{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T18:52:58Z","timestamp":1767898378903,"version":"3.49.0"},"reference-count":83,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T00:00:00Z","timestamp":1715817600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Applied Fundamental Research Program of Shanxi Province","award":["202303021221036"],"award-info":[{"award-number":["202303021221036"]}]},{"name":"Applied Fundamental Research Program of Shanxi Province","award":["2022-040"],"award-info":[{"award-number":["2022-040"]}]},{"name":"Applied Fundamental Research Program of Shanxi Province","award":["HZKY20220507"],"award-info":[{"award-number":["HZKY20220507"]}]},{"name":"Applied Fundamental Research Program of Shanxi Province","award":["20230135"],"award-info":[{"award-number":["20230135"]}]},{"DOI":"10.13039\/501100003398","name":"Research Project Supported by the Shanxi Scholarship Council of China","doi-asserted-by":"publisher","award":["202303021221036"],"award-info":[{"award-number":["202303021221036"]}],"id":[{"id":"10.13039\/501100003398","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003398","name":"Research Project Supported by the Shanxi Scholarship Council of China","doi-asserted-by":"publisher","award":["2022-040"],"award-info":[{"award-number":["2022-040"]}],"id":[{"id":"10.13039\/501100003398","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003398","name":"Research Project Supported by the Shanxi Scholarship Council of China","doi-asserted-by":"publisher","award":["HZKY20220507"],"award-info":[{"award-number":["HZKY20220507"]}],"id":[{"id":"10.13039\/501100003398","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003398","name":"Research Project Supported by the Shanxi Scholarship Council of China","doi-asserted-by":"publisher","award":["20230135"],"award-info":[{"award-number":["20230135"]}],"id":[{"id":"10.13039\/501100003398","id-type":"DOI","asserted-by":"publisher"}]},{"name":"\u201cChunhui Plan\u201d Collaborative Research Project","award":["202303021221036"],"award-info":[{"award-number":["202303021221036"]}]},{"name":"\u201cChunhui Plan\u201d Collaborative Research Project","award":["2022-040"],"award-info":[{"award-number":["2022-040"]}]},{"name":"\u201cChunhui Plan\u201d Collaborative Research Project","award":["HZKY20220507"],"award-info":[{"award-number":["HZKY20220507"]}]},{"name":"\u201cChunhui Plan\u201d Collaborative Research Project","award":["20230135"],"award-info":[{"award-number":["20230135"]}]},{"name":"Undergraduate Innovation and Entrepreneurship Training Program","award":["202303021221036"],"award-info":[{"award-number":["202303021221036"]}]},{"name":"Undergraduate Innovation and Entrepreneurship Training Program","award":["2022-040"],"award-info":[{"award-number":["2022-040"]}]},{"name":"Undergraduate Innovation and Entrepreneurship Training Program","award":["HZKY20220507"],"award-info":[{"award-number":["HZKY20220507"]}]},{"name":"Undergraduate Innovation and Entrepreneurship Training Program","award":["20230135"],"award-info":[{"award-number":["20230135"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In previous research simulating steelmaking ladles using cold water models, the dosage\/volume of the salt tracer solution is one of the factors that has been overlooked by researchers to a certain extent. Previous studies have demonstrated that salt tracers may influence the flow and measured mixing time of fluids in water models. Based on a water model scaled down from an industrial 130-ton ladle by a ratio of 1:3, this study investigates the impact of salt tracer dosage on the transport and mixing of tracers in the water model of gas-stirred ladle with a moderate gas flow rate. A preliminary uncertainty analysis of the experimental mixing time is performed, and the standard deviations were found to be less than 15%. It was observed in the experiments that the transport paths of tracers in the ladle can be classified into two trends. A common trend is that the injected salt solution tracer is asymmetrically transported towards the left sidewall of the ladle by the main circulation. In another trend, the injected salt solution tracer is transported both by the main circulation to the left side wall and by downward flow towards the gas column. The downward flow may be accelerated and become a major flow pattern when the tracer volume increases. For the dimensionless concentration curve, the sinusoidal type, which represents a rapid mixing, is observed at the top surface monitoring points, while the parabolic type is observed at the bottom monitoring points. An exception is the monitoring point at the right-side bottom (close to the asymmetric gas nozzle area), where both sinusoidal-type and parabolic-type curves are observed. Regarding the effect of tracer volume on the curve and mixing time, the curves at the top surface monitoring points are less influenced but curves at the bottom monitoring points are noticeably influenced by the tracer volume. A trend of decreasing and then increasing as the tracer volume increases was found at the top surface monitoring points, while the mixing times at the bottom monitoring points decrease with the increase in the tracer volume.<\/jats:p>","DOI":"10.3390\/sym16050619","type":"journal-article","created":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T11:26:17Z","timestamp":1715858777000},"page":"619","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Effect of Salt Solution Tracer Dosage on the Transport and Mixing of Tracer in a Water Model of Asymmetrical Gas-Stirred Ladle with a Moderate Gas Flowrate"],"prefix":"10.3390","volume":"16","author":[{"given":"Linbo","family":"Li","sequence":"first","affiliation":[{"name":"College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7953-1127","authenticated-orcid":false,"given":"Chao","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Xin","family":"Tao","sequence":"additional","affiliation":[{"name":"College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Hongyu","family":"Qi","sequence":"additional","affiliation":[{"name":"College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Tao","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Qiji","family":"Yan","sequence":"additional","affiliation":[{"name":"College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Feng","family":"Deng","sequence":"additional","affiliation":[{"name":"College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"},{"name":"State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, China"}]},{"given":"Arslan","family":"Allayev","sequence":"additional","affiliation":[{"name":"College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Wanming","family":"Lin","sequence":"additional","affiliation":[{"name":"College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Jia","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"},{"name":"College of Architecture, Taiyuan University of Technology, Taiyuan 030024, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Szekely, J., Carlsson, G., and Helle, L. (1989). Ladle Metallurgy, Springer.","DOI":"10.1007\/978-1-4612-3538-5"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2355\/isijinternational.35.1","article-title":"The physical and mathematical modelling of gas stirred ladle systems","volume":"35","author":"Mazumdar","year":"1995","journal-title":"ISIJ Int."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.2355\/isijinternational.41.1289","article-title":"The Use of Fundamental Process Models in Studying Ladle Refining Operations","volume":"41","author":"Jonsson","year":"2001","journal-title":"ISIJ Int."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"447","DOI":"10.2355\/isijinternational.44.447","article-title":"Macroscopic Models for Gas Stirred Ladles","volume":"44","author":"Mazumdar","year":"2004","journal-title":"ISIJ Int."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/s42243-023-01100-6","article-title":"Modeling of LF refining process: A review","volume":"31","author":"Xin","year":"2024","journal-title":"J. Iron Steel Res. Int."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2066","DOI":"10.1007\/s11663-023-02816-2","article-title":"3D CFD Model of Ladle Heat Transfer with Gas Injection","volume":"54","author":"Niu","year":"2023","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Conejo, A.N. (2020). Physical and Mathematical Modelling of Mass Transfer in Ladles due to Bottom Gas Stirring: A Review. Processes, 8.","DOI":"10.3390\/pr8070750"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1344","DOI":"10.1007\/s11663-022-02499-1","article-title":"Effect of the Nozzle Radial Position and Gas Flow Rate on Mass Transfer during Bottom Gas Injection in Ladles with One Nozzle","volume":"53","author":"Niu","year":"2022","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"52","DOI":"10.2355\/isijinternational.ISIJINT-2023-310","article-title":"Multiphase modeling of steel-slag mass transfer through distorted interface in bottom-stirred ladle","volume":"64","author":"Ji","year":"2024","journal-title":"ISIJ Int."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2100831","DOI":"10.1002\/srin.202100831","article-title":"Modeling Study of Steel\u2013Slag\u2013Inclusion Reactions During the Refining of Si\u2013Mn Killed Steel","volume":"94","author":"Podder","year":"2022","journal-title":"Steel Res. Int."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Podder, A., Coley, K.S., and Phillion, A.B. (2024, March 26). Simulation of Ladle Refining Reactions in Si\u2013Mn-Killed Steel. Available online: https:\/\/onlinelibrary.wiley.com\/doi\/full\/10.1002\/srin.202300330.","DOI":"10.1002\/srin.202300330"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2722","DOI":"10.1007\/s11663-018-1350-4","article-title":"Fluid Flow, Dissolution, and Mixing Phenomena in Argon-Stirred Steel Ladles","volume":"49","author":"Duan","year":"2018","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1800288","DOI":"10.1002\/srin.201800288","article-title":"Effect of melt superheat and alloy size on the mixing phenomena in argon-stirred steel ladles","volume":"90","author":"Duan","year":"2019","journal-title":"Steel Res. Int."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2174","DOI":"10.1007\/s11663-023-02825-1","article-title":"CFD Investigation of Melting Behaviors of Two Alloy Particles During Multiphase Vacuum Refining Process","volume":"54","author":"Liu","year":"2023","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_15","first-page":"954","article-title":"Water model experiment on motion and melting of scarp in gas stirred reactors","volume":"22","author":"Yang","year":"2022","journal-title":"Chin. J. Process Eng."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Li, X., Wang, H., Tian, J., Wang, D., Qu, T., Hou, D., Hu, S., and Wu, G. (2023). Investigation on the Alloy Mixing and Inclusion Removement through Using a New Slot-Porous Matched Tuyeres. Metals, 13.","DOI":"10.3390\/met13040667"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2200218","DOI":"10.1002\/srin.202200218","article-title":"Effect of CaF2 Contents in Slag on Inclusion Absorption in a Bearing Steel","volume":"94","author":"Wen","year":"2022","journal-title":"Steel Res. Int."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2523","DOI":"10.1007\/s11663-022-02548-9","article-title":"Effect of Physicochemical Properties of Slag on the Removal Rate of Alumina Inclusions in the Ruhrstahl\u2013Heraeus (RH) Refining Conditions","volume":"53","author":"Kim","year":"2022","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Li, X., Hu, S., Wang, D., Qu, T., Wu, G., Zhang, P., Quan, Q., Zhou, X., and Zhang, Z. (2022). Inclusion Removements in a Bottom-Stirring Ladle with Novel Slot-Porous Matched Dual Plugs. Metals, 12.","DOI":"10.3390\/met12010162"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1007\/s42243-023-00957-x","article-title":"A boundary layer model for capture of inclusions by steel\u2013slag interface in a turbulent flow","volume":"30","author":"Sun","year":"2023","journal-title":"J. Iron Steel Res. Int."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2300537","DOI":"10.1002\/srin.202300537","article-title":"Modeling of Motion of Inclusions in Argon-Stirred Steel Ladles","volume":"96","author":"Huang","year":"2024","journal-title":"Steel Res. Int."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Qiao, T., Cheng, G., Huang, Y., Li, Y., Zhang, Y., and Li, Z. (2022). Formation and Removal Mechanism of Nonmetallic Inclusions in 42CrMo4 Steel during the Steelmaking Process. Metals, 12.","DOI":"10.3390\/met12091505"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1007\/s11663-022-02711-2","article-title":"Formation and Evolution of Inclusions in AH36 Steel During LF\u2013RH\u2013CC Process: The Influences of Ca-Treatment, Reoxidation, and Solidification","volume":"54","author":"Zhong","year":"2023","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Ocampo Vaca, F.A., Hern\u00e1ndez Bocanegra, C.A., Ramos Banderas, J.\u00c1., Herrera-Ortega, M., L\u00f3pez Granados, N.M., and Solorio D\u00edaz, G. (2024, March 13). Effect of Ladle Shroud Blockage on Flow Dynamics and Cleanliness of Steel in Coupled Ladle\u2013Shroud\u2013Tundish System. Available online: https:\/\/onlinelibrary.wiley.com\/doi\/full\/10.1002\/srin.202300616.","DOI":"10.1002\/srin.202300616"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"914","DOI":"10.1007\/s11663-013-9829-5","article-title":"Effects of Top Layer, Nozzle Arrangement, and Gas Flow Rate on Mixing Time in Agitated Ladles by Bottom Gas Injection","volume":"44","author":"Conejo","year":"2013","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_26","first-page":"711","article-title":"Effect of Nozzle Diameter on Mixing Time During Bottom-Gas Injection in Metallurgical Ladles","volume":"45","author":"Terrazas","year":"2014","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.2355\/isijinternational.ISIJINT-2021-543","article-title":"Physical and Numerical Simulation of the Optimum Nozzle Radial Position in Ladles with One Nozzle and Bottom Gas Injection","volume":"62","author":"Feng","year":"2022","journal-title":"ISIJ Int."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1007\/s11663-021-02355-8","article-title":"Ladle Eye Formation Due to Bottom Gas Injection: A Reassessment of Experimental Data","volume":"53","author":"Conejo","year":"2022","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1703","DOI":"10.1007\/s11663-022-02481-x","article-title":"Large-Scale Test Facility for Modeling Bubble Behavior and Liquid Metal Two-Phase Flows in a Steel Ladle","volume":"53","author":"Wondrak","year":"2022","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1007\/s11663-021-02371-8","article-title":"The Flow Behavior of Molten Steel in an RH Degasser Under Different Ladle Bottom Stirring Processes","volume":"53","author":"Wang","year":"2022","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Jojo-Cunningham, Y., Guo, X., Zhou, C., and Liu, Y. (2024). Volumetric Flow Field inside a Gas Stirred Cylindrical Water Tank. Fluids, 9.","DOI":"10.3390\/fluids9010011"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.4028\/www.scientific.net\/AMR.284-286.1071","article-title":"Physical Modeling of Fluid Flow Characteristics in a Delta Shaped, Four-Strand Continuous Casting Tundish with Different Flow Control Devices","volume":"284","author":"Chen","year":"2011","journal-title":"Adv. Mater. Res."},{"key":"ref_33","unstructured":"Schwarz, M.P., and Koh, P.T.L. (1986, January 11\u201313). Numerical Modelling of Bath Mixing by Swirled Gas Injection. Proceedings of the SCANINJECT IV-4th International Conference on Injection Metallurgy, MEFOS, Lule\u00e5, Sweden. Part I, paper 6."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/0307-904X(88)90034-0","article-title":"Applicability of the standard k-\u03f5 turbulence model to gas-stirred baths","volume":"12","author":"Schwarz","year":"1988","journal-title":"Appl. Math. Model."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1080\/03019233.2022.2163072","article-title":"Mathematical modelling of novel combined stirring method during the final stage of ladle refining","volume":"50","author":"Nick","year":"2023","journal-title":"Ironmak. Steelmak."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1007\/s12613-022-2558-5","article-title":"Effect of gas blowing nozzle angle on multiphase flow and mass transfer during RH refining process","volume":"30","author":"Wang","year":"2023","journal-title":"Int. J. Miner. Metall. Mater."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/s11663-023-02933-y","article-title":"Modeling of Bubble Transportation, Expansion, as Well as Adhesion of Inclusions in a Ladle With Different Tuyeres","volume":"55","author":"Li","year":"2024","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4114","DOI":"10.1007\/s11663-022-02671-7","article-title":"Novel Evaluation Method to Determine the Mixing Time in a Ladle Refining Process","volume":"53","author":"Zhou","year":"2022","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Hua, C., Bao, Y., and Wang, M. (2022). Multiphysics numerical simulation model and hydraulic model experiments in the argon-stirred ladle. Processes, 10.","DOI":"10.3390\/pr10081563"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Tiwari, R., Girard, B., Labrecque, C., Isac, M.M., and Guthrie, R.I.L. (2023). CFD Predictions for Mixing Times in an Elliptical Ladle Using Single- and Dual-Plug Configurations. Processes, 11.","DOI":"10.3390\/pr11061665"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"947","DOI":"10.2355\/isijinternational.31.947","article-title":"Buoyancy and expansion power in gas-agitated baths","volume":"31","author":"Schwarz","year":"1991","journal-title":"ISIJ Int."},{"key":"ref_42","unstructured":"Schwarz, M.P., and Dang, P. (1995, January 2\u20135). Simulation of Blowthrough in Smelting Baths with Bottom Gas Injection. Proceedings of the 13th Process Technology Conference Proceedings, ISS, Nashville, TN, USA."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Ram\u00edrez-L\u00f3pez, A. (2024). Analysis of Mixing Efficiency in a Stirred Reactor Using Computational Fluid Dynamics. Symmetry, 16.","DOI":"10.3390\/sym16020237"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Ram\u00edrez-L\u00f3pez, A.A. (2023). Analysis of the Hydrodynamics Behavior Inside a Stirred Reactor for Lead Recycling. Fluids, 8.","DOI":"10.3390\/fluids8100268"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1034\/j.1600-0692.2001.300408.x","article-title":"Modelling of alloy mixing into steel: The influence of porous plug placement in the ladle bottom on the mixing of alloys into steel in a gas-stirred ladle. A comparison made by numerical simulation","volume":"30","author":"Jauhiainen","year":"2001","journal-title":"Scand. J. Metall."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1179\/174328107X167940","article-title":"Numerical modelling studies of flow and mixing phenomena in gas stirred steel ladles","volume":"35","author":"Ganguly","year":"2008","journal-title":"Ironmak. Steelmak."},{"key":"ref_47","unstructured":"Taylor, I.F., Dang, P., Schwarz, M.P., and Wright, J.K. (1989, January 2\u20135). An Improved Method for the Experimental Validation of Numerical Mixing Time Predictions. Proceedings of the 72nd Steelmaking Proceedings, ISS, Chicago, IL, USA."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s11665-997-0040-1","article-title":"Effects of gas injection condition on mixing efficiency in the ladle refining process","volume":"6","author":"Pan","year":"1997","journal-title":"J. Mater. Eng. Perform"},{"key":"ref_49","first-page":"101","article-title":"Physical model of 150 t ladle refining process","volume":"29","author":"Wen","year":"2007","journal-title":"J. Univ. Sci. Technol. Beijing"},{"key":"ref_50","first-page":"1056","article-title":"Effect of Inert Gas Flow Rate on Homogenization and Inclusion Removal in a Gas Stirred Ladle","volume":"81","author":"Ek","year":"2010","journal-title":"ISIJ Int."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Liu, Y., Bai, H., Liu, H., Ersson, M., J\u00f6nsson, P.G., and Gan, Y. (2019). Physical and Numerical Modelling on the Mixing Condition in a 50 t Ladle. Metals, 9.","DOI":"10.3390\/met9111136"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1900606","DOI":"10.1002\/srin.201900606","article-title":"Physical Modeling Evaluation on Refining Effects of Ladle with Different Purging Plug Designs","volume":"91","author":"Tan","year":"2020","journal-title":"Steel Res. Int."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Aguilar, G., Solorio-Diaz, G., Aguilar-Corona, A., Ramos-Banderas, J.A., Hern\u00e1ndez, C.A., and Salda\u00f1a, F. (2021). Study of the Effect of a Plug with Torsion Channels on the Mixing Time in a Continuous Casting Ladle Water Model. Metals, 11.","DOI":"10.3390\/met11121942"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"2263","DOI":"10.1007\/s11663-021-02170-1","article-title":"On the Limits of the Geometric Scale Ratio Using Water Modeling in Ladles","volume":"52","author":"Conejo","year":"2021","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_55","first-page":"30","article-title":"Physical simulation of 120 t ladle bottom blown argon gas","volume":"31","author":"Shi","year":"2021","journal-title":"China Metall."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"2185","DOI":"10.2355\/isijinternational.ISIJINT-2021-094","article-title":"Effect of the location of tracer addition in a ladle on the mixing time through physical and numerical modeling","volume":"61","year":"2021","journal-title":"ISIJ Int."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Cheng, R., Zhang, L., Yin, Y., and Zhang, J. (2021). Effect of side blowing on fluid flow and mixing phenomenon in gas-stirred ladle. Metals, 11.","DOI":"10.3390\/met11020369"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"792","DOI":"10.2355\/isijinternational.ISIJINT-2019-680","article-title":"Optimization of the Structure and Injection Position of Top Submerged Lance in Hot Metal Ladle","volume":"61","author":"Wang","year":"2021","journal-title":"ISIJ Int."},{"key":"ref_59","first-page":"45","article-title":"Physical Simulation of Bottom Blowing Argon in 150t Ladle","volume":"2","author":"Wu","year":"2022","journal-title":"Contin. Cast."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Li, Z., Ouyang, W., Wang, Z., Zheng, R., Bao, Y., and Gu, C. (2023). Physical Simulation Study on Flow Field Characteristics of Molten Steel in 70t Ladle Bottom Argon Blowing Process. Metals, 13.","DOI":"10.3390\/met13040639"},{"key":"ref_61","first-page":"35","article-title":"Water modeling on the transport phenomenon during bottom gas injection of a 210 t ladle","volume":"39","author":"Shan","year":"2023","journal-title":"Steelmaking"},{"key":"ref_62","unstructured":"Li, L., Chen, C., Wang, J., Tao, X., Liu, T., Zhao, Y., and Rong, Z. (2024, April 12). Flow field optimization and analysis on inclusion removal in elliptical ladle. Available online: https:\/\/link.cnki.net\/urlid\/11.3729.TF.20240407.1139.001."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1002\/srin.201200086","article-title":"Effects of Salt Tracer Amount, Concentration and Kind on the Fluid Flow Behavior in a Hydrodynamic Model of Continuous Casting Tundish","volume":"83","author":"Chen","year":"2012","journal-title":"Steel Res. Int."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s11663-014-0190-0","article-title":"A Mathematical Modeling Study of Tracer Mixing in a Continuous Casting Tundish","volume":"46","author":"Chen","year":"2015","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"914","DOI":"10.1016\/j.ces.2015.07.037","article-title":"A mathematical modeling study of the influence of small amounts of KCl solution tracers on mixing in water and residence time distribution of tracers in a continuous flow reactor-metallurgical tundishc","volume":"137","author":"Chen","year":"2015","journal-title":"Chem. Eng. Sci."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"3788","DOI":"10.1007\/s11663-021-02292-6","article-title":"Effects of Tracer Solute Buoyancy on Flow Behavior in a Single-Strand Tundish","volume":"52","author":"Ding","year":"2021","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Ding, C., Lei, H., Niu, H., Zhang, H., Yang, B., and Zhao, Y. (2021). Effects of Salt Tracer Volume and Concentration on Residence Time Distribution Curves for Characterization of Liquid Steel Behavior in Metallurgical Tundish. Metals, 11.","DOI":"10.3390\/met11030430"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"202000022","DOI":"10.1002\/srin.202000022","article-title":"Numerical Simulation of Tracers Transport Process in Water Model of a Vacuum Refining Unit: Single Snorkel Refining Furnace","volume":"91","author":"Zhang","year":"2020","journal-title":"Steel Res. Int."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Ouyang, X., Lin, W., Luo, Y., Zhang, Y., Fan, J., Chen, C., and Cheng, G. (2022). Effect of Salt Tracer Dosages on the Mixing Process in the Water Model of a Single Snorkel Refining Furnace. Metals, 12.","DOI":"10.3390\/met12111948"},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Xu, Z., Ouyang, X., Chen, C., Li, Y., Wang, T., Ren, R., Yang, M., Zhao, Y., Xue, L., and Wang, J. (2024). Numerical Simulation of the Density Effect on the Macroscopic Transport Process of Tracer in the Ruhrstahl\u2013Heraeus (RH) Vacuum Degasser. Sustainability, 16.","DOI":"10.3390\/su16103923"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"900","DOI":"10.1002\/srin.201200232","article-title":"Effect of Salt Tracer Amount on the Mixing Time Measurement in a Hydrodynamic Model of Gas-Stirred Ladle System","volume":"84","author":"Chen","year":"2013","journal-title":"Steel Res. Int."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"11","DOI":"10.29252\/jafm.11.01.27503","article-title":"Effect of Separation Angle and Nozzle Radial Position on Mixing Time in Ladles with Two Nozzles","volume":"11","author":"Conejo","year":"2018","journal-title":"J. Appl. Fluid Mec."},{"key":"ref_73","first-page":"50","article-title":"Numerical Simulation of Tracer Transport Process in Water Model of Gas-stirred Ladle","volume":"51","author":"Zhang","year":"2020","journal-title":"J. Taiyuan Univ. Technol."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"1486","DOI":"10.1007\/s11663-013-9943-4","article-title":"A critical review of the modified Froude number in Ladle Metallurgy","volume":"44","author":"Krishnapisharody","year":"2013","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_75","first-page":"98","article-title":"Study on Water model for 135t LF ladle bottom blowing argon process","volume":"46","author":"Zhan","year":"2017","journal-title":"Hot Work. Technol."},{"key":"ref_76","unstructured":"Oeters, F. (1994). Metallurgy of Steelmaking, Verlag Stahleisen GmbH."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1002\/srin.198700245","article-title":"Mixing Theories for Gas-Stirred Melts","volume":"58","author":"Mietz","year":"1987","journal-title":"Steel Res."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1002\/srin.198801606","article-title":"Model Experiments on Mixing Phenomena in Gas-stirred Melts","volume":"59","author":"Mietz","year":"1988","journal-title":"Steel Res."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1002\/srin.198901673","article-title":"Flow Field and Mixing with Eccentric Gas Stirring","volume":"60","author":"Mietz","year":"1989","journal-title":"Steel Res."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1179\/cmq.1989.28.1.19","article-title":"Model Studies of Mixing Phenomena in Stirred Melts","volume":"28","author":"Mietz","year":"1989","journal-title":"Can. Metall. Quart."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1002\/srin.199801600","article-title":"Model Experiments of Mixing in Steel Ladles with Continuous Addition of The Substance to be Mixed","volume":"69","author":"Becker","year":"1998","journal-title":"Steel Res."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1007\/BF02651408","article-title":"Experimental investigation of mixing phenomena in a gas stirred liquid bath","volume":"19","author":"Mehrotra","year":"1988","journal-title":"Metall. Trans. B"},{"key":"ref_83","unstructured":"Oymo, D., and Guthrie, R.I.L. (1984, January 3\u20134). Mixing Times in Combination Blowing Processes. Proceedings of the 4th Process Technology Conference Proceedings, ISS, Chicago, IL, USA."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/5\/619\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:43:38Z","timestamp":1760107418000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/5\/619"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,16]]},"references-count":83,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["sym16050619"],"URL":"https:\/\/doi.org\/10.3390\/sym16050619","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,16]]}}}