No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Turbulent Flow and Heat Transfer under Electromagnetic Force in Continuous Steel Casting Process
Abstract
In the continuous steel casting, an electromagnetic field, generated from the source current through the coil, is imposed to the system to control the fluid flow pattern and the steel solidification process. In this paper, we develop a mathematical model and numerical technique to study the coupled turbulent flow and heat transfer process in continuous steel casting under electromagnetic force. The complete set of field equations are established and solved numerically within the framework of the Galerkin finite element method. The influences of electromagnetic field on flow pattern of molten steel and temperature field as well as steel solidification are presented in the paper. It is found that the introduction of an electromagnetic field affects the flow field and temperature filed. In terms of the thickness of the solidified steel shell, the influence of electromagnetic field is very significant.
ResearchGate has not been able to resolve any citations for this publication.
In this paper, we develop a mathematical model to study the coupled turbulent two-fluid flow and heat transfer process in continuous steel casting. The complete set of field equations are established. The turbulence effect on a flow pattern of molten steel and lubricant oil, meniscus shape and temperature field as well as solidifi-cation are presented in the paper.
Centreline segregation in continuously cast billets has been decreased using thermal soft reduction (TSR) at the end of solidification in the caster. Full scale experiments have shown that it is possible to decrease the segregation ratio in steel with 0.51%C from 1·23 to 1·10. The segregation ratio is calculated as the mean value plus two standard deviations from 30 samples divided by the ladle composition. Multivariate data analysis (MDA) has been used to find the relationship between observed segregation and registered process variables. The MDA model's ability for explanation is sufficiently high to be used as a model for segregation prediction. The influence of different variables according to the MDA model agrees well with that determined by traditional methods of evaluation. The short range variation of segregation along the centreline can not be explained by the variables in the MDA model. Electromagnetic stirring in the mould alters the best position of the TSR cooling zone in the caster.
In order to develop the high frequency electromagnetic continuous casting technology for applying to steel, numerical analysis of the magnetic field and casting experiments using various parameters have been conducted. The method of using cold inserts was well established to lead to a reliable numerical model. According to this numerical model, it was predicted that while casting, the magnetic field would be concentrated on the common region occupied by the coil and the melt and further its maximum value would be seen just below the melt level, Casting experiments have been carried out using tin as a simulating material for steel, No oscillation mark was observed on the billets because the solidification started without hook. Under an optimum condition, billet surface roughness was improved to 1/10 of the conventionally cast billets. The surface quality of the billet was heavily dependent on the melt level, the casting speed, and the coil current. In case of the excessive coil current, wave marks other than the oscillation mark appeared on the billet surface. The billet with proper electromagnetic conditions showed a thinner solid shell at the early stage of the solidification and a thicker shell at the mold bottom in comparison with the conventional cast billet. It has been concluded that the Joule heat is a more dominant factor than the magnetic pressure in determining the surface quality of cast products in the high frequency electromagnetic continuous casting process.
A mathematical model has been developed to analyze the mass transfer in the sequence continuous casting process with the static magnetic field. The induced electromagnetic force is obtained by solving simultaneous equations for the momentum and the electromagnetic field. The application of static magnetic field affects the mass transfer by changing the flow field in the strand. The results of numerical calculation show a reasonable agreement of the calculated relative concentration of mixed steel with the measured one. The mixing of molten steel in the low part of the mold is significantly suppressed by the static magnetic field, and composition of new grade steel along the slab length in the transition zone increases significantly. The distribution of relative concentration averaged at cross section changes from parabolic to integral symbolic-like along the slab length, and the transition length is reduced about 50% by applying the magnetic field of 0.5T.
A numerical algorithm, based on the Galerkin finite element method and the enthalpy formulation, is developed for solving the coupled turbulent fluid flow and heat transfer problem in a domain with a moving phase-change boundary. The governing equations consist of the continuity equation, the Navier–Stokes equations, the energy equation and the modified K–ε equations. The formulation of the method is cast into the framework of the Bubnov–Galerkin finite element method. A numerical study shows that the developed numerical algorithm is stable and capable of capturing the rapid change of temperature and velocity near the phase-change boundary.
The high cost of empirical investigation in an operating steel plant makes it prudent to use all available tools in designing, troubleshooting and optimizing the process. Physical modeling, such as using water to simulate molten steel, enables significant insights into the flow behavior of liq- uid steel processes. The complexity of the continuous casting process and the phenomena which govern it, illustrated in Figs. 5.1 and 5.2, make it difficult to model. However, with the increasing
A single domain enthalpy control volume method is developed for solving the coupled fluid flow and heat transfer with solidification problem arising from the continuous casting process. The governing equations consist of the continuity equation, the Navier–Stokes equations and the convection–diffusion equation. The formulation of the method is cast into the framework of the Petrov–Galerkin finite element method with a step test function across the control volume and locally constant approximation to the fluxes of heat and fluid. The use of the step test function and the constant flux approximation leads to the derivation of the exponential interpolating functions for the velocity and temperature fields within each control volume. The exponential fitting makes it possible to capture the sharp boundary layers around the solidification front. The method is then applied to investigate the effect of various casting parameters on the solidification profile and flow pattern of fluids in the casting process.
In the continuous casting of steel, many problems, such as surface cracks in solidified steel and breakouts of molten steel from the bottom of moulds, frequently occur in practice. It is believed that the occurrence of these problems is directly related to the events in the mould, especially the transfer of heat from the strand surface across the lubricating mould powder and its interface with the mould wall to the mould cooling-water. However, as far as the authors are aware, there is no published work dealing with heat transfer across both the lubricating layer and the interface. Generally, a parameter representing the average overall heat transfer coefficient between the strand surface and the mould cooling-water is employed, instead of including the lubricating layer, the mould wall and their interface in the computation region. The existing treatment consequently does not permit analysis of some of the more important phenomena, such as the effect of mould powder properties and interface thermal contact resistance on the solidification of steel. In this paper, a novel finite element model is developed and the heat transfer across the interface between the lubricating layer and the mould wall is simulated by introducing a new type of element, referred to as the thermal contact element. The proposed model is used to investigate the effect of various casting parameters on heat transfer from the molten steel to the cooling-water. The results indicate that the thermal contact resistance between the mould wall and the mould powder is a key factor which dominates the thickness of the solidified steel shell and the heat extraction rate from the mould wall.
In the industrial process of continuous steel casting, flux added at the top of the casting mould melts and forms a lubricating layer in the gap between the steel and the oscillating mould walls. The flow of flux in the gap plays an essential role in smoothing the casting operation. The aim of the present work is to better understand the mechanics of flux flow, with an emphasis on such problems as how the flux actually moves down the mould, the physical parameters governing the consumption rate of the flux and the geometry of the lubricating layer. The problem considered is a coupled problem of liquid flow and multi-phase heat transfer. In the first part of the paper, the formation of the lubricating layer is analysed and a set of equations to describe the flux flow is derived. Then, based on an analysis of the heat transfer from the molten steel through the lubricating layer to the mould wall, a system of equations correlating the temperature field in the steel and flux with the geometry of the lubricating layer is derived. Subsequently, the equations for the flux flow are coupled with those arising from heat-transfer analysis and then a numerical scheme for the calculation of the consumption rate of flux, the geometry of the lubricating layer and the solidification surface of the steel is presented.
The continuous casting process employed in the steel industry is a many faceted big industrial problem which has given rise to many sub-problems. Here, we examine the problem involving the determination of the solid-liquid steel interface and we develop and extend a previously proposed model, which incorporates heat transfer through two layers of solid and liquid mould powder and the interface between the solid powder and the mould wall. The problem simplifies to the classical Stefan problem except that the condition on the boundary is nonlinear. Integral formulation procedures are used to establish the normalized pseudo steady state temperature as an upper bound to the normalized actual temperature. The pseudo steady state approximation yields an upper bound on the interface position, which an independent numerical enthalpy scheme confirms to be an extremely accurate approximation for the parameter values occurring in practice. The present work is important since it provides a simple method for the prediction of the solid-liquid steel interface and a bounding procedure which can be used to validate other estimates.
- B G Thomas
Thomas, B.G. 1990. Metallurgical Transactions B 21:387-400.
Calculation of the magnetic field due to the electromagnetic stirring of molten steel
- D R Jenkins
- De Hoog
Jenkins, D.R., and De Hoog, F.R. 1996. Calculation of the magnetic field due to the electromagnetic
stirring of molten steel. Numerical Methods in Engineering 96:332-336.
Mathematical analysis of the formation of oscillation marks in the continuous steel casting
- J M Hill
- Y H Wu
- B Wiwatanapataphee
Hill, J.M., Wu, Y.H., and Wiwatanapataphee, B. 1999. Mathematical analysis of the formation of
oscillation marks in the continuous steel casting. Engineering Mathematics 36:311-326.