Model of Gas Flow Through Porous Refractory Applied to an Upper Tundish Nozzle
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ARGON gas is widely used in metallurgical processes for many purposes, such as gas injection through a porous plug to stir the ladle, gas injection to remove inclusions in the tundish, and gas injection through the upper tundish nozzle (UTN) during continuous casting to prevent reoxidation and nozzle clogging[1] as shown in Figure 1.[2] This injected gas significantly affects flow in these vessels, and may be detrimental if not properly controlled. Extensive research has investigated gas–liquid two-phase interactions in those vessels (e.g., ladle,[3–6] tundish,[7,8] and continuous casting[9–14]), via physical and mathematical modeling. Physical models provide qualitative understanding of the gas–liquid two-phase interactions and can be used to validate computational models. However, physical model results from an air–water system differ from an otherwise similar argon–metal system due to some differences in material properties (e.g., surface tension and density) and in operation conditions (e.g., temperature gradient) between these two systems.[10] Thus mathematical modeling becomes a necessary tool to study gas–metal two-phase flows in commercial processes. Computational models have been applied
RUI LIU, formerly Ph.D. Student with the Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, is now Process Research Engineer with ArcelorMittal, Inc. Global R&D, East Chicago, IN. BRIAN G. THOMAS, Gauthier Professor, is with the Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign. Contact email: [email protected] Manuscript submitted February 11, 2014. METALLURGICAL AND MATERIALS TRANSACTIONS B
extensively to study argon gas effects on steel continuous casting using mixture models,[10,14] Eulerian–Eulerian models[9,11] and Eulerian–Lagrangian models.[12,13] The accuracy of these modeling efforts depends on two key parameters: the volumetric flow rate of argon gas entering the steel in the hot condition, and the initial bubble size distribution. Both parameters have been investigated in previous work.[10,14,16] The volumetric flow rate of the injected argon gas is usually measured in the ‘‘cold’’, standard temperature and pressure (STP) condition well before entering the nozzle, in standard liters per minute (SLPM). This is usually much smaller than the flow rate entering the molten metal in hot condition through refractory walls, due to gas thermal expansion. This effect is accounted for with the ideal gas law, as implemented in Reference 10 to estimate volumetric flow rate in the hot condition exiting the SEN port during continuous casting: T0 p1 ; ½1 Qg;hot ¼ Qg;cold T1 p1 þ qgLn where Qg is the gas flow rate (m3/s), T0 is the casting temperature (K), T¥ is the ambient temperature (K), p¥ is the ambient pressure (Pa), and Ln is the pressure head of molten steel above the gas injection region (m). This calculated gas flow rate in the ‘‘hot’’ condition is then used to find the bubble size distribution
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