Physical and Mathematical Modeling of Flow Structures of Liquid Steel in Ladle Stirring Operations
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DUCTION
GAS injection into steel melts is a routine practice in steelmaking to eliminate thermal and chemical gradients, to remove particles and to enhance chemical reactions and mass transfer between metal and snag phases. The final aim of the process is to obtain clean steel with controlled chemistry and temperature before sending the ladle to the caster. The wide spectrum of phenomena like hydrodynamics, mass and heat transfer, flotation of inclusions promoted by melt stirring with gas injection has attracted numerous contributions addressing practically each one of these aspects. The span of flow rates of gas in the industry is 0.001 to 0.01 RODOLFO D. MORALES and FABIA´N ANDRE´S CALDERO´N-HURTADO are with the Department of Metallurgy and Materials Engineering, Instituto Polite´cnico Nacional-ESIQIE. Ed. 7 UPALM, Zacatenco, 07369, Mexico City, Mexico and with the Department of Materials Science and Engineering, University of Toronto, 184 College Street, Suite140, Toronto, ON, M5S 3E4, Canada and also with K&E Technologies, Manizales 88, San Pedro Zacatenco, 07369, Mexico City, Mexico. Contact e-mail: [email protected] KINNOR CHATTOPADHYAY is with the Department of Materials Science and Engineering, University of Toronto. SERGIO JAVIER GUARNEROS GUARNEROS is with K&E Technologies. Manuscript submitted May 28, 2019.
METALLURGICAL AND MATERIALS TRANSACTIONS B
Nm3/min ton to provide gentle or strong stirring. From the flow structure point of view, this range of gas flow rates is in the bubbling regime.[1] It is generally accepted[2–4] that in the vicinity of the gas injection device (either nozzle or porous plug), bubble dynamics are being very dependent on the local turbulence and kinetic energy. Outside this region, these variables will not have an influence on the development of the two-phase plume. The volume of the gas-liquid plume represents only about 3 pct of the total volume of the melt, i.e., it is practically immersed in an infinitum medium. Large bubbles leaving the injection region will disintegrate or coalesce (depending on the physical properties of the fluids and local turbulence). During their travel to the bath surface, gas bubbles reach a dynamic equilibrium yielding a distribution of sizes and space (volumes) along the plume height. Many researchers have characterized bubbles in the plume using electro-resistivity techniques, providing information about bubble sizes, volume fractions of gas in the plume and plume diameter.[5–10] Finally, when the bubbles reach the bath surface or spout, they burst out providing a radial flow along the bath surface to the liquid. Rather than the kinetic energy of the gas phase, it is the buoyancy energy of bubbles that is responsible for moving the liquid through a convection mechanism (bulk motion) independent from the viscous forces[11,12] of the liquid. Mixing times have also been a matter of
discussion in numerous studies; the works of Mazumdar and Guthrie[13] have provided a widely accepted correlation, derived from macroscopic momentum balances based on stirring en
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