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We investigate the migration of bubbles in several flow patterns occurring within the gap between a rotating inner cylinder and a concentric fixed outer cylinder. The time-dependent evolution of the two-phase flow is predicted through three-dimensional Euler-Lagrange simulations. Lagrangian tracking of spherical bubbles is coupled with direct numerical simulation of the Navier-Stokes equations. We assume that bubbles do not influence the background flow ͑one-way coupling simulations͒. The force balance on each bubble takes into account buoyancy, added-mass, viscous drag, and shear-induced lift forces. For increasing velocities of the rotating inner cylinder, the flow in the fluid gap evolves from the purely azimuthal steady Couette flow to Taylor toroidal vortices and eventually a wavy vortex flow. The migration of bubbles is highly dependent on the balance between buoyancy and centripetal forces ͑mostly due to the centripetal pressure gradient͒ directed toward the inner cylinder and the vortex cores. Depending on the rotation rate of the inner cylinder, bubbles tend to accumulate alternatively along the inner wall, inside the core of Taylor vortices or at particular locations within the wavy vortices. A stability analysis of the fixed points associated with bubble trajectories provides a clear understanding of their migration and preferential accumulation. The location of the accumulation points is parameterized by two dimensionless parameters expressing the balance of buoyancy, centripetal attraction toward the inner rotating cylinder, and entrapment in Taylor vortices. A complete phase diagram summarizing the various regimes of bubble migration is built. Several experimental conditions considered by Djéridi, Gabillet, and Billard ͓Phys.

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A variant of the quadrature method of moments (QMOM) for solving multiple population balance equations (PBE) is developed with the objective of application to steel industry processing. During the process of oxygen removal in a steel ladle, a large panel of oxide inclusions may be observed depending on the type of oxygen removal and addition elements. The final quality of the steel can be improved by accurate numerical simulation of the multi-component precipitation. The model proposed in this article takes into account the interactions between three major aspects of steelmaking modeling, namely fluid dynamics, thermo-kinetics and population balance. A commercial CFD code is used to predict the liquid steel hydrodynamics, whereas a home-made thermo-kinetic code adjusts chemical composition with nucleation and diffusion growth, and finally a set of PBE tracks the evolution of inclusion size with emphasis on particle aggregation. Each PBE is solved by QMOM, the first PBE/QMOM system describing the clusters and each remaining PBE/QMOM system being dedicated to the elementary particles of each inclusion species. It is shown how this coupled model can be used to investigate the cluster size and composition of a particular grade of steel (i.e., Fe-Al-Ti-O).

The topic of this paper is the study of inclusion properties and behaviour inside a ladle containing liquid steel. A new numerical tool tracks the size and the composition of inclusions during the oxygen removal and the steel refining. Commercial CFD codes (Fluent TM ), home-made thermokinetics code and population balance model have been associated to follow oxide precipitates. The long-term scientific goal of this study consists in proposing actuators to prevent or to eliminate harmful inclusions based on results predicted by the numerical model.

No abstract

In the steel industry, metallurgical operations on liquid steel before casting take place at secondary metallurgy processes, and are usually held in a reactor called a ladle.The main steps in the secondary metallurgy are vacuum degassing, the decrease in the sulphur concentration, the control of non-metallic inclusions and the composition adjustment of the steel. For each treatment, an effective mixing is necessary to accelerate the reactions. This mixing is usually done by injecting an inert gas through porous plugs and/or one or more lances immersed in the liquid-steel bath.The ladle can contain up to 330 tons of liquid steel and any flows produced by the rising of bubbles are turbulent. The inclusions are mostly oxides, resulting from the addition of oxidizers in the ladle (such as aluminum). To be removed, the inclusions must be transported to the surface, which is covered by a slag layer, absorbing the inclusions as quickly as possible.The first flow predictions inside a ladle started almost 30 years ago and a lot of papers have already been published on this subject, [1][2][3][4][5][6][7] initially with mixing models, which were progressively replaced by two-phase flow models (EulerEuler, Euler-Lagrange). Later, inclusion behavior inside the ladle was considered with more-and-more-sophisticated mechanisms: inclusion elimination at interfaces, [8] inclusion nucleation and agglomeration growth by collisions. [9][10][11][12][13] The coupling between computational fluid dynamics computation fluid dynamics (CFD) and thermodynamics had already been applied to desulphurization prediction [14][15][16] and is currently extended to get the inclusion composition from the local steel composition. [17,18] Due to the continuous increase of computer capacity, it has also become possible to predict the shape of the moving interfaces [19,20] in 3D. For the interaction of inclusions with bubbles, Zhang and Taniguchi [21] presented an exhaustive status of the modelling, but it was limited to only one bubble, ignoring both the flow interaction with the other bubbles that occurs when a bubble swarm is considered and also the thermodynamics mechanisms affecting the adhesion stability. More recently, the influence of the shape of the bubble in a swarm was investigated. [22] It was observed that a migration of the particle away from the bubble wake can occur, which is not obtained when a single bubble is considered. Although a lot of work has already been done for ladle modelling, little attention has been paid to consider both interface tracking, which is continuously deforming, and inclusion entrapment at those interfaces. This is a key point to really evaluate the capacity of the ladle process to eliminate the inclusions.The purpose of this communication is the prediction of the respective inclusion entrapment at the different interfaces through the extensive use of numerical modelling. Mathematical ModellingFor these studies, ArcelorMittal selected the commercial CFD software Fluent TM , making it more robust by comparing the ...

An important stage has been reached in the development of a comprehensive model of a steelmaking reactor with the realization of a numerical simulation coupling a thermodynamic module (CEQCSI for Chemical EQuilibrium Calculation for the Steel Industry), developed by Arcelor Research, and a commercial fluid dynamic software (Fluent). Fluent performs computations for liquid steel and determines the temperature and distribution of dissolved chemical elements and nonmetallic inclusions. These are regularly transferred to CEQCSI, which, assuming local equilibrium conditions, calculates the new state of equilibrium of the dissolved elements and the evolution of the inclusions population. Based on this weak two-way coupling, the first numerical results concerning the deoxidation process of liquid steel by aluminum during the secondary refinement are obtained. Al, O and Al 2 O 3 concentrations are predicted within the studied reactor (RH) and heterogeneities in the volume can be highlighted. This tool gives the possibility to study the effect of different factors on the process and on the final quality of the products (metal cleanliness). The model can moreover give precise information for a better understanding of the nozzle clogging due to the alumina inclusions formation. Numerisches Modell zur Vorhersage und Optimierung von Desoxidationsprozessen durch Kopplung von Strömungsdy-namik und Thermochemie. Ein wichtiger Schritt in der Entwicklung eines umfangreichen Stahlreaktor-Modells wurde durch numerische Kopplung eines thermodynamischen Moduls (CEQCSI, Chemische Gleichgewichtsberechnung für die Stahlindustrie), entwickelt von Arcelor Research, und einer kommerziellen Software für Strömungsdynamik (Fluent) erreicht. Fluent berechnet die Temperatur und die Verteilung von gelösten chemischen Elementen und nichtmetallischen Einschlüssen in der Stahlschmelze. Diese Daten werden regelmäßig zur CEQCSI gesendet, welche, unter der Annahme lokaler Gleichgewichtsbedingungen, den neuen Stand von gelösten Elementen im chemischen Gleichgewicht und die Entwicklung der Einschlusspopulation berechnet. Basierend auf dieser simplen Zweifachkopplung, wurden die ersten numerischen Ergebnisse eines Desoxidationsprozesses mit Aluminium errechnet. Al-, O-und Al 2 0 3 -Konzentrationen zeigten im untersuchten Reaktor (RH) Heterogenitäten. Dieses Modell macht die Untersuchung der Wirkung verschiedener Faktoren auf den Prozess und auf die Qualität des Endproduktes (Reinheitsgrad des Stahls) möglich. Das Modell gibt zusätzlich wertvolle Informationen für ein besseres Verständnis vom Zuwachsen des Tauchrohres durch die Bildung von Aluminiumoxid-Einschlüssen.