{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T09:47:55Z","timestamp":1785836875625,"version":"3.56.0"},"reference-count":27,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T00:00:00Z","timestamp":1785801600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52374322"],"award-info":[{"award-number":["52374322"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["52374322"],"award-info":[{"award-number":["52374322"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["FRF-AT-26-018"],"award-info":[{"award-number":["FRF-AT-26-018"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>In the continuous casting process, the flow velocity of molten steel at the surface of the mold directly influences the melting of the flux, slag entrainment behavior, and the uniformity of heat transfer. Fast and accurate prediction of the magnitude and distribution of surface-flow velocity is crucial for defect suppression and ensuring continuous casting quality. In this study, a three-dimensional electromagnetic\u2013fluid dynamic coupled model was established and validated to simulate the molten steel flow behavior under various casting speeds, Electromagnetic Stirring (EMS) currents, EMS frequencies, and Submerged Entry Nozzle (SEN) immersion depth. Subsequently, the maximum surface velocity in the mold was fitted to derive a predictive formula under different conditions; the median range and width of the surface high-velocity range were predicted in a similar way. As a result, a regression model derived from Computational Fluid Dynamics (CFD) was built to predict the maximum mold surface velocity and the high-velocity range within milliseconds. The reliability of the regression model was verified by newly generated simulation results, with the relative error between the predicted and simulated maximum surface velocities kept within 2%. It was shown that the maximum surface velocity increases with casting speed and EMS current but decreases with EMS frequency. The median range of the high-velocity range decreases with increasing casting speed and current. The immersion depth of SEN had a minimal impact on the maximum surface velocity in the mold and the high-velocity range. This regression model is beneficial for rapid mold design and for predicting potential slag entrainment, breakout risks, and billet defects, for the purpose of intelligent continuous casting.<\/jats:p>","DOI":"10.3390\/ma19153309","type":"journal-article","created":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T09:15:22Z","timestamp":1785834922000},"page":"3309","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["CFD-Derived Regression Model to Predict Surface Velocity for a Continuous-Casting Round Billet Mold"],"prefix":"10.3390","volume":"19","author":[{"given":"Guangchao","family":"Guo","sequence":"first","affiliation":[{"name":"State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiangshan","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengjing","family":"Zhao","sequence":"additional","affiliation":[{"name":"Metallurgical and Building Materials Business Department, China International Engineering Consulting Corporation, Beijing 100048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shufeng","family":"Yang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaotan","family":"Zuo","sequence":"additional","affiliation":[{"name":"Wuhu Xinxing Ductile Iron Pipes Co., Ltd., Wuhu 241002, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8980-2250","authenticated-orcid":false,"given":"Qing","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.2355\/isijinternational.41.1181","article-title":"Mathematical modeling of fluid flow in continuous casting","volume":"41","author":"Thomas","year":"2001","journal-title":"ISIJ Int."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1007\/s41230-017-7171-2","article-title":"A coupled model on fluid flow, heat transfer and solidification in continuous casting mold","volume":"14","author":"Zhang","year":"2017","journal-title":"China Foundry"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"670","DOI":"10.2355\/isijinternational.41.670","article-title":"Perspectives of research on high-speed conventional slab continuous casting of carbon steels","volume":"41","author":"Suzuki","year":"2001","journal-title":"ISIJ Int."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/S0924-0136(02)01009-9","article-title":"Numerical simulation of three-dimensional flow, heat transfer, and solidification of steel in continuous casting mold with electromagnetic brake","volume":"133","author":"Ha","year":"2003","journal-title":"J. Mater. Process. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1016\/S1006-706X(13)60062-X","article-title":"Multiphase flow and thermo-mechanical behaviors of solidifying shell in continuous casting mold","volume":"20","author":"Zhu","year":"2013","journal-title":"J. Iron Steel Res. Int."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1179\/174328105X15788","article-title":"Performance and properties of mould fluxes","volume":"32","author":"Mills","year":"2005","journal-title":"Ironmak. Steelmak."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"196","DOI":"10.4028\/www.scientific.net\/AMR.402.196","article-title":"Study on Fluid Flow in a Large Round Bloom Continuous Casting Mold","volume":"402","author":"Zhong","year":"2012","journal-title":"Adv. Mater. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF02665205","article-title":"Water-modeling study of the surface disturbances in continuous slab caster","volume":"25","author":"Gupta","year":"1994","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Li, G., Wang, S., and Zheng, G. (2023). Flow and Heat Transfer on the Surface of Molten Steel Slag Layer in Continuous Casting Mold. Coatings, 13.","DOI":"10.3390\/coatings13091551"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Tian, Y., Zhou, H., Wang, G., Xu, L., Qiu, S., and Zhu, R. (2023). Numerical modeling of transient flow characteristics on the top surface of a steel slab continuous casting strand using a large eddy simulation combined with volume of fluid model. Materials, 16.","DOI":"10.3390\/ma16165665"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2300346","DOI":"10.1002\/srin.202300346","article-title":"Optimization of port angle for narrow-width mold flow field under high casting speed based on large eddy simulation and high-temperature measurement of velocity","volume":"95","author":"Guo","year":"2024","journal-title":"Steel Res. Int."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Du, F., Zhao, J., Zheng, Y., Li, T., and Zheng, G. (2022). Research on the influence of process parameters on the flow field in mold. Coatings, 12.","DOI":"10.3390\/coatings12101547"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1016\/j.jmapro.2024.11.077","article-title":"Large eddy simulation of novel EMBr effect on flow pattern in thin slab casting mold with multi-port SEN and ultra-high casting speed","volume":"133","author":"Cui","year":"2025","journal-title":"J. Manuf. Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4361","DOI":"10.1007\/s11663-024-03238-4","article-title":"Numerical Modeling and Plant Trial on the Optimization of SEN Designs in a Large Round Billet Mold","volume":"55","author":"Qin","year":"2024","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.paerosci.2005.02.001","article-title":"Surrogate-based analysis and optimization","volume":"41","author":"Queipo","year":"2005","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00158-001-0160-4","article-title":"Comparative studies of metamodelling techniques under multiple modelling criteria","volume":"23","author":"Jin","year":"2001","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_17","unstructured":"Zhou, H., Luo, Y., Li, H., Ji, C., He, W., and Hao, N. (2023). Online prediction of surface velocity, vortex position and fluid flow pattern in Mold. Contin. Cast., 80\u201386."},{"key":"ref_18","first-page":"103","article-title":"Online prediction method of slag entrainment in mold based on numerical simulation","volume":"57","author":"Zhou","year":"2022","journal-title":"Iron Steel"},{"key":"ref_19","first-page":"30","article-title":"Multiphysics prediction of electromagnetic stirring in a slab mold based on mechanistic model and large model","volume":"44","author":"Huang","year":"2025","journal-title":"Contin. Cast."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"78231","DOI":"10.1109\/ACCESS.2022.3192541","article-title":"Quality prediction of continuous casting slabs based on weighted extreme learning machine","volume":"10","author":"Liu","year":"2022","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/s11663-024-03350-5","article-title":"Real-time prediction of molten pool velocity distribution in converter steelmaking based on deep learning","volume":"56","author":"Wang","year":"2025","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Launder, B., and Spalding, D. (1983). Paper 8\u2014The numerical computation of turbulent flows. Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion, Elsevier.","DOI":"10.1016\/B978-0-08-030937-8.50016-7"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wang, P., Xiao, H., Zhang, Z., Li, S., and Zhang, J. (2022). Behavior of mold electromagnetic stirring for round bloom castings and its eccentric stirring problem. Materials, 15.","DOI":"10.3390\/ma15248814"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1007\/s12540-024-01629-5","article-title":"Modelling of meniscus behavior and slag consumption during initial casting stage of continuous casting process","volume":"30","author":"Tong","year":"2024","journal-title":"Met. Mater. Int."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1179\/1743281214Y.0000000201","article-title":"Coupled numerical simulation on electromagnetic field and flow field in the round billet mould with electromagnetic stirring","volume":"42","author":"Wang","year":"2015","journal-title":"Ironmak. Steelmak."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1657","DOI":"10.1007\/s11663-012-9737-0","article-title":"Numerical simulation of fluid flow in a round bloom mold with in-mold rotary electromagnetic stirring","volume":"43","author":"Liu","year":"2012","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2000547","DOI":"10.1002\/srin.202000547","article-title":"Clogging-induced asymmetrical and transient flow pattern in a steel continuous casting slab strand measured using nail boards","volume":"92","author":"Zhou","year":"2021","journal-title":"Steel Res. Int."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/19\/15\/3309\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T09:24:38Z","timestamp":1785835478000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/19\/15\/3309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,4]]},"references-count":27,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2026,8]]}},"alternative-id":["ma19153309"],"URL":"https:\/\/doi.org\/10.3390\/ma19153309","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,4]]}}}