Solidified Shell Thickness Research Articles

Control of Macrosegregation Behavior by Applying Final Electromagnetic Stirring for Continuously Cast High Carbon Steel Billet

Solidification behavior of continuously cast high carbon steel billets was investigated with an objective of producing high quality billets by determining the optimum final electromagnetic stirring (F-EMS) parameters. Characteristics of centerline segregation were analyzed for lots of billet samples collected from the plant through obtaining the carbon concentrations of drill chips, which were correlated with the operating parameters of the caster and stirrers, but a problem occurred that segregation control results of trial billets with the same casting and stirring parameters often have drastic fluctuations. An attempt was made to find out the induced reasons of this problem by measuring the electromagnetic torque, analyzing the secondary dendrite arm spacing (SDAS) and the corresponding cooling rate of the typical specimens, and observing the longitudinal profile of etched billet samples. Then a simple dynamic secondary cooling model was developed based on the solidified shell thickness control mode, by which the maximum carbon segregation index was reduced effectively, and thus the segregation fluctuation problem was basically solved. Finally, the most favourable stirring parameters were determined as the casting speed of 1.65 m/min, the liquid core thickness of 40 mm, stirring current of 360 A and frequency of 12 Hz.

Mold transient heat transfer behavior based on measurement and inverse analysis of slab continuous casting

In this present paper, a two-dimensional (2D) transient finite-difference model was developed. By solving appropriate inverse problem from the measured temperatures by thermocouples buried at various locations in the mold wall, the unknown heat flux between the strand and mold was identified. The temperature calculated in present model agreed well with actual plant data, and the results gave obvious non-uniform characteristics of heat flux and shell thickness, which could better reflect the real casting conditions of strand. The influence of casting speed on average heat flux and shell thickness at the mold outlet was calculated as follows: increase of casting speed caused increase of average heat flux and decrease of solidified shell thickness at the mold outlet. Furthermore, the relationship between average longitudinal heat flux and shell thickness of mold outlet was discussed, and it resulted in that the heat transfer from the strand to the mold remarkably determined the thickness and non-uniformity of the solidified shell.

Effect of Mold Coating on Shell Morphology in Solidification

The mold-shell interface plays a very important role during the earliest stages of metal casting processes. Heat is extracted from the molten metal through this interface resulting in the growth of the shell. Small spatial variations in heat extraction can lead to shell morphological instability where certain regions of the solidification front grow preferentially over others. This may cause cracks in the shell which can greatly reduce the integrity of the final cast product. Mold coating at the mold-shell interface is one of the most important factors controlling the heat transfer and, hence, it has very important role on the solidification rate and development of microstructure. In this paper, a linear perturbation method is used to solve a two-dimensional heat conduction problem in which a liquid, becomes solidified by heat transfer to a planar mold of finite thickness. The influence of physical parameters such as the coating material thickness, conductivity and thermal contact resistance on the growth of solidified shell thickness is investigated. The present work can form the thermal part of a subsequent investigation of related thermo elastic stress problems.

Effect of Mold Coating on Shell Morphology in Solidification

The mold-shell interface plays a very important role during the earliest stages of metal casting processes. Heat is extracted from the molten metal through this interface resulting in the growth of the shell. Small spatial variations in heat extraction can lead to shell morphological instability where certain regions of the solidification front grow preferentially over others. This may cause cracks in the shell which can greatly reduce the integrity of the final cast product. Mold coating at the mold-shell interface is one of the most important factors controlling the heat transfer and, hence, it has very important role on the solidification rate and development of microstructure. In this paper, a linear perturbation method is used to solve a two-dimensional heat conduction problem in which a liquid, becomes solidified by heat transfer to a planar mold of finite thickness. The influence of physical parameters such as the coating material thickness, conductivity and thermal contact resistance on the growth of solidified shell thickness is investigated. The present work can form the thermal part of a subsequent investigation of related thermo elastic stress problems.

Effects of Mold Surface Grooves on Uneven Thickness of Initial Solid Shell

Effects of Mold Surface Grooves on Uneven Thickness of Initial Solid Shell

A Mathematical Modeling of Heat Transfer in Continuous Casting Slab

A two-dimensional (2-D) heat transfer and solidification model has been established and applied to calculate the temperature distribution and solid shell thickness profile of a continuous casting slab in a steel plant. A finite difference method was used for the numerical simulation. For thermal analysis, the 2-D slice unsteady-state heat conduction equation with enthalpy convention was used. Meanwhile, non-linear material properties of specific heat and thermal conductivity as well as phase changes during solidification were considered in the model. The temperature distribution and solid shell thickness calculated by mathematical model agree with those predicted by industrial and experimental measurements. The model could also be used to predict the optimum process parameters on casting speed, heat removal rates and the water distribution of secondary cooling zone.

New analytical estimation of solid shell thickness at length of continuous casting mould

A new analytical formula for the estimation of solid shell thickness over the length of a continuous casting mould has been developed. The precision of this formula was experimentally compared to that of the classic analytical solution of Stefan and the results of finite difference (FDM) and finite point (FPM) models of the process. The results showed that the new approach estimated the thickness of the solid shell along the continuous mould with greater precision than the Stefan solution and that the precision of the new approach was comparable to those of the FDM and FPM approaches. Therefore, despite its simplicity, the equation has potential to be used as a quick, inexpensive and relatively accurate tool to estimate the thickness of the solid shell in continuous casting moulds and some other solidification processes.

Simulation of heat transfer in steel billets during continuous casting

This work is focused on the development of computational algorithms to create a simulator for solving the heat transfer during the continuous casting process of steel. The temperatures and the solid shell thickness profiles were calculated and displayed on the screen for a billet through a defined continuous casting plant (CCP). The algorithms developed to calculate billet temperatures, involve the solutions of the corresponding equations for the heat removal conditions such as radiation, forced convection, and conduction according to the billet position through the CCP. This is done by a simultaneous comparison with the kinematics model previously developed. A finite difference method known as Crank-Nicholson is applied to solve the two-dimensional computational array (2D model). Enthalpy (HI,J) and temperature (TI,J) in every node are updated at each step time. The routines to display the results have been developed using a graphical user interface (GUI) in the programming language C++. Finally, the results obtained are compared with those of industrial trials for the surface temperature of three steel casters with different plant configurations in different casting conditions.

Modeling on Dendrite Growth of Medium Carbon Steel during Continuous Casting

AbstractDendrite growth is an important phenomenon during steel solidification. In the current paper, a numerical method was used to analyse and calculate the dendrite tip radius, dendrite growth velocity, liquid concentration, temperature gradient, cooling rate, secondary dendrite arm spacing, and the dendrite tip temperature in front of the solid/liquid (S/L) interface for the solidification process of medium carbon steels during continuous casting. The current model was well validated by published models and measurement data. The results show that in the continuous casting process, the dendrite growth rate is dominated by the casting speed. Dendrite growth rate, liquid concentration at the S/L interface, temperature gradient and cooling rate decrease with proceeding solidification and solid shell thickness growth, while other parameters such as dendrite tip radius, secondary dendrite arm spacing, and dendrite tip temperature in front of the S/L interface become larger with solidification progress and solid shell thickness growth. Parametric investigations were carried out. The effects of the stability coefficient, temperature gradient and casting speed on the micro‐structural parameters were discussed. Under the same conditions, higher casting speed promotes coarser secondary dendrite arm spacing and enlarges the dendrite tip radius, while decreasing temperature gradient, reducing the dendrite growth rate and making the solute distribute more uniform.

Applying Finite Point Method in Solidification Modeling during Continuous Casting Process

In the present work a meshless method called Finite Point Method (FPM) is developed to simulate the solidification process of continuously cast steel bloom in both primary and secondary cooling region. The method is based on the use of a weighted least-square interpolation procedure. A transverse slice of bloom as it moves with casting speed is considered as computational domain and two dimensional heat transfer equation is solved in the computational domain. The present work is verified by the comparison of the surface temperature simulated by both FPM (as the present method) and finite volume method (FVM) as a usual method. Furthermore the solidified shell thickness simulated by the present FPM is compared with the solidified shell measured on a breakout bloom. In the secondary cooling region, the surface temperatures simulated by the FVM and measured by the thermovision machine are applied to validate the surface temperature simulated by the present FPM. The results reveal that the present FPM could be used successfully for the thermal analysis of the steel bloom to determine the temperature field and solidified shell thickness.

Solidification model for continuous steel casting with focus on flow modelling

In continuous casting of steel, the slow solidification results in a flat increase of the solidified shell thickness. Thus, the liquid core reaches up to 20 m into the strand. In most of the numerical flow simulations of continuous steel casting, the solidification process and its influence on the flow are completely neglected. Furthermore, only the upper part of the liquid core is simulated, which requires the introduction of an unphysical boundary condition at the lower bound of the simulated domain. On the other hand, the flow of the liquid steel in numerical solidification simulations is often not considered because of the complexity of solidification models. In this paper, a model that considers the shape of the solidification front in the flow simulation as well as the loss of material through the solidification front is presented. Therefore, the shell thickness has to be known a priori from theoretical or empirical results. Thus it is possible to model a great part of the liquid core inside the strand with respect to inclusion behaviour and variations of the solidified shell thickness due to the flow. Applications to intermediate, thick and thin slab casters as well as round bloom casters will be described.

Approximate analytical and numerical solutions for a two-dimensional Stefan problem

This paper proposes an approximate analytical and a numerical solution method to a two-dimensional heat conduction problem in which a liquid becomes solidified by heat transfer to a planar mold surface by using a linear perturbation method. It is assumed that the cooling rate is perturbed by a small spatially sinusoidal heat flux at the shell–mold interface. This leads to a corresponding undulation of the solidified shell thickness. Approximate analytical results are obtained for the solid/melt moving interface as a function of time and for the temperature field in the shell. The approximate analytical solution is compared with a numerical solution, and a very good agreement has been found. A limiting analytical solution in which diffusivity of the solidified shell material is assumed to be infinitely large is also obtained, and compared with the numerical predictions to establish the validity of the model and the numerical approach. It is demonstrated that solidified shell materials with higher thermal diffusivities may result in irregular growth of the shell thickness which, generally, causes cracking near the surface.

A New Semi-analytical Model for Prediction of the Strand Surface Temperature in the Continuous Casting of Steel in the Mold Region

In this research, a new semi-analytical model is presented for the strand surface temperature in the continuous casting of steel. Firstly with a dimensional analysis approach a general relation between the strand surface temperature and the other effective variables such as conductivity of the steel, pouring temperature, casting velocity, distance from the meniscus, volume rate of cooling water, solidus temperature and heat flux density at the meniscus is deduced. The constants appeared as coefficients or powers of variables in presented relation were computed by a numerical simulation of continuous casting for a breakout bloom. The resulted semi-analytical model for strand surface temperature was extended to predict the solidified shell thickness. The resulted semi-analytical model was validated with comparison to experimental, analytical and numerical results of slab, billet and bloom and good agreement was seen. The new presented model at this research is in versus of controllable parameters and specifications of the mold and it can be used for design of a process control system for continuous casting of slab, billet and bloom.

Approximate analytical solution of a two-dimensional heat conduction problem with phase-change on a sinusoidal mold

A two-dimensional heat conduction problem in which a liquid becomes solidified by heat transfer to a sinusoidal mold of finite thickness is solved by using a linear perturbation method. The liquid perfectly wets the sinusoidal mold surface prior to the beginning of solidification. This leads to a corresponding undulation of the solidified shell thickness. Both surfaces of the mold follow a sinusoidal lay for which the ratio of the amplitude to the wavelength, or aspect ratio, is much less than one. This makes the aspect ratio a convenient perturbation parameter for the problem since it is indicative of the spatial variation in the surfaces. Temperature at the outer surface of the mold is assumed to be constant. Results are obtained for the solid/melt moving interface as a function of time and for the temperature distributions in the shell and mold. The inverse problem, in which the solid/melt boundary is prescribed and the mold outer surface temperature determined, is also briefly discussed. The present work can form the thermal part of a subsequent investigation of related thermoelastic stress problems.

Thermal deflection analysis of the solidified shell in continuous casting of slab

The thermal deformation problem in the continuous casting of a slab subjected to thermal loading because of the temperature gradient along the solidified shell thickness is investigated. On the basis of the reciprocal theorem of work or Betti-Maxwell’s reciprocal theorem and the superposition principle, the deflection expressions for a rectangular plate with the two opposite edges simply supported, and the other two opposite edges clamped under the action of the uniformly distributed load and nonuniform temperature field are derived respectively. The meaning of each term in the deflection expression obtained by the reciprocal theorem of work is explained. Then the practical example is given to calculate the thermal deformation and the bulging deformation of the solidified shell under three tension speeds. This research is useful for analyzing the bulging deformation in the continuous casting of a slab under the static pressure of the molten steel and the thermal loading because of the temperature gradient along the solidified shell thickness.

Sinusoidal perturbation solution for solidification of pure materials on a planar mold of finite thickness

A linear perturbation method is used to solve two-dimensional heat conduction problem in which a liquid becomes solidified by heat transfer to a plane mold of finite thickness. Heat flux drawn from the lower surface of the mold is approximately uniform, but contains a small sinusoidal perturbation in one space dimension. Numerical results are obtained for the consequent sinusoidal perturbation in the solid/melt boundary as a function of time. Analytical results are obtained for the limiting case in which diffusivities of the solidified shell and the mold materials are infinitely large. These results are then compared with the numerical predictions to establish the validity of the model and the numerical approach. The results document the effects of both solidified shell and the mold material diffusivities on the growth of a perturbation in a nominally plane solidification front. It is demonstrated that the magnitude of this perturbation increases with the diffusivity of the mold, and this effect of mold diffusivity is overweighed by the diffusivity of the casting material. The influence of other process parameters such as the mold thickness, thermal contact resistance at the mold–shell interface, and thermal conductivity ratio on the growth of solidified shell thickness is also investigated in detail.

Perturbation solution for solidification of pure metals on a sinusoidal mold surface

A linear perturbation method is used to solve two-dimensional heat conduction problem in which a liquid, becomes solidified by heat transfer to a sinusoidal mold of finite thickness. The finite difference method is used to discretize the governing equations. The molten metal perfectly wets the mold surface prior to the beginning of solidification, and this leads to a corresponding undulation of the metal shell thickness. The influence of physical parameters such as the thermal capacities of shell and mold materials, and mold surface wavelength on the growth of solidified shell thickness is investigated. Analytical results are obtained for the limiting case in which diffusivities of the solidified shell and the mold materials are infinitely large, and compared with the numerical predictions to establish the validity of the model and the numerical approach.

Effect of complex electromagnetic stirring on inner quality of high carbon steel bloom

To obtain a better internal quality of high carbon steel bloom, complex electromagnetic stirring combined M-EMS with F-EMS was designed. In order to find a proper location for positioning the F-EMS stirrer, the solid shell thickness profile of a continuous casting bloom was computed. It was found that the F-EMS stirrer should be placed 11.39 m below the meniscus. Based on the finding, an industrial plant trial was conducted on the operating bloom casting machine at Baotou Iron and Steel (Group) Corp. The results show that the problem of inner porosity and composition segregation can be solved with the complex electromagnetic stirring technique. The ratio and index of central segregation and porosity can be reduced significantly. Therefore, good casting technique, optimum mould design and final electromagnetic stirring are all important for improving the inner quality of high carbon steel.

Computational modeling and control system of continuous casting process

A finite difference model was developed and applied to calculate the temperature distribution and solid shell thickness profile of continuous cast in a steel plant and to control the process of continuous casting. In the developed model, the optimization module of the water distribution of secondary cooling zone was established according to the metallurgical criterion for billet and target temperature controlling principle. The quantitative relation expressions of casting speed and water amount can be regressed by the result data. Meanwhile, the non-linear material properties of specific heat and thermal conductivity as well as phase changes during solidification were considered in the model. The calculated results of the model were in good accordance with measured data in the steel plant. Finally, a continuous casting and control system was developed based on the model. The relations between technology parameters including casting speed, cooling intensity, superheat of melt, and the casting process were analyzed with the system. The system could also be used to predict the optimum process parameters and the water distribution of secondary cooling zone on the new steel grade continuous casting.

THERMAL DEFLECTION ANALYSIS OF THE SOLIDIFIED SHELL IN THE CONTINUOUS CASTING OF SLAB

Thermal deformation problem in the continuous casting of slab subjected to the thermal loading due to the temperature gradient along the solidified shell thickness is investigated. Based on the reciprocal theorem of work or Betti-Maxwell's reciprocal theorem and the superposition principle, the deflection expressions for a rectangular plate with two opposite edges simply supported and the other two opposite edges clamped under the action of the uniformly distributed load and non-uniform temperature field are derived respectively, and the meaning of each term in the deflection expression obtained by the reciprocal theorem of work is explained. Then the practical example is given to calculate the thermal deformation and the bulging deformation of the solidified shell under three tension speeds. Above research is useful for analyzing the bulging deformation in the continuous casting of slab under the static pressure of molten steel and the thermal loading due to the temperature gradient along the solidified shell thickness.