Intermixing model of continuous casting during a grade transition

Huang, Xiaofeng; Thomas, Brian G.

doi:10.1007/bf02915660

Cited by 44 publications

(36 citation statements)

References 4 publications

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“…In order to predict the final composition distribution within the final product, a further model must account for the cessation of intermixing after the shell has solidified. [133][134][135][136] Figure 11 shows example composition distributions in a continuous cast slab calculated using such a model. 133,134) To ensure accuracy, extensive verification and calibration were undertaken for each submodel.…”

Section: Solute Transport Phenomenamentioning

confidence: 99%

Mathematical Modeling of Iron and Steel Making Processes. Mathematical Modeling of Fluid Flow in Continuous Casting.

2001

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Fluid flow is very important to quality in the continuous casting of steel. With the high cost of empirical investigation and the increasing power of computer hardware and software, mathematical modeling is becoming an important tool to understand fluid flow phenomena. This paper reviews recent developments in modeling phenomena related to fluid flow in the continuous casting mold region, and the resulting implications for improving the process. These phenomena include turbulent flow in the nozzle and mold, the transport of bubbles and inclusion particles, multi-phase flow phenomena, the effect of electromagnetic forces, heat transfer, interfacial phenomena and interactions between the steel surface and the slag layers, the transport of solute elements and segregation. The work summarized in this paper can help to provide direction for further modeling investigation of the continuous casting mold, and to improve understanding of this important process.KEY WORDS: mathematical modeling; computational simulation; review; continuous casting; nozzles; molds; multiphase; turbulent; fluid flow; electromagnetic; coupled solidification; inclusion entrapment; segregation.steel. This paper will review recent developments in modeling each of the phenomena above, which are related to fluid flow in the continuous casting mold, and the resulting implications for improving the continuous casting process. Fluid Flow ModelingA typical three dimensional fluid flow model solves the continuity equation and Navier Stokes equations for incompressible Newtonian fluids, which are based on conserving mass (one equation) and momentum (three equations) at every point in a computational domain. 17,18) The solution of these equations, given elsewhere in this issue, 19) yields the pressure and velocity components at every point in the domain. At the high flow rates involved in this process, these models must incorporate turbulent fluid flow. Many different turbulence models have been employed by different researchers for fluid flow in continuous casting, such as effective viscosity models 20,21) (for the cylindrical mold and straight nozzle), one equation turbulence models (turbulent energy plus a given length-scale), 22) two-equation turbulence models such as the K-e Model, 19,23) LES (Large Eddy Simulation), [24][25][26][27][28] possibly with a SGS (sub-grid scale) model, 29,30) and DNS (Direction Numerical Simulation). 19)Among these models, direct numerical simulation is the simplest yet most computationally-demanding method. DNS uses a fine enough grid (mesh), to capture all of the turbulent eddies and their motion with time. To achieve more computationally-efficient results, turbulence is usually modeled on a courser grid using a time-averaged approximation, such as the popular K-e model, 23) which averages out the effect of turbulence using an increased effective viscosity field, m eff . This approach requires solving two additional partial differential equations for the transport of turbulent kinetic energy and its dissipation rate.19...

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Section: Solute Transport Phenomenamentioning

confidence: 99%

Mathematical Modeling of Iron and Steel Making Processes. Mathematical Modeling of Fluid Flow in Continuous Casting.

2001

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“…Turbulent flow within the liquid pool may bring mixed molten steel far below the position of the meniscus. Huang and Thomas 10,11) have simulated the composition difference between the center and the surface in a section of the mixed zone according to the casting speed. They found that a slower casting speed greatly reduces the extent of mixing in the strand.…”

Section: Extending Cho and Kim's Tundish Model To The Strandmentioning

confidence: 99%

“…Pioneers in the area of developing an efficient intermixing model to predict the mixed region during a grade transition, Huang and Thomas 10,11) have developed a model for predicting the intermixed region within several seconds as opposed to the conventional methods that used to take several days or even weeks. Their model is designed to consider the mixing within both the tundish and the strand.…”

Section: Introductionmentioning

confidence: 99%

A Practical Model for Predicting Intermixed Zone During Grade Transition

Cho

Kim

2010

ISIJ Int.

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“…Many studies on the casting transition process have been reported. Huang and Thomas 30,31) developed a mathematical model, using a three-dimensional fluid flow model and one-dimensional mixing at various places in the tundish and strand. Cho and Kim 32) investigated the steel grade transition in a tundish using both water model and numerical simulation.…”

Section: Steel Grade Change Processmentioning

confidence: 99%

Transient Fluid Flow Phenomena during Continuous Casting: Part II—Cast Speed Change, Temperature Fluctuation, and Steel Grade Mixing

Wang

Zhang

2010

ISIJ Int.

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where H is enthalpy or heat content in J/kg, k is thermal conductivity in W/m · K, and T is the temperature in K.Particles were modeled using both Eulerian and Lagrangian approaches. The Eularian approach considers them as continuous phase, whereas the Lagrangian approach treats them as a discrete phase.16) Due to the low volume fraction of particles, the Lagrangian approach is always used to calculate the trajectory of particles by considering the force balance acting on them 17) ......... (2) where u Pi is particle velocity at direction i in m/s, t is time in seconds, C D is a dimensionless drag coefficient, Re P is a particle Reynolds number, d P is particle diameter in m, r P is inclusion density in kg/cm 3 . The first term here is the drag force per unit of particle mass, the second term is gravitational force, the third term is the virtual mass force accelerating the fluid surrounding the particle, 18) and the fourth term is the force stemming from the pressure gradient in the fluid.To incorporate the stochastic effect of turbulent fluctuations on particle motion, the random walk model 19) was used. In this model, particle velocity fluctuations are based on a Gaussian-distributed random number chosen according to the kinetic energy of the local turbulence. The random number is changed, to produce a new instantaneous velocity fluctuation at a frequency equal to the characteristic lifetime of the eddy. (4) where ū is the mean fluid phase velocity in m/s, uЈ is random velocity fluctuation in m/s; x is a random number and k is the local level of turbulent kinetic energy in m 2 /s 2 . The application of Lagrangian approach in discrete phase model requires the particle flow must be dilute (volume fraction Ͻ12 %). Generally, inclusions in molten steel only take a very small volume fraction. If the total oxygen in the molten steel is 30 ppm, and if it is assumed that all of the inclusions are with a density of 3 500 kg/m 3 , then the volume fraction of inclusions in the molten steel is approximately 0.013 %. In our current study, assuming there are 10 000 particles with diameter of 50 mm. where p(x, y) is the pressure at the top surface at location (x, y), p mean is the mean value of the pressure across the entire top surface, r l is the density of the molten steel, r top is the density of the top slag, and g is the gravitational acceleration rate.The dimensions, parameters, and boundary conditions of the slab mold were listed in Table 1. A half mold was simulated. During the iteration, convergence was assumed if all the normalized unscaled residuals were smaller than 10 Ϫ6 . More than 10 000 inclusions with the diameter of 15 mm and 50 mm were injected into the slab mold through the inlet respectively. As boundary conditions for the particle motion, particles escaped from the top surface and the open bottom, and were reflected at the symmetry plane. For the entrapment of the inclusions on the wide or narrow faces, it is very complex; it has received well-deserved attention in recent work. 23,24) There are two cr...

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Intermixing model of continuous casting during a grade transition

Cited by 44 publications

References 4 publications

Mathematical Modeling of Iron and Steel Making Processes. Mathematical Modeling of Fluid Flow in Continuous Casting.

Mathematical Modeling of Iron and Steel Making Processes. Mathematical Modeling of Fluid Flow in Continuous Casting.

A Practical Model for Predicting Intermixed Zone During Grade Transition

Transient Fluid Flow Phenomena during Continuous Casting: Part II—Cast Speed Change, Temperature Fluctuation, and Steel Grade Mixing

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