{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T18:00:47Z","timestamp":1780941647130,"version":"3.54.1"},"reference-count":40,"publisher":"Public Library of Science (PLoS)","issue":"6","license":[{"start":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T00:00:00Z","timestamp":1780876800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>\n                    Flow passage optimization is an essential approach for enhancing the efficiency and operational stability of vertical mixed-flow pump units. To address the limitations of the traditional single-factor control variable method\u2014which ignores parameter interaction effects and relies on empirical judgment for scheme screening, leading to low optimization efficiency and insufficient engineering adaptability\u2014this study proposes a multi-factor interactive flow passage optimization methodology that deeply couples orthogonal experimental design with Computational Fluid Dynamics (CFD) simulations. A multi-indicator quantitative evaluation system encompassing \u201chydraulic loss, velocity uniformity, and weighted average angle\u201d was constructed. Taking a large-scale drainage pumping station as the research object, key parameter combinations were systematically covered through orthogonal experiments. The optimal intake flow passage scheme was screened via CFD simulation, which was verified to have a hydraulic loss of only 0.104 m, an outlet velocity uniformity of 97.06%, and a weighted average angle of 84.82\u00b0, approaching the ideal vertical inflow, thereby effectively reducing flow impact losses. The optimal discharge flow passage scheme demonstrated smooth flow patterns without significant flow separation and was fully compatible with the spatial layout of the pumping station. Model test validation showed that under the design head condition of 7.1 m, the pump unit efficiency reached 77.34% with a flow rate of 11.38 m\n                    <jats:sup>3<\/jats:sup>\n                    \/s. The error between CFD simulation and experimental results was less than 5%, meeting the design requirements. This study provides a scientifically efficient and engineeringly feasible technical pathway for flow passage optimization in similar vertical mixed-flow pump units.\n                  <\/jats:p>","DOI":"10.1371\/journal.pone.0343448","type":"journal-article","created":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T17:31:17Z","timestamp":1780939877000},"page":"e0343448","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-factor orthogonal optimization and experimental performance study of flow passages in a vertical mixed-flow pump 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under various operating conditions","volume":"141","author":"P Kumar","year":"2019","journal-title":"J Fluids Eng"},{"issue":"6","key":"pone.0343448.ref002","doi-asserted-by":"crossref","first-page":"065212","DOI":"10.1063\/5.0273064","article-title":"Optimization research on the inlet and outlet passage of shaft tubular pump based on CFD","volume":"15","author":"Y Miao","year":"2025","journal-title":"AIP Advances"},{"key":"pone.0343448.ref003","doi-asserted-by":"crossref","first-page":"1387837","DOI":"10.3389\/fenrg.2024.1387837","article-title":"Test and analysis of energy characteristics of large vertical submersible pumps","volume":"12","author":"C Yang","year":"2024","journal-title":"Front Energy Res"},{"issue":"5","key":"pone.0343448.ref004","first-page":"055121","article-title":"Optimization and experimental validation of a mixed-flow pump based on CFD and entropy production analysis","volume":"34","author":"Y Liu","year":"2022","journal-title":"Phys Fluids"},{"issue":"9","key":"pone.0343448.ref005","first-page":"04018033","article-title":"A study on the design standards and performance evaluation of large-scale pumping stations","volume":"144","author":"SS Yang","year":"2018","journal-title":"J Irrig Drain Eng"},{"key":"pone.0343448.ref006","first-page":"220","article-title":"Hydraulic performance improvement of an existing pumping station through impeller and diffuser redesign","volume":"162","author":"H Zhang","year":"2020","journal-title":"Renew Energy"},{"issue":"7","key":"pone.0343448.ref007","first-page":"182","article-title":"Optimization design of inlet and outlet passages for tank-type axial-flow pumping station","volume":"68","author":"F Wang","year":"2019","journal-title":"Irrig Drain"},{"issue":"4","key":"pone.0343448.ref008","first-page":"1010","article-title":"Experimental investigation of flow patterns in pump sump and its effects on pump performance","volume":"19","author":"BG Paik","year":"2005","journal-title":"J Mech Sci Technol"},{"issue":"1","key":"pone.0343448.ref009","first-page":"325","article-title":"Intelligent optimization of axial-flow pump using physics-considering machine learning","volume":"11","author":"K Kan","year":"2023","journal-title":"J Comput Des Eng"},{"issue":"10","key":"pone.0343448.ref010","first-page":"101102","article-title":"High-efficiency design of a mixed-flow pump using a surrogate model","volume":"132","author":"JH Kim","year":"2010","journal-title":"J Fluids Eng"},{"issue":"5","key":"pone.0343448.ref011","article-title":"Effects of the radial gap between impeller tips and volute tongue influencing the performance and pressure pulsations of pump as turbine","volume":"136","author":"S-S Yang","year":"2014","journal-title":"J Fluids Eng"},{"issue":"11","key":"pone.0343448.ref012","first-page":"2301","article-title":"Hydraulic optimization of a siphon outlet conduit in a large pumping station based on CFD and model test","volume":"11","author":"Y Long","year":"2019","journal-title":"Water"},{"issue":"12","key":"pone.0343448.ref013","first-page":"1","article-title":"Numerical simulation of the full flow field in a pumping station intake sump and its application to optimize the flow pattern","volume":"9","author":"Y Zhang","year":"2017","journal-title":"Adv Mech Eng"},{"issue":"10","key":"pone.0343448.ref014","doi-asserted-by":"crossref","first-page":"728","DOI":"10.3390\/pr7100728","article-title":"Performance optimization of high specific speed centrifugal pump based on orthogonal experiment design method","volume":"7","author":"Z Li","year":"2019","journal-title":"Processes"},{"issue":"3","key":"pone.0343448.ref015","first-page":"06017033","article-title":"Comparative analysis of hydraulic performance between siphon and straight discharge passages in a low-lift pumping station","volume":"144","author":"L Cheng","year":"2018","journal-title":"J Hydraul Eng"},{"issue":"2","key":"pone.0343448.ref016","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1115\/1.1457452","article-title":"Numerical simulation of the dynamic effects due to impeller-volute interaction in a centrifugal pump","volume":"124","author":"J Gonza\u00b4lez","year":"2002","journal-title":"J Fluids Eng"},{"key":"pone.0343448.ref017","first-page":"4203","article-title":"A review of internal flow analysis and optimization methods for centrifugal pumps","volume":"34","author":"L Ji","year":"2020","journal-title":"J Mech Sci Technol"},{"issue":"8","key":"pone.0343448.ref018","first-page":"081102","article-title":"Experimental investigation of the influence of blade geometry on the performance of a centrifugal pump running in turbine mode","volume":"131","author":"P Singh","year":"2009","journal-title":"J Fluids Eng"},{"issue":"8","key":"pone.0343448.ref019","doi-asserted-by":"crossref","first-page":"1598","DOI":"10.2514\/3.12149","article-title":"Two-equation eddy-viscosity turbulence models for engineering applications","volume":"32","author":"FR Menter","year":"1994","journal-title":"AIAA J"},{"key":"pone.0343448.ref020","first-page":"108275","article-title":"Numerical and experimental investigation of the flow in a 30\u00b0 inclined intake channel and its effect on pump performance","volume":"219","author":"C Wu","year":"2021","journal-title":"Ocean Eng"},{"key":"pone.0343448.ref021","first-page":"79101","article-title":"Experimental study and numerical simulation of internal flow characteristics in mixed-flow pump","volume":"14","author":"X Liu","year":"2024","journal-title":"Sci Rep"},{"issue":"2","key":"pone.0343448.ref022","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1061\/(ASCE)0733-9429(1998)124:2(123)","article-title":"Numerical model for simulation of pump-intake flow and vortices","volume":"124","author":"GS Constantinescu","year":"1998","journal-title":"J Hydraul Eng"},{"key":"pone.0343448.ref023","doi-asserted-by":"crossref","first-page":"120959","DOI":"10.1016\/j.enconman.2025.120959","article-title":"Investigation of energy dissipation mechanisms and unsteady flow characteristics of a cooling pump based on sweeping jet inflow","volume":"351","author":"H Chang","year":"2026","journal-title":"Energy Convers Manag"},{"key":"pone.0343448.ref024","first-page":"221","article-title":"Hydraulic characteristics of a box culvert discharge passage in a low-head pumping station: experiment and numerical simulation","volume":"65","author":"M Tan","year":"2019","journal-title":"Flow Meas Instrum"},{"key":"pone.0343448.ref025","article-title":"Entropy production analysis for energy dissipation of a vertical mixed-flow pump","author":"Y Zheng","year":"2022","journal-title":"Proc Inst Mech Eng Part A: J Power Energy"},{"issue":"10","key":"pone.0343448.ref026","first-page":"1991","article-title":"Entropy production analysis of a vertical mixed-flow pump device with different guide vane meridians","volume":"10","author":"Z Li","year":"2022","journal-title":"Processes"},{"key":"pone.0343448.ref027","first-page":"103062","article-title":"Transient characteristics during startup of a vertical mixed-flow pump system with optimized inlet conduit","volume":"42","author":"L Gao","year":"2021","journal-title":"J Energy Storage"},{"key":"pone.0343448.ref028","first-page":"307","article-title":"CFD simulation and PIV measurement of the flow field in a pump intake sump","volume":"20","author":"S Huang","year":"2017","journal-title":"J Vis"},{"issue":"3","key":"pone.0343448.ref029","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1115\/1.2173294","article-title":"Steady and unsteady radial forces for a centrifugal pump with impeller to tongue gap variation","volume":"128","author":"J Gonz\u00e1lez","year":"2005","journal-title":"J Fluids Eng"},{"issue":"11","key":"pone.0343448.ref030","doi-asserted-by":"crossref","first-page":"1540","DOI":"10.1061\/(ASCE)0733-9429(1984)110:11(1540)","article-title":"Scale effects in pump sump models","volume":"110","author":"M Padmanabhan","year":"1984","journal-title":"J Hydraul Eng"},{"issue":"1","key":"pone.0343448.ref031","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1115\/1.2816813","article-title":"Relationship between unsteady flow, pressure fluctuations, and noise in a centrifugal pump\u2014Part A: use of PDV data to compute the pressure field","volume":"117","author":"S Chu","year":"1995","journal-title":"J Fluids Eng"},{"issue":"1","key":"pone.0343448.ref032","first-page":"1","article-title":"A method for parameterized design and rapid optimization of axial-flow pump impeller","volume":"19","author":"Y Zhang","year":"2025","journal-title":"Eng Appl Comput Fluid Mech"},{"issue":"5","key":"pone.0343448.ref033","first-page":"554","article-title":"Model test and numerical simulation of the flow in a forebay with asymmetric inflows","volume":"54","author":"L Lu","year":"2016","journal-title":"J Hydraul Res"},{"key":"pone.0343448.ref034","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/j.renene.2020.11.060","article-title":"Spike-type disturbances due to inlet distortion in a centrifugal pump","volume":"165","author":"P Cao","year":"2021","journal-title":"Renew Energy"},{"issue":"13","key":"pone.0343448.ref035","first-page":"4658","article-title":"Numerical study on entropy generation of the multi-stage centrifugal pump","volume":"15","author":"L Zhang","year":"2022","journal-title":"Energies"},{"key":"pone.0343448.ref036","first-page":"1764","article-title":"Customized design and experimental validation of an axial-flow pump for a specific operating condition based on CFD","volume":"146","author":"W Shi","year":"2020","journal-title":"Renew Energy"},{"issue":"1","key":"pone.0343448.ref037","article-title":"Effect mechanism of 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