{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T11:00:51Z","timestamp":1771930851299,"version":"3.50.1"},"reference-count":93,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,21]],"date-time":"2025-05-21T00:00:00Z","timestamp":1747785600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Applied Fundamental Research Programs of Shanxi Province","award":["202403021222046"],"award-info":[{"award-number":["202403021222046"]}]},{"name":"Applied Fundamental Research Programs of Shanxi Province","award":["2024KY277"],"award-info":[{"award-number":["2024KY277"]}]},{"name":"Graduate Innovation Project of Shanxi Province","award":["202403021222046"],"award-info":[{"award-number":["202403021222046"]}]},{"name":"Graduate Innovation Project of Shanxi Province","award":["2024KY277"],"award-info":[{"award-number":["2024KY277"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Mixing time, as a key parameter for evaluating ladle refining efficiency, has long attracted extensive attention from researchers. In typical experimental studies, salt solution tracers are introduced into ladle water models to assess the degree of mixing within the ladle. Previous studies have demonstrated that the volume of tracer can significantly influence the measured mixing time. However, the gas flow rates employed in these studies are generally relatively high, whereas, in industrial operations, especially during final composition adjustments, lower gas flow rates are often applied. To systematically investigate the effect of the salt solution tracer volume on the mixing efficiency in a ladle water model under asymmetrical gas stirring with a low gas flow rate, a 1:3-scaled water model was developed based on a 130-ton industrial ladle. The mixing behaviors corresponding to different tracer volumes were comprehensively analyzed. The results indicate that the relationship between tracer volume and mixing time is non-monotonic. As the tracer volume increases, the mixing time first decreases and then increases, reaching a minimum at 185 mL. When the tracer volume was small, the dimensionless concentration curves at Monitoring Point 4 exhibited two distinct patterns: A parabolic profile, which was when the tracer initially moved through the left and central regions and then slowly crossed the gas plume to reach the monitoring point. A sinusoidal profile, which was when the tracer predominantly circulated along the right side of the ladle. When the tracer volume exceeded 277 mL, the concentration curves at Monitoring Point 4 consistently exhibited a sinusoidal pattern. Compared with moderate gas flow conditions (8.3 L\/min), the peak concentration at Monitoring Point 3 was significantly lower under a low gas flow (2.3 L\/min), and the overall mixing time was longer, indicating reduced mixing efficiency. Based on the findings, a recommended tracer volume range of 185\u2013277 mL is proposed for low gas flow conditions (2.3 L\/min) to achieve accurate and efficient mixing time measurements with minimal disturbance to the flow field. It was also observed that when the tracer concentration was relatively low, the mixing behavior throughout the ladle became more uniform.<\/jats:p>","DOI":"10.3390\/sym17050802","type":"journal-article","created":{"date-parts":[[2025,5,21]],"date-time":"2025-05-21T13:59:43Z","timestamp":1747835983000},"page":"802","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Assessment of the Measured Mixing Time in a Water Model of Asymmetrical Gas-Stirred Ladle with a Low Gas Flowrate Part II: Effect of the Salt Solution Tracer Volume and Concentration"],"prefix":"10.3390","volume":"17","author":[{"given":"Yansong","family":"Zhao","sequence":"first","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":"Linbo","family":"Li","sequence":"additional","affiliation":[{"name":"College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Zhijie","family":"Guo","sequence":"additional","affiliation":[{"name":"Collaborative Innovation Center of Steel Technology, University of Science and Technology Beijing, Beijing 100083, China"}]},{"given":"Hongyu","family":"Qi","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 and Arts, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"given":"Kun","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Mechanics, 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":"Jinping","family":"Fan","sequence":"additional","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"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Szekely, J., Carlsson, G., and Helle, L. 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