Population Balance Modeling of Polydispersed Bubbly Flow in Continuous-Casting Using Multiple-Size-Group Approach
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TRANSPORT of argon bubbles dispersed in a turbulent immiscible flow is a common phenomenon in the continuous-casting process. The gas disintegrates into small bubbles of varying sizes as it issues out of the submerged entry nozzle (SEN). The bubble size distribution within the turbulence flow plays an important role in various physical–chemical processes, such as flow pattern change, heat transfer, bubble and non-metallic inclusion absorption, multi-phase reactions, phase change, etc. However, fine argon bubbles were sometimes observed inside the continuous-casting slabs[1,2] which were trapped by the solidified shell, as shown in Figure 1. In the subsequent rolling process, these bubbles can lead to the formation of pinhole defects. So understanding the bubble size distribution inside the mold is essential for designing effective methods to remove fine bubbles. ZHONGQIU LIU and LINMIN LI, Ph.D. Candidates, FENGSHENG QI, Lecturer, BAOKUAN LI and MAOFA JIANG, Professors, are with of Materials and Metallurgy, Northeastern University, Shenyang 110819, P.R. China. Contact e-mail:libk@ smm.neu.edu.cn FUMITAKA TSUKIHASHI, Professor, is with the Department of Advanced Materials, Graduate School of Frontier Science, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561, Japan. Manuscript submitted October 8, 2013. METALLURGICAL AND MATERIALS TRANSACTIONS B
Several water model experiments have been used to study the bubble size distribution in the SEN[3,4] or mold[5,6] after air is injected through the SEN. Bai and Thomas[3] studied the bubble formation during gas injection into turbulent downward-flowing water using high-speed camera; the effects of liquid velocity, gasinjection flow rate, injection hole diameter, and gas composition are investigated. Lee et al.[4] used the water model to investigate initial bubble behavior in the SEN using specially-coated samples of porous with different permeability. Ramos-Banderas et al.[5] analyzed the coalescence-breakup phenomena of bubbles; a half width of a mold was arbitrarily divided into four zones, and the bubbles population was calculated by dividing the number of bubbles in an average frame between the area of each zone. Kwon et al.[6] studied the bubble dispersion inside the mold using a water model; the results indicate that the mean bubble diameter decreases with increasing the water circulation rate, and increases with increasing the gas injection rate. Several mathematical models[5–11] have been applied to study the twophase flow in the mold. The results showed that argon bubbles can alter the flow pattern in the upper recirculation zone, shift the impingement point on the narrow wall, and promote the floatation of non-metallic inclusions from the liquid steel. However, except Yuan and Thomas et al.,[12] relatively little work has been reported on bubble size distribution, bubble breakup and coalescence processes in the mold.
Two approaches are mostly used to simulate the twophase flow in continuous-casting process: the Eulerian– Lagrange[13,14] and Eulerian–Euleri
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