Turbulent Flow and Heat Transfer Problem in the Electromagnetic Continuous Casting Process Theeradech Mookum, Benchawan Wiwatanapataphee, and Yong Hong Wu Abstract— This paper aims to study the effect of turbulence on the flow of two fluids and the heat transfer - solidification process in electromagnetic continuous steel casting. The complete set of field equations is established. The flow pattern of the fluids, the meniscus shape and temperature field as well as solidification profiles obtained from the model with and with no turbulence effect are presented. The results show that the model with turbulence gives a large circulation zone above the jet, much larger variation of the meniscus geometry, a slow solidification rate and higher temperature in the top part of the strand region. Keywords— Electromagnetic continuous steel casting process, turbulent flow, heat transfer, two-fluid flow, level set method. I. I NTRODUCTION T HE surface control of continuous steel casting products is important to steel quality. Over the last decade, the technologies used to control the quality of the continuous casting products have been proposed such as neural networks [23], fuzzy logic [24], optimization [27], and electromagnetic contin- uous casting process [10], [15]. The electromagnetic steel casting process is a relatively new effective heat extraction process in which molten steel is withdrawn at a specified speed. In comparison with the normal continuous casting process, the electro- magnetic continuous casting process possesses many advantages such as improving the surface quality, controlling the flow pattern of liquid steel, and re- moving the inclusions and gas bubbles [16], [28]. Manuscript received April 7, 2011; revised May 30, 2011. This work was supported by the Office of the Higher Education Commission and the Thailand Research Fund through the Royal Golden Jubilee Ph.D. Program (Grant No. PHD/0212/2549), and an Australia Research Council Discovery project grant. T. Mookum is with School of Science, Mae Fah Luang University, 333 Moo 1, Thasud, Muang, Chiang Rai 57100 THAILAND (e-mail:t.mookum@sci.mfu.ac.th). B. Wiwatanapataphee is with Department of Mathematics, Faculty of Science, Mahidol University, 272 Rama 6 Road, Rajthevee, Bangkok 10400 THAILAND (corresponding author; e-mail:scbww@mahidol.ac.th). Y.H. Wu is with Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845 AUSTRALIA (e-mail:yhwu@maths.curtin.edu.au). Due to these advantages, great efforts have been made to develop this process over the last decade and the percentage of steel in the world produced by this process is increasing. In the electromagnetic casting, a coil is mounted around the casting mould. The magnetic field gener- ated from the source current through the coil induces the electric current in the steel pool. This current not only heats the molten steel but also generates an electromagnetic force in the molten steel. During the process, the molten steel is poured from a ladle into an intermediate container known as a tundish. The molten steel from the tundish is transferred through a submerged entry nozzle into a water-cooled mould, where intense cooling causes a thin solidified steel shell to form around the edge of the steel, leaving a large molten core inside the shell. To facilitate the process, mould powder or lubricant oil is added at the top of the mould to prevent the steel from oxidizing. The interface between the molten steel and lubricant oil is known as a “meniscus”. The mould is oscillated vertically and then the lubricant liquid is dragged into the gap between the solidified strand and the mould walls. This can prevent the steel from sticking to the solidifying shell. After leaving the mould, the solidified strand is supported by a set of rollers, cooled down by water sprays and then subsequently cooled through radiation. When the casting has attained the desired length, it is cut off with a cutter. The electromagnetic field imposed to the process is the effective technology to control heat transport and solidification [2], [5], [20], [25], [26]. The elec- tromagnetic force can reduce the molten steel flow from hitting the wall [7], [28] and push the meniscus away from the mould during casting [19], which reduces the surface contact between the melt and the wall. The behavior of electromagnetic stirring, fluid flow, heat transfer with solidification and oscillation marks on the steel surface is crucial to the quality and productivity of the process. The effect of the electromagnetic field on turbulent flow has also been investigated [8], [6], [22], [28]. With the limitation of experiments in the contin- uous casting process, mathematical models become an important tool to understand the physical phenom- INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTERS IN SIMULATION Issue 4, Volume 5, 2011 310