Modeling of trajectory and residence time of metal droplets in slag-metal-gas emulsions in oxygen steelmaking
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I. INTRODUCTION
IN basic oxygen steelmaking, large numbers of metal droplets are generated and ejected into the slag through the high-speed injection of oxygen. The generation of droplets accelerates the overall kinetics of various steelmaking reactions through the creation of a large interfacial area. Since the invention of oxygen steelmaking, many studies[1–25] have been carried out to understand the kinetic phenomena associated with slag-metal-gas emulsions. In several studies,[1,2,11–15] slag samples were recovered from industrial furnaces and the size distribution of droplets in the slag was measured. Other investigators have carried out more fundamental studies on the interaction of metal droplets in oxidizing slags, including studies using X-ray fluoroscopy to observe reaction phenomena.[3–7] These experimental observations show that the decarburization of metal droplets in oxidizing slags significantly affects the motion of metal droplets through the rapid evolution of gas from the droplets. In oxygen steelmaking, the refining rate is dependent not only on the reaction kinetics but also on the residence time of the metal droplets in the slag.[10] The generation of droplets through top blowing has been the subject of several studies, including recent papers by the authors.[16–25] Most of these studies have concentrated on the mechanical aspects of droplet generation and have largely ignored the issue of droplet residence time. Subagyo et al.[24] developed a model to predict droplet GEOFFREY BROOKS formerly Associate Professor, and YUHUA PAN, formerly Post Doctoral Fellow, with the Steel Research Centre, McMaster University, Hamilton, ON, Canada L8S 4L7, are Principal Research Scientist and Research Scientist, respectively, with CSIRO Minerals, Clayton South, VIC 3169, Australia. Contact e-mail: [email protected] SUBAGYO, formerly Post Doctoral Fellow, with the Steel Research Centre, McMaster University, is Senior Lecturer, with the Department of Mechanical and Industrial Engineering, Gadjah Mada University, Yogyakarta 55281, Indonesia. KEN COLEY, Associate Professor, is with the Steel Research Centre, McMaster University. Manuscript submitted July 30, 2004. METALLURGICAL AND MATERIALS TRANSACTIONS B
generation rate and more recently proposed a method to predict size distribution.[10] However, their attempts to predict droplet residence time were not entirely successful. Therefore, it is the purpose of the present work to analyze the ballistic behavior of ejected metal droplets, in order to develop a model that will predict residence times in slag under various conditions. In particular, this study aims at combining the chemical kinetics and fluid mechanics of droplet behavior in the emulsion. II. MODEL DEVELOPMENT A. Model for Ballistic Motion of Metal Droplets in Slag without Decarburization 1. Governing equations The concept behind this study is to calculate the trajectory of a single iron droplet moving in slag by using the ballistic motion principle. This concept was originally applied by Subagyo et a
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