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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).

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The reduction of the weight of high performance materials together with the improvement of mechanical properties and the increase of the recycling of used metal are new challenges which emphasize the importance of metal cleanliness. Ladle treatment of specialty steels has long been described as the secondary metallurgical process mainly responsible for the non-metallic inclusion derived from the deoxidation process. The treatment is accomplished by blowing argon through one or more porous plugs for the purposes of desulfurization, minor composition adjustments, and inclusion removal. Gas injection is applied on routine basis to achieve both the stirring of the liquid bath (thermal and chemical homogenization) and the entrapment of the inclusions by the bubbles (flotation). Furthermore, the turbulence produced in bubble swarms enhances the probability of inclusion collisions and makes aggregation the first mechanism for particle removal. The physical processes involved in gas stirred ladles are numerous and complex owing to the three dimensional and multiphase (metal-gas and inclusions) nature of the reactor. Despite these difficulties, the population balance equations (PBEs) can be implemented in CFD code [1,2] and combined CFD-PBM (computational fluid dynamicspopulation balance method) models are investigated for steel ladle processes [3,4] and produce very promising results in terms of inclusion removal efficiency. Current research focused on the mathematical formulation of the system and an approach, the quadrature method of moments (QMOM), has been formulated and applied. [5] A natural alternative of the QMOM is the classes method (CM) in which the particle size distribution (PSD) is represented through a finite number of inclusion classes. [6] Very few authors [7][8][9][10] implemented these two techniques in CFD code with the aim of discussing their relative advantages and disadvantages. It should be noted that all of the simulation were performed for a 2D (or more recently 3D) gas-bubble or liquid-liquid reactor and comparison applied to ladle treatment is nonexistent in literature. Therefore the main focus of this work is to simulate the behavior of non-metallic inclusions in an industrial gasThe ladle treatment of liquid steel is mainly responsible for the steel cleanliness, since it generates as well as eliminates most of the oxide inclusions. Today, the combination of computational fluid dynamics and population balance modeling makes the numerical simulation of this complex threephase reactor possible. First, the comprehensive three-dimensional turbulent multiphase flow model is developed to study the behavior of argon bubbles in liquid steel based on the geometry and operating conditions corresponding to the real industrial process. This simulation is validated by comparing the calculated mixing time with the experimental value predicted from ladle sampling. Then, the balanced equation for a population of oxide inclusions with aggregation mechanism is coupled with the hydrodynamic modeling. To obtain ...

The purposes of the paper are twofold: (i) to present a rational approach to the modeling of inertial particle transport in anisotropic turbulent flows and (ii) to show how the anisotropy of fluid turbulence timescales affects the particle fluctuating velocities in homogeneous shear flow. For these purposes, the directional dependence of the Lagrangian autocorrelations of fluid velocities is incorporated into the statistical probability density function (PDF) model proposed previously. The anisotropic timescale (ATS) model is evaluated against numerical simulations for homogeneous shear turbulent flows and is compared to results predicted by the isotropic timescale (ITS) model. The new ATS model for the PDF of the particle velocity distribution in turbulent flow appears to yield slightly improved results over the ITS model.

As intermediate quantities available from various existing numerical computations, the fluid Lagrangian time scales are of primary importance in the development of probability density function models for turbulent flows. Similarly, the time scales of the fluid seen by discrete particles in two-phase flows are essential for the development of dispersion models based on stochastic differential equations. Such time scales are obviously depending not only on the particle properties but also on the fluid Lagrangian and Eulerian time scales. A model is proposed here to estimate the directional dependence of the fluid Lagrangian time scales and drift coefficients in one-directional equilibrium turbulent shear flows, based on a local homogeneity assumption in the frame of the generalized Langevin model. Through comparison with available direct and large eddy simulation predictions in channel flows and in a homogeneous shear flow, the model is shown to lead to significant improvements in the streamwise and spanwise directions, where the existing empirical laws for the Lagrangian time scales are far from being satisfactory. We examine the way this model can be used to build a suitable stochastic process for the fluid seen by inertial particles in such basic turbulent shear flows.