A Model for Slag Eyes in Steel Refining Ladles Covered with Thick Slag
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INTRODUCTION
DURING inert-gas purging in steel ladles, the upward liquid flow from the bubble plume turns sideways at the bath surface and pushes the overlying slag layer to the sides. If the slag layer is sufficiently thin, this process exposes an area of liquid metal to the atmosphere, termed the ‘‘eye’’. The region raised on the bath surface by the escaping gas bubbles is usually called the ‘‘spout’’.[1–3] These regions are important sites for various slag-metal reactions, as well as unwanted phenomena such as slag entrainment and oxygen and nitrogen pick up which are detrimental to the steel quality. The hydrodynamic and physical characteristics of these regions are of great practical significance. The phenomenon of slag eye formation has been the subject of some recent work,[4–9] but many aspects need further investigation. In a previous work,[8] the authors studied the eye formation in ladles with a thin slag layer, which typically results in relatively large eyes. A mechanistic model was also derived to predict the eye size under this regime. As a complementary effort, the present study examines the alternative case of ladle eyes in a bath covered with a thick slag layer, where the eyes formed are often smaller than the cross-section of the two-phase plume. A mathematical model is derived by extending the previous mechanistic-based approach used for the thin slag practice. Some cold model experiments have also been carried out in the present work.
II.
MATHEMATICAL MODEL FOR THICK SLAG PRACTICE
A. Previous Work on Ladle Eyes Previous studies on the eye formation resulted in a number of mathematical expressions for the eye size.[4–9] Most of them, empirically obtained by statistical analysis of eye-size data in a particular system, have been shown to not to be generally applicable to other conditions.[8] In a recent work,[8] the present authors undertook an extensive experimental study of ladle eye formation. It was found that if the slag layer is relatively thin, it can be pushed aside relatively easy resulting generally in eyes that are larger than the spout region, as depicted schematically in Figure 1. For the above regime, a mathematical model for the eye size was developed from first principles based on the following considerations:[8] (1) At steady state, the eye formation is the result of various forces acting in the vicinity of the eye (region ABCD in Figure 1), so an analysis of these forces may clarify the eye formation mechanics. (2) A control-volume-based approach was adopted and a linear momentum balance was performed over the section ABCD by considering the various forces acting on this control volume. The resulting mechanistic mathematical model for the eye size was presented as:[8] Ae 1=2 ¼ a þ b FrD Ap
K. KRISHNAPISHARODY, Research Associate, is with the Innovation, Saarstahl AG, Vo¨lklingen 66330, Germany. Contact e-mail: [email protected] G.A. IRONS, Dofasco Professor of Ferrous Metallurgy and Director, is with the Steel Research Centre, McMaster University, Hamilton, ON L8S 4L7, Canada. Manus
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