the assessment of hydraulic loss.<\/jats:p>","DOI":"10.3390\/e24070923","type":"journal-article","created":{"date-parts":[[2022,7,2]],"date-time":"2022-07-02T11:12:35Z","timestamp":1656760355000},"page":"923","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Numerical Study on Entropy Generation of the Multi-Stage Centrifugal Pump"],"prefix":"10.3390","volume":"24","author":[{"given":"Baoxin","family":"Fan","sequence":"first","affiliation":[{"name":"Key Laboratory of High-Efficiency and Clean Mechanical Manufacture, National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhaoyu","family":"Liang","sequence":"additional","affiliation":[{"name":"Key Laboratory of High-Efficiency and Clean Mechanical Manufacture, National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruonan","family":"Fan","sequence":"additional","affiliation":[{"name":"Key Laboratory of High-Efficiency and Clean Mechanical Manufacture, National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2367-8802","authenticated-orcid":false,"given":"Songying","family":"Chen","sequence":"additional","affiliation":[{"name":"Key Laboratory of High-Efficiency and Clean Mechanical Manufacture, National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1115\/1.1478061","article-title":"CFD Calculation of a Mixed Flow Pump Characteristic from Shutoff to Maximum Flow","volume":"124","author":"Holbein","year":"2002","journal-title":"J. Fluids Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1115\/1.1881697","article-title":"Hydrodynamic Design of Rotodynamic Pump Impeller for Multiphase Pumping by Combined Approach of Inverse Design and CFD Analysis","volume":"127","author":"Cao","year":"2004","journal-title":"J. Fluids Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1177\/095440620421800407","article-title":"Numerical simulation of the stalled flow within a vaned centrifugal pump","volume":"218","author":"Guleren","year":"2004","journal-title":"ARCHIVE Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.apm.2010.05.021","article-title":"The flow simulation of a low-specific-speed high-speed centrifugal pump","volume":"35","author":"Jafarzadeh","year":"2011","journal-title":"Appl. Math. Model."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1088\/1755-1315\/15\/3\/032051","article-title":"Internal flow numerical simulation of double-suction centrifugal pump using DES model","volume":"15","author":"Zhou","year":"2012","journal-title":"IOP Conf. Ser. Earth Environ. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1603","DOI":"10.1007\/s12206-016-0315-2","article-title":"Influence of tip clearance on pressure fluctuations in an axial flow pump","volume":"30","author":"Feng","year":"2016","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_7","first-page":"322","article-title":"Effect of Multi Stage Centrifugal Pump on the Guide Vane Based on CFD Simulation","volume":"38","author":"Zhu","year":"2017","journal-title":"J. North Univ. China Nat. Sci. Ed. (China)"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1115\/1.3167072","article-title":"Entropy Generation Through Heat and Fluid Flow","volume":"50","author":"Bejan","year":"1983","journal-title":"J. Appl. Mech."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Spurk, J.H. (1997). Fluid Mechanics, Springer.","DOI":"10.1007\/978-3-642-58277-6"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1016\/j.ijheatfluidflow.2005.03.005","article-title":"Entropy production calculation for turbulent shear flows and their implementation in CFD codes","volume":"26","author":"Kock","year":"2005","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhang, H.C., Schmandt, B., and Herwig, H. (2009, January 18\u201321). Determination of Loss Coefficients for Micro-Flow Devices: A Method Based on the Second Law Analysis (SLA). Proceedings of the ASME 2009 2nd Micro\/Nanoscale Heat & Mass Transfer International Conference MNHMT, Shanghai, China.","DOI":"10.1115\/MNHMT2009-18192"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1016\/j.ijthermalsci.2008.07.001","article-title":"Entropy generation analysis of two-dimensional high-temperature confined jet","volume":"48","author":"Chu","year":"2009","journal-title":"Int. J. Therm. Sci."},{"key":"ref_13","first-page":"143","article-title":"A numerical research on energy loss evaluation in a centrifugal pump system based on local entropy production method","volume":"2016","author":"Hou","year":"2016","journal-title":"Therm. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.jngse.2016.10.017","article-title":"Numerical analysis of entropy production on a LNG cryogenic submerged pump","volume":"36","author":"Hou","year":"2016","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4637","DOI":"10.1177\/0954406217753458","article-title":"Entropy generation analysis for the cavitating head-drop characteristic of a centrifugal pump","volume":"232","author":"Li","year":"2018","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1177\/16878140211034622","article-title":"Numerical study on the flow characteristics of centrifugal compressor impeller with crack damage","volume":"13","author":"Liang","year":"2021","journal-title":"Adv. Mech. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/j.renene.2021.10.094","article-title":"Energy analysis of Francis turbine for various mass flow rate conditions based on entropy production theory","volume":"183","author":"Yu","year":"2022","journal-title":"Renew. Energy"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"137","DOI":"10.3901\/JME.2018.22.137","article-title":"Study on Flow Loss Characteristics of Side Channel Pump Based on Entropy Production","volume":"54","author":"Zhang","year":"2018","journal-title":"J. Mech. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/j.ijheatmasstransfer.2018.09.070","article-title":"Entropy production diagnostic analysis of energy consumption for cavitation flow in a two-stage LNG cryogenic submerged pump","volume":"129","author":"Wang","year":"2019","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1036","DOI":"10.1016\/j.renene.2020.08.102","article-title":"A numerical study on mechanisms of energy dissipation in a pump as turbine (PAT) using entropy generation theory","volume":"162","author":"Ghorani","year":"2020","journal-title":"Renew. Energy"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Li, S., Wu, P., and Wu, D. (2016, January 10\u201314). Hydraulic Optimization and Loss Analyses of a Low Specific-Speed Centrifugal Pump with Variable-Thickness Blades. Proceedings of the Fluids Engineering Division Summer Meeting, Washington, DC, USA.","DOI":"10.1115\/FEDSM2016-7814"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1177\/1687814016679568","article-title":"Effects of distance between impeller and guide vane on losses in a low head pump by entropy production analysis","volume":"8","author":"Pei","year":"2016","journal-title":"Adv. Mech. Eng."},{"key":"ref_23","first-page":"277","article-title":"Application of entropy production method to centrifugal pump energy loss evaluation","volume":"35","author":"Zhang","year":"2017","journal-title":"Paiguan Jixie Gongcheng Xuebao\/J. Drain. Irrig. Mach. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4711","DOI":"10.1007\/s12206-018-0918-x","article-title":"An experimental study on the cavitation vibration characteristics of a centrifugal pump at normal flow rate","volume":"32","author":"Li","year":"2018","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_25","first-page":"10","article-title":"Transition process characteristics of centrifugal pump with power-off based on entropy production theory","volume":"36","author":"Feng","year":"2020","journal-title":"Trans. Chin. Soc. Agric. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5316","DOI":"10.1177\/0954406219843573","article-title":"Flow loss analysis of a two-stage axially split centrifugal pump with double inlet under different channel designs","volume":"233","author":"Wang","year":"2019","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"061302","DOI":"10.1115\/1.4041876","article-title":"Influence of Guide Ring on Energy Loss in a Multistage Centrifugal Pump","volume":"141","author":"Ren","year":"2019","journal-title":"J. Fluids Eng.-Trans. Asme"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"373","DOI":"10.5293\/IJFMS.2021.14.4.373","article-title":"Influence of Diffuser Vane Number on Energy Loss of Multistage Centrifugal Pump","volume":"14","author":"Wu","year":"2021","journal-title":"Int. J. Fluid Mach. Syst."},{"key":"ref_29","unstructured":"Spurk, J.H., and Aksel, N. (1989). Str\u00f6mungslehre, Springer."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s00231-006-0086-x","article-title":"Direct and indirect methods of calculating entropy generation rates in turbulent convective heat transfer problems","volume":"43","author":"Herwig","year":"2007","journal-title":"Heat Mass Transf."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1017\/S0022112001005420","article-title":"The cavitation instability induced by the development of a re-entrant jet","volume":"444","author":"Callenaere","year":"2001","journal-title":"J. Fluid Mech."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2205","DOI":"10.1016\/j.ijheatmasstransfer.2003.11.025","article-title":"Local entropy production in turbulent shear flows: A high-Reynolds number model with wall functions","volume":"47","author":"Kock","year":"2004","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_33","first-page":"22","article-title":"Comparison of Different Turbulence Models for Numerical Simulation of Internal Flow of Centrifugal Compressor","volume":"38","year":"2010","journal-title":"Fluid Mach."},{"key":"ref_34","first-page":"86","article-title":"Application of 3-D RNG k-\u03b5 turbulence model of meandering river","volume":"26","author":"Zhang","year":"2007","journal-title":"J. Hydroelectr. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.jngse.2015.12.022","article-title":"Quasi-3D hydraulic design in the application of an LNG cryogenic submerged pump","volume":"29","author":"Zhang","year":"2016","journal-title":"J. Nat. Gas Sci. Eng."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/7\/923\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:42:01Z","timestamp":1760139721000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/7\/923"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,2]]},"references-count":35,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["e24070923"],"URL":"https:\/\/doi.org\/10.3390\/e24070923","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,2]]}}}