{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:08:47Z","timestamp":1772118527229,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T00:00:00Z","timestamp":1772064000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["No. 2021YFC3090105"],"award-info":[{"award-number":["No. 2021YFC3090105"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"China Power Construction Technology Projects","award":["No. DJ-ZDXM-2022-05"],"award-info":[{"award-number":["No. DJ-ZDXM-2022-05"]}]},{"name":"Guizhou Provincial Project for Building Science and Technology Innovation Talent Teams","award":["CXTD\uff082025\uff09061"],"award-info":[{"award-number":["CXTD\uff082025\uff09061"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Thermal stratification in deep reservoirs can cause ecologically problematic cold-water releases, and many existing selective-withdrawal phenomena rely on a limited set of fixed intake levels, which constrains their ability to follow seasonal shifts in the thermocline. Stepless stratified intakes with continuously adjustable flap gates offer quasi-continuous control of withdrawal depth, but their multi-gate, multi-brace layouts generate complex internal hydraulics whose energy-loss mechanisms are not well captured by conventional head-loss and resistance-coefficient metrics. In this study, physical-model measurements are combined with a validated three-dimensional numerical model, and entropy-production theory is used as a diagnostic to resolve where and by which mechanisms mechanical energy is irreversibly degraded inside a single-unit stepless stratified intake. The analysis shows that turbulent entropy production accounts for more than 98% of total dissipation, concentrated mainly in the flow channel and gate shaft, while the reservoir and outlet pipe contribute only weakly. Local entropy-production-rate fields indicate that dominant irreversibilities are associated with flow turning at the active gate leaves and with separation and wake development around horizontal and vertical braces, which generate low-velocity bands across gate levels and a low-velocity corridor in the shaft. Five geometric modification schemes targeting gate-entrance shaping and brace layout are evaluated; a combined brace-alignment and edge-rounding configuration most effectively weakens dissipation hotspots, improves discharge sharing among gate levels and reduces total entropy production. These findings show that entropy-based diagnostics can complement traditional hydraulic indicators and provide effective guidance for the design and refinement of stepless stratified intake structures.<\/jats:p>","DOI":"10.3390\/e28030256","type":"journal-article","created":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T13:58:03Z","timestamp":1772114283000},"page":"256","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Entropy Production Analysis and Fluid\u2013Structure Refinement of a Stepless Stratified Intake"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-2752-306X","authenticated-orcid":false,"given":"Jiahuan","family":"Qi","sequence":"first","affiliation":[{"name":"Nanjing Hydraulic Research Institute, Nanjing 210029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ke","family":"Liu","sequence":"additional","affiliation":[{"name":"Nanjing Hydraulic Research Institute, Nanjing 210029, China"},{"name":"Science and Technology Research Centre, China Yangtze Power Co., Ltd., Wuhan 430010, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingen","family":"Wang","sequence":"additional","affiliation":[{"name":"PowerChina Guiyang Engineering Corporation Limited, Guiyang 553304, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianping","family":"Zhao","sequence":"additional","affiliation":[{"name":"Nanjing Hydraulic Research Institute, Nanjing 210029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Li","sequence":"additional","affiliation":[{"name":"Nanjing Hydraulic Research Institute, Nanjing 210029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"125665","DOI":"10.1016\/j.jhydrol.2020.125665","article-title":"Assessment of the impact of selective withdrawal on downstream fish habitats using a coupled hydrodynamic and habitat modeling","volume":"593","author":"Kim","year":"2021","journal-title":"J. Hydrol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"131484","DOI":"10.1016\/j.jhydrol.2024.131484","article-title":"Impacts of cascade hydropower development on river ecosystem homeostasis: A review","volume":"638","author":"Wang","year":"2024","journal-title":"J. Hydrol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1038\/s43017-024-00596-0","article-title":"Hydropower impacts on riverine biodiversity","volume":"5","author":"He","year":"2024","journal-title":"Nat. Rev. Earth Environ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4014063","DOI":"10.1061\/(ASCE)WR.1943-5452.0000447","article-title":"Optimizing selective withdrawal from reservoirs to manage downstream temperatures with climate warming","volume":"141","author":"Rheinheimer","year":"2015","journal-title":"J. Water Resour. Plan. Manag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"32214","DOI":"10.1038\/s41598-025-18027-5","article-title":"Enhancing water security through integrated decision-making and selective withdrawal for sustainable reservoir management","volume":"15","author":"Alizadeh","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"115474","DOI":"10.1016\/j.eswa.2021.115474","article-title":"Optimization of selective withdrawal systems in hydropower reservoir considering water quality and quantity aspects","volume":"184","author":"Saadatpour","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"111294","DOI":"10.1016\/j.ecolind.2023.111294","article-title":"Optimization of selective withdrawal strategy in a warm monomictic reservoir based on thermal stratification","volume":"158","author":"Wang","year":"2024","journal-title":"Ecol. Indic."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"123659","DOI":"10.1016\/j.watres.2025.123659","article-title":"Joint thermal regulation by selective withdrawal in serial cascade reservoir systems effectively improves reservoir and downstream ecological health","volume":"281","author":"Hu","year":"2025","journal-title":"Water Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1061\/(ASCE)WR.1943-5452.0000348","article-title":"Planning the optimal operation of a multioutlet water reservoir with water quality and quantity targets","volume":"140","author":"Castelletti","year":"2014","journal-title":"J. Water Resour. Plan. Manag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s11431-011-4602-y","article-title":"Spatial-temporal effects of temperature control device of stoplog intake for Jinping I hydropower station","volume":"54","author":"Deng","year":"2011","journal-title":"Sci. China Technol. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1002\/rra.3453","article-title":"Mitigation of cold-water thermal pollution downstream of a large dam with the use of a novel thermal curtain","volume":"35","author":"Gray","year":"2019","journal-title":"River Res. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"144423","DOI":"10.1016\/j.scitotenv.2020.144423","article-title":"Thermal stratification responses of a monomictic reservoir under different seasons and operation schemes","volume":"767","author":"Duka","year":"2021","journal-title":"Sci. Total Environ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"106864","DOI":"10.1016\/j.ecoleng.2022.106864","article-title":"Thermal response of a deep monomictic reservoir to selective withdrawal of the upstream reservoir","volume":"187","author":"Wang","year":"2023","journal-title":"Ecol. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"110560","DOI":"10.1016\/j.ecolind.2023.110560","article-title":"Prediction model of the outflow temperature from stratified reservoir regulated by stratified water intake facility based on machine learning algorithm","volume":"154","author":"Lu","year":"2023","journal-title":"Ecol. Indic."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"123794","DOI":"10.1016\/j.jenvman.2024.123794","article-title":"Thermal response of deep monomictic reservoir under different selective withdrawal types","volume":"373","author":"Hu","year":"2025","journal-title":"J. Environ. Manag."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1186\/s12302-019-0202-4","article-title":"Variable withdrawal elevations as a management tool to counter the effects of climate warming in Germany\u2019s largest drinking water reservoir","volume":"31","author":"Mi","year":"2019","journal-title":"Environ. Sci. Eur."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"99","DOI":"10.2166\/wqrj.2023.030","article-title":"Decision support system for selective withdrawal in water supply reservoirs: An approach based on thermal stratification","volume":"58","author":"Soyer","year":"2023","journal-title":"Water Qual. Res. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"167527","DOI":"10.1016\/j.scitotenv.2023.167527","article-title":"Future projections of thermal regimes and mixing characteristics in a monomictic reservoir under climate change","volume":"906","author":"Wang","year":"2024","journal-title":"Sci. Total Environ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"142347","DOI":"10.1016\/j.jclepro.2024.142347","article-title":"Climate warming effects in stratified reservoirs: Thorough assessment for opportunities and limits of machine learning techniques versus process-based models in thermal structure projections","volume":"454","author":"Mi","year":"2024","journal-title":"J. Clean. Prod."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"129184","DOI":"10.1016\/j.jhydrol.2023.129184","article-title":"Numerical simulation of thermal stratification in lake qiandaohu using an improved WRF-lake model","volume":"618","author":"Wang","year":"2023","journal-title":"J. Hydrol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.jes.2023.06.025","article-title":"Optimizing selective withdrawal strategies to mitigate hypoxia under water-level reduction in Germany\u2019s largest drinking water reservoir","volume":"146","author":"Mi","year":"2024","journal-title":"J. Environ. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"117459","DOI":"10.1016\/j.jenvman.2023.117459","article-title":"Diurnal variation characteristics of thermal structure in a deep reservoir and the effects of selective withdrawal","volume":"333","author":"He","year":"2023","journal-title":"J. Environ. Manag."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Liu, L., Tuo, Y., Xia, H., Deng, Y., Zhang, X., and Wang, H. (2023). Assessment of stoplog gates\u2019 operational effectiveness for improving discharged-water temperatures during the thermal stratification period in a reservoir. Water, 15.","DOI":"10.3390\/w15234145"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"118030","DOI":"10.1016\/j.watres.2021.118030","article-title":"The influence of hydraulic characteristics on algal bloom in three gorges reservoir, China: A combination of cultural experiments and field monitoring","volume":"211","author":"Yang","year":"2022","journal-title":"Water Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"136358","DOI":"10.1016\/j.jclepro.2023.136358","article-title":"Can selective withdrawal control algal blooms in reservoirs? The underlying hydrodynamic mechanism","volume":"394","author":"Song","year":"2023","journal-title":"J. Clean. Prod."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"279","DOI":"10.2166\/ws.2016.133","article-title":"Optimal control of reservoir release temperature through selective withdrawal intake at hydropower dam","volume":"17","author":"Zheng","year":"2016","journal-title":"Water Supply"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1016\/j.renene.2022.12.029","article-title":"Study on the water temperature distribution characteristics of a mixed pumped storage power station reservoir: A case study of Jinshuitan reservoir","volume":"202","author":"Yang","year":"2023","journal-title":"Renew. Energy"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"52001","DOI":"10.1088\/1755-1315\/510\/5\/052001","article-title":"Numerical computation of multi-level intake of diversion project","volume":"510","author":"Wang","year":"2020","journal-title":"IOP Conf. Ser. Earth Environ. Sci"},{"key":"ref_29","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_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":"2006","journal-title":"Heat Mass Transf."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1016\/j.icheatmasstransfer.2007.01.015","article-title":"Entropy generation minimization in turbulent mixed convection flows","volume":"34","author":"Balaji","year":"2007","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"119211","DOI":"10.1016\/j.apenergy.2022.119211","article-title":"Application of entropy production theory for energy losses and other investigation in pumps and turbines: A review","volume":"318","author":"Zhou","year":"2022","journal-title":"Appl. Energy"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1636","DOI":"10.1007\/s11431-013-5229-y","article-title":"Application of entropy production theory to hydro-turbine hydraulic analysis","volume":"56","author":"Gong","year":"2013","journal-title":"Sci. China Technol. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1016\/j.renene.2021.07.041","article-title":"Investigations of the thermodynamic entropy evaluation in a hydraulic turbine under various operating conditions","volume":"180","author":"Yu","year":"2021","journal-title":"Renew. Energy"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.enconman.2017.07.024","article-title":"Entropy production analysis of hysteresis characteristic of a pump-turbine model","volume":"149","author":"Li","year":"2017","journal-title":"Energy Convers. Manag."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Yan, X., Kan, K., Zheng, Y., Chen, H., and Binama, M. (2022). Entropy production evaluation within a prototype pump-turbine operated in pump mode for a wide range of flow conditions. Processes, 10.","DOI":"10.3390\/pr10102058"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Shi, F., Zhang, D., Wang, P., Wang, X., and Feng, C. (2025). Analysis of the Energy Loss Mechanism in Hydraulic Turbines with Different Guide-Vane Numbers Based on Entropy Generation Theory. Processes, 13.","DOI":"10.3390\/pr13061899"},{"key":"ref_38","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_39","doi-asserted-by":"crossref","first-page":"104784","DOI":"10.1016\/j.icheatmasstransfer.2020.104784","article-title":"Diagnosis of internal energy characteristics of mixed-flow pump within stall region based on entropy production analysis model","volume":"117","author":"Ji","year":"2020","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1687814016679568","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_41","doi-asserted-by":"crossref","first-page":"104526","DOI":"10.1016\/j.icheatmasstransfer.2020.104526","article-title":"Energy loss evaluation in a side channel pump under different wrapping angles using entropy production method","volume":"113","author":"Zhang","year":"2020","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"116553","DOI":"10.1016\/j.enconman.2022.116553","article-title":"Evaluating energy loss with the entropy production theory: A case study of a micro horizontal axis river ducted turbine","volume":"276","author":"Wang","year":"2023","journal-title":"Energy Convers. Manag."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.renene.2020.08.109","article-title":"Application of enstrophy dissipation to analyze energy loss in a centrifugal pump as turbine","volume":"163","author":"Lin","year":"2021","journal-title":"Renew. Energy"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"128719","DOI":"10.1016\/j.applthermaleng.2025.128719","article-title":"Energy distribution in radial-inflow turbines following enthalpy gradient magnitude method","volume":"281","author":"Wan","year":"2025","journal-title":"Appl. Therm. Eng."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"138233","DOI":"10.1016\/j.energy.2025.138233","article-title":"Investigation of the impact of trapezoidal suction surface impeller on internal flow and energy conversion in side channel pumps","volume":"335","author":"Wu","year":"2025","journal-title":"Energy"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1016\/j.energy.2019.05.053","article-title":"On the accuracy of turbulence models for CFD simulations of vertical axis wind turbines","volume":"180","author":"Rezaeiha","year":"2019","journal-title":"Energy"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"112783","DOI":"10.1016\/j.jcp.2024.112783","article-title":"A cell-based smoothed finite element model for the analysis of turbulent flow using realizable k-\u03b5 model and mixed meshes","volume":"501","author":"Liu","year":"2024","journal-title":"J. Comput. Phys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0021-9991(81)90145-5","article-title":"Volume of fluid (VOF) method for the dynamics of free boundaries","volume":"39","author":"Hirt","year":"1981","journal-title":"J. Comput. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"132957","DOI":"10.1016\/j.energy.2024.132957","article-title":"Influence of gate cutoff effect on flow mode conversion and energy dissipation during power-off of prototype tubular pump system","volume":"308","author":"Zhang","year":"2024","journal-title":"Energy"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/3\/256\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T14:01:19Z","timestamp":1772114479000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/3\/256"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,26]]},"references-count":49,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["e28030256"],"URL":"https:\/\/doi.org\/10.3390\/e28030256","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,26]]}}}