{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T05:47:12Z","timestamp":1778824032977,"version":"3.51.4"},"reference-count":42,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,4,2]],"date-time":"2024-04-02T00:00:00Z","timestamp":1712016000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Engineering Research Center of High-efficiency and Energy-saving Large Axial Flow Pumping Station, Jiangsu Province, Yangzhou University","award":["ECHEAP001"],"award-info":[{"award-number":["ECHEAP001"]}]},{"name":"Engineering Research Center of High-efficiency and Energy-saving Large Axial Flow Pumping Station, Jiangsu Province, Yangzhou University","award":["52079142"],"award-info":[{"award-number":["52079142"]}]},{"name":"Engineering Research Center of High-efficiency and Energy-saving Large Axial Flow Pumping Station, Jiangsu Province, Yangzhou University","award":["BK20220587"],"award-info":[{"award-number":["BK20220587"]}]},{"name":"Engineering Research Center of High-efficiency and Energy-saving Large Axial Flow Pumping Station, Jiangsu Province, Yangzhou University","award":["2023M732979"],"award-info":[{"award-number":["2023M732979"]}]},{"name":"Engineering Research Center of High-efficiency and Energy-saving Large Axial Flow Pumping Station, Jiangsu Province, Yangzhou University","award":["HZKY20220117"],"award-info":[{"award-number":["HZKY20220117"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["ECHEAP001"],"award-info":[{"award-number":["ECHEAP001"]}],"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":["52079142"],"award-info":[{"award-number":["52079142"]}],"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":["BK20220587"],"award-info":[{"award-number":["BK20220587"]}],"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":["2023M732979"],"award-info":[{"award-number":["2023M732979"]}],"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":["HZKY20220117"],"award-info":[{"award-number":["HZKY20220117"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["ECHEAP001"],"award-info":[{"award-number":["ECHEAP001"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["52079142"],"award-info":[{"award-number":["52079142"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20220587"],"award-info":[{"award-number":["BK20220587"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["2023M732979"],"award-info":[{"award-number":["2023M732979"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["HZKY20220117"],"award-info":[{"award-number":["HZKY20220117"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["ECHEAP001"],"award-info":[{"award-number":["ECHEAP001"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["52079142"],"award-info":[{"award-number":["52079142"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["BK20220587"],"award-info":[{"award-number":["BK20220587"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2023M732979"],"award-info":[{"award-number":["2023M732979"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["HZKY20220117"],"award-info":[{"award-number":["HZKY20220117"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ministry of Education\u2019s \u201cChunhui Program\u201d","award":["ECHEAP001"],"award-info":[{"award-number":["ECHEAP001"]}]},{"name":"Ministry of Education\u2019s \u201cChunhui Program\u201d","award":["52079142"],"award-info":[{"award-number":["52079142"]}]},{"name":"Ministry of Education\u2019s \u201cChunhui Program\u201d","award":["BK20220587"],"award-info":[{"award-number":["BK20220587"]}]},{"name":"Ministry of Education\u2019s \u201cChunhui Program\u201d","award":["2023M732979"],"award-info":[{"award-number":["2023M732979"]}]},{"name":"Ministry of Education\u2019s \u201cChunhui Program\u201d","award":["HZKY20220117"],"award-info":[{"award-number":["HZKY20220117"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In hydro turbines, the draft tube vortex rope is one of the most crucial impact factors causing pressure pulsation and vibration. It is affected by operating conditions due to differences in the flow rate and state and can be symmetric or asymmetric along the rotational direction. It may influence the stability of draft tube flow. To achieve a better understanding, in this work, dynamic mode decomposition is used in a draft tube case study of a simplification of a vortex rope. As the flow rate increases, the shape of the vortex rope becomes clear, and the flow rotation becomes more significant as the inlet flow rate increases. Dynamic mode decomposition was used to determine the relative frequencies, which were 0 (averaged), 0.7 times, and 1.4 times the features of the reference frequency. As the inlet flow rate increases, the order of high-energy modes and their influence on the vortex rope gradually increase, and this characteristic is exhibited further downstream of the draft tube. When the inlet flow rate is low, the impact of mode noise is greater. As the flow velocity increases, the noise weakens and the rotation mode becomes more apparent. Identifying the mode of the vortex flow helps extract characteristics of the vortex rope flow under different operating conditions, providing a richer data-driven basis for an in-depth analysis of the impact of operating conditions on the flow stability of a draft tube.<\/jats:p>","DOI":"10.3390\/sym16040416","type":"journal-article","created":{"date-parts":[[2024,4,2]],"date-time":"2024-04-02T10:58:31Z","timestamp":1712055511000},"page":"416","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Comparative Study of the Mode-Decomposed Characteristics of the Asymmetricity of a Vortex Rope with Flow Rate Variation"],"prefix":"10.3390","volume":"16","author":[{"given":"Shujing","family":"Li","sequence":"first","affiliation":[{"name":"College of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weilong","family":"Guang","sequence":"additional","affiliation":[{"name":"College of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3431-019X","authenticated-orcid":false,"given":"Yang","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Hydraulic Science and Engineering, Yangzhou University, Yangzhou 225009, China"},{"name":"Engineering Research Center of High-Efficiency and Energy-Saving Large Axial Flow Pumping Station, Jiangsu Province, Yangzhou University, Yangzhou 225009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Puxi","family":"Li","sequence":"additional","affiliation":[{"name":"College of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruofu","family":"Xiao","sequence":"additional","affiliation":[{"name":"College of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, China"},{"name":"Beijing Engineering Research Center of Safety and Energy Saving Technology for Water Supply Network System, China Agricultural University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3566-5339","authenticated-orcid":false,"given":"Di","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Engineering, China Agricultural University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Faye","family":"Jin","sequence":"additional","affiliation":[{"name":"College of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ran","family":"Tao","sequence":"additional","affiliation":[{"name":"College of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, China"},{"name":"Engineering Research Center of High-Efficiency and Energy-Saving Large Axial Flow Pumping Station, Jiangsu Province, Yangzhou University, Yangzhou 225009, China"},{"name":"Beijing Engineering Research Center of Safety and Energy Saving Technology for Water Supply Network System, China Agricultural University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1038\/s41467-020-14555-y","article-title":"Global resource potential of seasonal pumped hydropower storage for energy and water storage","volume":"11","author":"Hunt","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1002\/er.3283","article-title":"Clean energy systems as mainstream energy options: Clean energy systems","volume":"40","author":"Lund","year":"2016","journal-title":"Int. J. Energy Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1016\/j.apenergy.2019.04.125","article-title":"Modeling a pumped storage hydropower integrated to a hybrid power system with solar-wind power and its stability analysis","volume":"248","author":"Xu","year":"2019","journal-title":"Appl. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1016\/j.renene.2017.07.055","article-title":"A nonlinear generalized predictive control for pumped storage unit","volume":"114","author":"Li","year":"2017","journal-title":"Renew. Energy"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"114222","DOI":"10.1016\/j.oceaneng.2023.114222","article-title":"Evaluation of the rotor eccentricity added radial force of oscillating water column","volume":"276","author":"Tao","year":"2023","journal-title":"Ocean Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.rser.2016.09.121","article-title":"Fluid-structure interactions in Francis turbines: A perspective review","volume":"68","author":"Trivedi","year":"2017","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1303","DOI":"10.1061\/(ASCE)0733-9429(2006)132:12(1303)","article-title":"Validation of a Large-Eddy Simulation Model to Simulate Flow in Pump Intakes of Realistic Geometry","volume":"132","author":"Tokyay","year":"2006","journal-title":"J. Hydraul. Eng."},{"key":"ref_8","unstructured":"Stefan, D., Hudec, M., Uruba, V., Proch\u00e1zka, P., Urban, O., and Rudolf, P. (2021, January 21\u201326). Experimental investigation of swirl number influence on spiral vortex structure dynamics. Proceedings of the 30th IAHR Symposium on Hydraulic Machinery and Systems (IAHR 2020), Lausanne, Switzerland."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"72035","DOI":"10.1088\/1755-1315\/240\/7\/072035","article-title":"Cavitation pressure fluctuation characteristics of a prototype pump-turbine analysed by using CFD","volume":"240","author":"Wen","year":"2019","journal-title":"IOP Conf. Ser. Earth Environ. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1016\/j.renene.2019.04.023","article-title":"DDES analysis of the unsteady wake flow and its evolution of a centrifugal pump","volume":"141","author":"Zhang","year":"2019","journal-title":"Renew. Energy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"041102","DOI":"10.1115\/1.4035224","article-title":"Vortex Rope Formation in a High Head Model Francis Turbine","volume":"139","author":"Goyal","year":"2017","journal-title":"J. Fluids Eng.-Trans. ASME"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"114026","DOI":"10.1016\/j.oceaneng.2023.114026","article-title":"Study of vortex rope for the flow field pulsation law","volume":"273","author":"Jin","year":"2023","journal-title":"Ocean Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1016\/j.renene.2019.09.096","article-title":"Investigation of the correlation mechanism between cavitation rope behavior and pressure fluctuations in a hydraulic turbine","volume":"147","author":"Yu","year":"2020","journal-title":"Renew. Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"33","DOI":"10.5293\/IJFMS.2013.6.1.033","article-title":"An Outlook on the Draft-Tube-Surge Study","volume":"6","author":"Michihiro","year":"2013","journal-title":"Int. J. Fluid Mach. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wang, L., Cui, J., Shu, L., Jiang, D., Xiang, C., Li, L., and Zhou, P. (2022). Research on the Vortex Rope Control Techniques in Draft Tube of Francis Turbines. Energies, 15.","DOI":"10.3390\/en15249280"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Yang, J., Zhou, L.J., and Wang, Z.W. (2015, January 6\u201310). The numerical research of runner cavitation effects on spiral vortex rope in draft tube of Francis turbine. Proceedings of the 9th International Symposium on Cavitation (CAV2015), Lausanne, Switzerland.","DOI":"10.1088\/1742-6596\/656\/1\/012076"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s12206-017-1217-7","article-title":"Numerical investigation on radial impeller induced vortex rope in draft tube under partial load conditions","volume":"32","author":"Ni","year":"2018","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"06004","DOI":"10.1051\/matecconf\/201711506004","article-title":"Vortex rope patterns at different load of hydro turbine model","volume":"115","author":"Skripkin","year":"2017","journal-title":"MATEC Web Conf."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.renene.2019.11.014","article-title":"Investigation of Rotating Vortex Rope formation during load variation in a Francis turbine draft tube","volume":"151","author":"Sotoudeh","year":"2020","journal-title":"Renew. Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1177\/0957650917692153","article-title":"Unsteady vortical flow simulation in a Francis turbine with special emphasis on vortex rope behavior and pressure fluctuation alleviation","volume":"231","author":"Luo","year":"2017","journal-title":"Proc. Inst. Mech. Eng. Part A-J. Power Energy"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11433-016-0022-6","article-title":"New omega vortex identification method","volume":"59","author":"Liu","year":"2016","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Ji, L., Xu, L., Peng, Y., Zhao, X., Li, Z., Tang, W., Liu, D., and Liu, X. (2022). Experimental and Numerical Simulation Study on the Flow Characteristics of the Draft Tube in Francis Turbine. Machines, 10.","DOI":"10.3390\/machines10040230"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Kim, S., Suh, J., Choi, Y., Park, J., Park, N., and Kim, J. (2019). Inter-Blade Vortex and Vortex Rope Characteristics of a Pump-Turbine in Turbine Mode under Low Flow Rate Conditions. Water, 11.","DOI":"10.3390\/w11122554"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"105494","DOI":"10.1016\/j.icheatmasstransfer.2021.105494","article-title":"Entropy production analysis for vortex rope of a Francis turbine using hybrid RANS\/LES method","volume":"127","author":"Yu","year":"2021","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1016\/j.renene.2022.08.078","article-title":"Study of vortex rope based on flow energy dissipation and vortex identification","volume":"198","author":"Li","year":"2022","journal-title":"Renew. Energy"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.renene.2021.05.038","article-title":"Optimization of axial water injection to mitigate the Rotating Vortex Rope in a Francis turbine","volume":"175","author":"Maddahian","year":"2021","journal-title":"Renew. Energy"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2072051534","DOI":"10.1177\/1687814018824468","article-title":"Numerical and experimental investigation of the effect of baffles on flow instabilities in a Francis turbine draft tube under partial load conditions","volume":"11","author":"Zhou","year":"2019","journal-title":"Adv. Mech. Eng."},{"key":"ref_28","first-page":"2164619","article-title":"Numerical investigation of air admission influence on the precessing vortex rope in a Francis turbine","volume":"17","author":"Sun","year":"2023","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"179","DOI":"10.5293\/IJFMS.2011.4.1.179","article-title":"Experimental investigations on upper part load vortex rope pressure fluctuations in Francis turbine draft tube","volume":"4","author":"Nicolet","year":"2011","journal-title":"Int. J. Fluid Mach. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"41301","DOI":"10.1063\/5.0142102","article-title":"Data-driven mode decomposition methods as feature detection techniques for flow problems: A critical assessment","volume":"35","author":"Begiashvili","year":"2023","journal-title":"Phys. Fluids"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.renene.2019.02.055","article-title":"Dynamic mode decomposition of cavitating flow around ALE 15 hydrofoil","volume":"139","author":"Liu","year":"2019","journal-title":"Renew. Energy"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.expthermflusci.2019.05.001","article-title":"Experimental investigation of the precessing vortex core in annular swirling jet flows in the transitional regime","volume":"106","author":"Vanierschot","year":"2019","journal-title":"Exp. Therm. Fluid Sci."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Litvinov, I., Sharaborin, D., Gorelikov, E., Dulin, V., Shtork, S., Alekseenko, S., and Oberleithner, K. (2022). Modal Decomposition of the Precessing Vortex Core in a Hydro Turbine Model. Appl. Sci., 12.","DOI":"10.3390\/app12105127"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1017\/S0022112010001217","article-title":"Dynamic mode decomposition of numerical and experimental data","volume":"656","author":"Schmid","year":"2010","journal-title":"J. Fluid Mech."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s00162-010-0203-9","article-title":"Applications of the dynamic mode decomposition","volume":"25","author":"Schmid","year":"2011","journal-title":"Theor. Comput. Fluid Dyn."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2567659","DOI":"10.1155\/2019\/2567659","article-title":"Study on Flow Characteristics in Volute of Centrifugal Pump Based on Dynamic Mode Decomposition","volume":"2019","author":"Li","year":"2019","journal-title":"Math. Probl. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1016\/j.renene.2019.03.015","article-title":"Dynamic mode decomposition of gas-liquid flow in a rotodynamic multiphase pump","volume":"139","author":"Liu","year":"2019","journal-title":"Renew. Energy"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"199","DOI":"10.5293\/IJFMS.2011.4.1.199","article-title":"Unsteady Simulations of the Flow in a Swirl Generator, Using OpenFOAM","volume":"4","author":"Petit","year":"2011","journal-title":"International Int. J. Fluid Mach. Syst."},{"key":"ref_39","unstructured":"Susan-Resiga, R., Muntean, S., Bosioc, A., Stuparu, A., Milos, T., Baya, A., Bernad, S., and Anton, L.E. (2007, January 24\u201326). Swirling flow apparatus and test rig for flow control in hydraulic turbines discharge cone. Proceedings of the 2nd IAHR International Meeting Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Timisoara, Romania."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"081106","DOI":"10.1115\/1.4033416","article-title":"Experimental and Numerical Investigation of the Precessing Helical Vortex in a Conical Diffuser, With Rotor\u2014Stator Interaction","volume":"138","author":"Javadi","year":"2016","journal-title":"J. Fluids Eng.-Trans. ASME"},{"key":"ref_41","first-page":"625","article-title":"Ten Years of Industrial Experience with the SST Turbulence Model","volume":"4","author":"Menter","year":"2003","journal-title":"Turbul. Heat Mass Transf."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.expthermflusci.2018.09.015","article-title":"Swirling flow in a hydraulic turbine discharge cone at different speeds and discharge conditions","volume":"100","author":"Skripkin","year":"2019","journal-title":"Exp. Therm. Fluid Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/4\/416\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:22:28Z","timestamp":1760106148000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/4\/416"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,2]]},"references-count":42,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["sym16040416"],"URL":"https:\/\/doi.org\/10.3390\/sym16040416","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,2]]}}}