Mathematical Modeling of Impingement of an Air Jet in a Liquid Bath
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Mathematical Modeling of Impingement of an Air Jet in a Liquid Bath. J. Solórzano-López1, R. Zenit2, M.A. Ramírez-Argáez1. 1 Facultad de Química, Universidad Nacional Autónoma de México, México, D.F. 2 Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México. [email protected], [email protected], [email protected].
ABSTRACT Physical and mathematical modeling of jet-bath interactions in electric arc furnaces represent valuable tools to obtain a better fundamental understanding of oxygen gas injection into the furnace. In this work, a 3D mathematical model is developed based on the two phase approach called Volume of Fluid (VOF), which is able to predict free surface deformations and it is coded in the commercial fluid dynamics software FLUENT™. Validation of the mathematical model is achieved by measurements on a transparent water physical model. Measurements of free surface depressions through a high velocity camera and velocity patterns are recorded through a Particle Image Velocimetry (PIV) Technique. Flow patterns and depression geometry are identified and characterized as function of process parameters like distance from nozzle to bath, gas flow rate and impingement angle of the gas jet into the bath. A reasonable agreement is found between simulated and experimental results. INTRODUCTION The oxygen jets are used in several steelmaking processes such the Electric Arc Furnace (EAF). These jets play an important role in these processes because they control bath mixing, chemical reaction kinetics, energy consumption, foaming slag formation, bath recirculation and the occurrence of splashing since they exchange momentum, heat and mass with the slag and the molten steel [1, 2]. To evaluate the momentum exchange between the gas jets and the liquid bath, the geometry of the formed depression in the liquid free surface must be determined as well as the liquid velocity profiles induced by the impingement and shear of the gas jet respectively. Mathematical modeling is a tool able to simulate these complex systems. Also, physical modeling, using water and transparent vessels, is an important tool to perform these studies in a laboratory scale at low cost and safe conditions [3]. Several groups of researchers have measured the size of the depth of the depression formed by the impingement of a gas jet on a liquid bath and they have obtained results in the form of empirical correlations of the dimensionless depth size as a function of the main experimental parameters [4]. Some of these correlations are obtained from measurements in pilot furnaces [3, 5] but most of them are obtained by physical modelling experiments [6, 7, 8, 9]. Additionally, the velocity profile in the bath induced by the momentum transfer from the gas jet is important in the mixing phenomena and in reactions kinetics governed by mass transport of species. In the literature there are works that describe recirculation in the liquid by mathematical models [10, 11, 12]. Regarding the cavity geometry, some researchers h
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