A water model and numerical study of the spout height in a gas-stirred vessel
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INTRODUCTION
DUE to the enormous importance of gas injection and stirring in metallurgical processes, there have been numerous publications on physical and numerical modeling of such vessels.[1–9] Modeling of the free surface is one of the remaining hurdles to a complete understanding of such processes. At the free surface, there are often important chemical phenomena occurring that require a good understanding of the fluid flow; these would include reoxidation of steel and splash and fume formation. Furthermore, to understand the details of slag-metal interactions such as slag entrainment, metal losses to slag, and the transport phenomena associated with refining reactions, it is necessary to understand the plume and spout interactions first. There have only been a few experimental studies on the free surface in gas-injected ladles[10,11,12] and even less on its numerical modeling. Sahajwalla et al.[10] studied the gas void fraction in the spout region, using a double-tip electrical resistance probe. This sensor cannot distinguish between gas in gas bubbles (liquid continuous phase) and gas in the freeboard (gas continuous phase). Thus, it is a matter of judgment as to the position of the free surface. Yonezawa and Schwerdtfeger[11] used a single probe configuration and a counterelectrode in the liquid, so that the height of the continuous liquid phase was unambiguously determined. Kishimoto et al.[12] measured the spout height by ultrasonic and electrical capacitance techniques. These techniques were as reliable as the resistance techniques, but were restricted to low flow rates. In the present study, a wide range of flow rates was investigated with a photographic technique. Analysis of the data shows that they are consistent with those of other workers, and correlations were developed for spout height and width over a very wide range of conditions. A mathematical model was developed to overcome some of the limitations with existing codes for free surface computations. The model D. GUO, Senior Research Associate, and G.A. IRONS, Dofasco Professor of Ferrous Metallurgy and Director, are with the Steel Research Centre, Department of Materials Science and Engineering, Hamilton, ON, Canada L8S 4L7. Contact e-mail: [email protected] Manuscript submitted June 25, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS B
provides additional insight into the phenomena at play in the spout area. II. WATER MODEL STUDY A. Apparatus and Procedure Figure 1 shows the layout of the apparatus. A digital camera was used to photograph the free surface. A frame grabber transferred the images to a computer. A series of 12 consecutive images, limited by the memory size of the computer, was captured and transferred to the hard drive for subsequent processing. A square container, with dimensions of 500 ⫻ 500 ⫻ 400 mm, was used, instead of a cylinder, to eliminate distortion of the images. At higher gas flow rates (greater than 10 L/min), the surface oscillations became quite strong, preventing a reproducible averaging process. Consequently,
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