A dynamic model of alumina inclusion collision growth in the continuous caster

Lei, Hong; He, Jicheng

doi:10.1016/j.jnoncrysol.2006.05.032

Cited by 14 publications

(7 citation statements)

References 27 publications

(46 reference statements)

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“…The boundary condition can be found in the reference. 10,11) The partial differential equations for the inclusion's variables C and N were discretized by the finite-volume method, and the convergence criterion was < 10 -8 , where K is the iteration number.…”

Section: Boundary Conditions and Numerical Methodsmentioning

confidence: 99%

Mathematical Model for Cluster-Inclusion’s Collision-Growth in Inclusion Cloud at Continuous Casting Mold

Lei¹,

Zhao

Geng³

2014

ISIJ Int.

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The inclusion's morphology and size play a strong role in the steel product quality, so it is very important to have a deep insight into the inclusion's collision-growth in the continuous caster. In order to describe the formation of the cluster-inclusion, a mathematical model and the related source code are developed to trace the inclusion's movement and collision-growth in the inclusion cloud. Such a model includes two sub-models. Firstly, the spatial distribution of turbulent flow and the inclusion's number density and the characteristic radius after Stokes collision and turbulent collision are obtained by Eulerian approach. Secondly, the inclusion's trajectory and the related inclusion fractal growth are predicted by Lagrangian approach. Numerical results show that the spatial distributions of the inclusion volumetric concentration, number density and characteristic radius have some features of the upper and lower recirculation zone due to the fluid flow. For an inclusion particle, the bigger inclusion has more chances to catch other inclusions and forms a more complex cluster-structure. Among the forces acting on the inclusion, the pressure gradient force, Basset history force, the visual mass force, the gravitational force and the buoyancy force should be considered in order to describe the inclusion's exact motion. Furthermore, the pressure gradient force, the Basset force, the visual mass force follow the same variation rule along with the inclusion's trajectory.

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Section: Boundary Conditions and Numerical Methodsmentioning

confidence: 99%

Mathematical Model for Cluster-Inclusion’s Collision-Growth in Inclusion Cloud at Continuous Casting Mold

Lei¹,

Zhao

Geng³

2014

ISIJ Int.

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“…................... (6) where s represents the interfacial free energy between nuclei and molten steel, and the change of the free energy per (8) and S is the supersaturation degree [14][15][16][17][18] ........ (9) Here, the subscripts 'ss' and 'eq' mean a supersaturation state and 'eq' means an equilibrium state, respectively.…”

Section: Thermodynamics Of Homogeneous Nucleationmentioning

confidence: 99%

“…Based on the Smoluchowski's model, Miki et al 5) and Zhang et al 6) simulated inclusion agglomeration and removal in different metallurgical reactors, and Nakaoka et al 7) proposed particle-size-grouping (PSG) method and studied the fractal dimension of agglomeration. On the base of particle's mass-population conservation model and stochastic collision model, Lei et al 8,9) studied spatial distribution of alumina inclusions and its dynamic fractal-growth process in the continuous casting mold. Among previous mathematical models, a general nucleation-growth model is perhaps the most attractive because it can predict the time-dependent particle size distribution of inclusions in molten steel, and usually PSG method is introduced to speed up the solution for population balance equations according to Zhang et al 10,11) However, in the current nucleation-growth model, the diffusion coefficient of a molecule is assigned to take the same value of the diffusion coefficient of oxygen in the molten steel, 10,11) and the predicted number density is far (10 to 100 times) greater than the experimental data.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Model for Nucleation, Ostwald Ripening and Growth of Inclusion in Molten Steel

Lei¹,

Nakajima

Jiang³

2010

ISIJ Int.

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Numerical simulation is a powerful tool to investigate inclusion behavior in the molten steel. Although many mathematical models have been developed to predict inclusion collision-growth behavior in different metallurgical reactors, the inclusion size distribution had to be obtained by experiment or assumption. Thus, a general nucleation-growth model, which involves in chemical reaction, homogeneous nucleation and growth kinetics, is developed to investigate the inclusion nucleation, Ostwald ripening, Brownian collisiongrowth, Stokes collision-growth and turbulent collision-growth. In order to speed up the calculation, the deoxidation products are divided into two parts. The first part only consists of embryos, and directly numerical simulation is used to solve the differential equations. The second part only consists of inclusion particles, and particle-size-grouping method is introduced to solve the related equations. Numerical results showed that the predicted inclusion size distributions are consistent with previous experimental data. With the increasing diffusion coefficient, the peak-value diameter keeps unchanged and the maximum number density decreases. With the increasing turbulent energy dissipation rate, the peak-value diameter and the maximum number density decrease under the assumption on floating-out of larger inclusions.

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“…Lei and He [8] developed a three-dimensional, Eulerian-Lagrangian method to predict the dynamic growth of alumina inclusion in a continuous caster. They concluded that the cluster formation depends on turbulent flow which determines the inclusion growth mechanism.…”

Section: Introductionmentioning

confidence: 99%

Performance Optimization of a Six-Strand Tundish

Gupta¹,

Dewan²

2013

WJM

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The aims of the present study are to predict and improve inclusion separation capacity of a six strand tundish by employing flow modifiers (dams and weirs) and to assess the influence of inclusion properties (diameter and density) together with velocity of liquid steel at the inlet gate on the inclusion removal efficiency of a six-strand tundish. Computational solutions of the Reynolds-Averaged Navier-Strokes (RANS) equations together with the energy equation are performed to obtain the steady, three-dimensional velocity and temperature fields using the standard k-ε model of turbulence. These flow fields are then used to predict the inclusion sepapration by numerically solving the inclusion transport equation. To account for the effects of turbulence on particle paths a discrete random walk model is employed. It was observed that with the employment of flow modifiers, the inclusion separation capacity of tundish increases without any large variation in the outlet temperatures. It is shown that inclusion properties and velocity are important parameters in defining the operating conditions of a six-strand tundish.

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A dynamic model of alumina inclusion collision growth in the continuous caster

Cited by 14 publications

References 27 publications

Mathematical Model for Cluster-Inclusion’s Collision-Growth in Inclusion Cloud at Continuous Casting Mold

Mathematical Model for Cluster-Inclusion’s Collision-Growth in Inclusion Cloud at Continuous Casting Mold

Mathematical Model for Nucleation, Ostwald Ripening and Growth of Inclusion in Molten Steel

Performance Optimization of a Six-Strand Tundish

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