Numerical investigation of the free surface in a continuous steel casting mold model
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INTRODUCTION
The viability of the steel industry depends strongly on product quality and improved efficiency. Steelmakers are aiming for higher casting speeds of liquid steel in continuous casting operations, which have the effect of increased surface waviness and turbulence levels at the steel-slag interface; beyond a certain casting speed, emulsification takes place. It is of basic importance to establish the limits of operating conditions for clean product. The aim of the present study is to contribute to the understanding of the flow conditions prevailing at the steel slag interface; of major concern is the flow condition at the free surface, so that the established stratification remains undisturbed, to allow for the dissolution of rising impurities by the slag. Also, the steel slag interfacial disturbances should be kept at a minimum to avoid any re-entrainment of impurities into steel, or emulsification. Mathematical modeling of the flow conditions within the caster and particularly at the interface presents the method for establishing the critical conditions that lead to the preceding phenomena. In this work, the presence of slag at the top surface of the mold has not been modeled and air is assumed above the water body. Standing waves may be generated at the free surface of deep water contained between two parallel vertical walls. Lamb[1] first studied this problem and proved the existence of such waves with wave numbers integral multiples of p/l, where l is the distance between the walls. A field of great interest is the stability of these waves and the study of the conditions under which these waves become unstable. Rottman[2] conducted an extensive search on that topic. The mathematical formulation of the problem assumes irrotational motion of inviscid and incompressible fluids. The method Rottman uses is a semianalytical one, containing a perturbation-expansion procedure. Concerning the way the instability of the waves is observed, free-surface waves are limited by the interface becoming vertical at the crest. The maximum wave-height-to-wavelength ratio (H/l, Figure 1) has been estimated at about 0.21. Gupta and Lahiri,[3] in a water-modeling study of the surG.A. PANARAS, Mechanical Engineer, A. THEODORAKAKOS, Research Assistant, Department of Mechanical Engineering, and G. BERGELES, Professor, Fluids Section, Laboratory of Aerodynamics, are with the National Technical University of Athens, 15773 Athens, Greece. Manuscript submitted May 19, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS B
face disturbances in a continuous slab caster, observed that the free surface is wavy and the wave amplitude shows a parabolic variation with the nozzle exit velocity. The waves present at the interface indicate that only one prominent wave is present with changing frequency. Najjar et al.[4] have conducted a numerical study of the turbulent flow through bifurcated nozzles in continuous casting by using a finite element methodology coupled with the k-ε model of turbulence. The effects of nozzle design and castin
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