Mathematical Modeling of Impinging Gas Jets on Liquid Surfaces
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AN enduring problem in process metallurgy is the mathematical description of impinging gas jets on liquid surfaces. The most prominent application is the top lancing of oxygen in the basic oxygen steelmaking process. The momentum of the oxygen jet destabilizes the slag and metal phases to create what is known as the slag–metal emulsion. At the same time, the oxygen reacts with the slag and the metal at extremely high rates and generates a large amount of heat. Therefore, a complex interplay takes place between fluid flow, heat transfer, and mass transfer that has not been captured in a detailed mathematical model of the process. The present work is a contribution to the fluid mechanical aspects of the impinging jet with liquid surfaces, focusing on aspects of surface instability and droplet formation. Several approaches have been developed to solve this problem analytically and numerically. Conformal mapping techniques,[1] local force balances,[2,3] and solving the Bernoulli equation for the surface wave[4–6] provide analytical solutions for the surface shape but cannot account for the momentum transfer to the liquid. HO YONG HWANG, formerly Graduate Student with Steel Research Centre, McMaster University, Hamilton, Ontario L8S 4L7, Canada, is now with Esser Steel Algoma Inc., Sault Ste. Marie, Ontario P6A 7B4, Canada. GORDON A. IRONS, Dofasco Professor of Ferrous Metallurgy and Director, is with the Steel Research Centre, McMaster University. Contact e-mail: [email protected] Manuscript submitted January 8, 2011. Article published online February 19, 2011. METALLURGICAL AND MATERIALS TRANSACTIONS B
Progress also has been made in the application of some computational fluid dynamics techniques for free surface representation. Qian et al.[7,8] constructed the surface with the impinging gas pressure field and solved the momentum equation according to the constructed surface. Olivares et al.[9] used the volume of fluid (VOF) method with a renormalization group k – e turbulence model. Some computations have used commercial software[10,11]; most recently, Odenthal et al.[12] used FLUENT (ANSYS, Canonsburg, PA) to solve fluid flow, heat transfer, and mass transfer for the basic oxygen steelmaking and the argon-oxygen decarburization processes. In most free surface problems, the flow of the denser fluid is more important and the source of momentum is in the denser fluid; stirring of liquids in vessels is an example. In these circumstances, it is a reasonable approximation to neglect the shear stress to the less dense phase. However, in the case of an impinging gas jet on a liquid surface, the gas phase is the source of momentum, so it is necessary to apply the full stress boundary condition to represent the physical situation properly.[13] Height function methods or unstructured grid adaptation[14–16] can handle this boundary condition, but these methods are not as capable of dealing with multiple interfaces when droplets are generated. For the current study, the VOF[17] method and the Piecewise Line Interface Construction (PLIC)[
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