Simulation Of Continuous Casting Research Articles

Optimal control of three-dimensional unsteady partial differential equations with convection term in continuous casting

In this paper, we investigate an optimal control problem (OCP) for three-dimensional (3D) unsteady partial differential equations with convection term (UPDECT), extensively applied to the solidification process of billets. Firstly, we introduce the mathematical model of OCP and adopt a life cycle model method (LCMM) to numerically solve the 3D UPDECT. Secondly, the Lipschitz continuity of the cost function gradient is proved using the adjoint approach as a numerical method for designing optimal control systems. The cost function gradient of OCP for 3D UPDECT is analyzed based on a Hamiltonian costate system. Thirdly, we propose a modified trinomial conjugate gradient method (MTCGM) to solve the OCP for 3D UPDECT and prove the global convergence of MTCGM. Finally, the MTCGM is applied to the experimental simulation of continuous casting. According to experiment results, the optimizer based on MTCGM can significantly accelerate the convergence speed and reduce the iterative numbers, and the MTCGM provides a more stable temperature control effect.

Simulation of BB-2 beam billet conti-nuous casting for production of large-sized I-beams

In connection with expansion of construction sector, it is planned to develop 80‒90‒100 I-beams. For these I-beams, universal section of continuously cast billet BB-2 (1050×450×120) was developed. The purpose of this work was to check casting parameters of given billet in a simulation model, using LVMFlow software, to confirm analytical calculations. Following parameters were chosen as parameters to be evaluated: geometric shape of the cast billet, temperature and dynamic parameters of casting. For maximum reliability, boundary conditions were set similar to real parameters of the CCM-3 at EVRAZ NTMK JSC, however, as assumptions, the calculation was carried out only in zone of direct contact with mold sleeve, and plane deformation condition was set along casting. Simulation results showed possibility of using LVMFlow to simulate the beam blanks casting processes with high degree of convergence. Casting BB-2 billet is technically possible in the conditions of continuous caster No. 3 at JSC EVRAZ NTMK, when the mold is replaced. Hydrodynamic pressure is created only on walls of crystallizer; there is vacuum on remaining surfaces due to lack of crystallizer walls narrowing sleeve towards cooling. Crystallization occurs most slowly along the interface between the wall and the BB flanges, however, there are no defects in the form of splashes, due to the low hydrodynamic pressure in these zones

Simulation of BB-2 beam billet conti-nuous casting for production of large-sized I-beams

In connection with expansion of construction sector, it is planned to develop 80‒90‒100 I-beams. For these I-beams, universal section of continuously cast billet BB-2 (1050×450×120) was developed. The purpose of this work was to check casting parameters of given billet in a simulation model, using LVMFlow software, to confirm analytical calculations. Following parameters were chosen as parameters to be evaluated: geometric shape of the cast billet, temperature and dynamic parameters of casting. For maximum reliability, boundary conditions were set similar to real parameters of the CCM-3 at EVRAZ NTMK JSC, however, as assumptions, the calculation was carried out only in zone of direct contact with mold sleeve, and plane deformation condition was set along casting. Simulation results showed possibility of using LVMFlow to simulate the beam blanks casting processes with high degree of convergence. Casting BB-2 billet is technically possible in the conditions of continuous caster No. 3 at JSC EVRAZ NTMK, when the mold is replaced. Hydrodynamic pressure is created only on walls of crystallizer; there is vacuum on remaining surfaces due to lack of crystallizer walls narrowing sleeve towards cooling. Crystallization occurs most slowly along the interface between the wall and the BB flanges, however, there are no defects in the form of splashes, due to the low hydrodynamic pressure in these zones

Influence of the Slag Rim on the Heat Transfer Behavior of a Mold

To explore the influence of the slag rim on the heat transfer behavior of a mold, a slag rim was extracted from a stainless steel production factory for high-temperature continuous casting simulation experiments. The 2DIHCP (Two-Dimensional Inverse Heat Conduction Problem) two-dimensional inverse problem calculation model was used to analyze the heat transfer characteristics in the mold, and the temperature and heat flux distribution of the hot surface of the mold copper wall under different working conditions were investigated. The results showed that under a casting speed of 0.5 Â m/min, vibration frequency of 2 Hz, and amplitude of 10 mm, the seepage flow of the mold flux was 9.314 and 6.326 g with and without the slag rim, respectively, the thickness of the slag film was 2.1 and 1.3 mm, respectively, the temperature of the mold hot surface was 118.24 and 134.83°C, respectively, and the maximum heat flux density of the mold was 0.98 and 1.95 MW/m2, respectively. Through data comparison, when there is a slag rim, the amount of slag infiltration decreased by 32%, the thickness of the slag film decreased by 38%, the temperature of the hot surface of the mold increased by 14%, the heat flux density increased by 99%, and the internal crystal morphology of the slag film was complete. This indicates that the slag rim affects the heat transfer behavior in the mold by restricting the inflow of the mold flux and affecting the formation of the slag film.

Process simulation of Ohno continuous casting for single crystal copper prepared from scrap copper in waste printed circuit boards

How to realize the high value-added utilization of scrap copper from e-waste is a meaningful topic. In the study, an Ohno Continuous Casting (OCC) process is an existing method you applied to purify the copper. Based onthe model of diffusion-controlled grain growth kinetics, the redistribution of impurity of tin in the scrap copper were studied under the different continuous casting speed and mold temperature. On the centerline, macrosegregation in the axial direction of the tin was more obvious with the decrease of continuous casting speed. The small continuous casting rate was beneficial to the segregation and enrichment of tin. The axial segregation gradually decreased with the increase of the mold temperature. The flattening of the liquid–solid interface resulted in a weakening of the solute enrichment at the root of the interface with the increase of temperature. Morphology, electron backscattered diffraction (EBSD) analysis showed the structure of single crystal copper. The range of resistance of single crystal copper was from 5 × 10-6 to 3 × 10-5 Ω m. Obviously, the resistance of the single crystal copper was significantly smaller than that of ordinary copper wire (9.0 × 10-3 Ω m). This study provided a key theoretical and practical basis for the high value-added reuse of copper in e-waste.

CURRENT PROBLEMS AND PERSPECTIVES OF COMPUTER SIMULATION OF CONTINUOUS STEEL CASTING

Nowadays we can see increase in using of engineering analysis systems in the field of continuous steel casting simulation due to their high accuracy and convergence with industrial experiments results. Such powerful systems as «ANSYS» and «ProCast» allows solving gas-, hydrodynamic and thermal problems, the parallel interaction of which constitutes the essence of most metallurgical processes. Group of authors from the LSTU Chair “Metallurgical technology” have successfully carried out computer experiments in tundish and continuous casting mold processes simulation. The experiments were aimed at first, on studying of further improving in liquid steel flow modifiers (partitions, turbo-stops, thresholds) design, at second, on influence of argon blowing regime on liquid steel flow parameters in the 50-ton tundish workspace, and, at third, on influence of submerged nozzles design on the liquid steel flow in crystallizer, assuming deterministic-dynamic operation mode. The results of calculations are velocity fields of liquid steel flow and flow temperatures fields in tundish and crystallizer, as well as temperature fields in the tundish refractory lining. An equation of primary flow average velocity change on exit from submerged nozzle was also formulated. These preliminary results allow us to assess the velocity changes and direction of the melt flow and formation of volumes with different melt temperatures when using flow modifiers in the ladle, including using of “argon curtain” in the casting chamber. Obtained data on melt flow motion and on location of erosion spots in crystallizing «crust», also on the presence of temperature gradient zones in various regions of crystallizer workspace may be useful to practice engineers engaged in choice of crystallizer submerged nozzle design. Effective control of melt flow in tundish and in crystallizer allows significant improvements in continuous cast slabs and rolled products quality in context of reducing metal products rejection due to defects associated with slag or nonmetallic inclusions presence and due to cracks formed as the result of insufficient thickness of crystallized «crust».

Composition, Microstructure, Phase Constitution and Fundamental Physicochemical Properties of Low-Melting-Point Multi-Component Eutectic Alloys

Low-melting-point alloys have an extensive applications in the fields of materials processing, phase change energy storage, electronic and electrical automatic control, continuous casting simulation, welding, etc. Specifically, the eutectic compositions make up a large number of low-melting-point alloys that are exploited because of their desirable features like single melting peaks, excellent operational reliability, and casting fluidity. However, the fundamental physicochemical properties from the current available literature on low-melting-point multi-component eutectic alloys (LMP-MCEAs) are rather rare and lowly accurate, including the exact melting temperatures and compositions, constituent phases, microstructures and morphologies, melting enthalpies, specific heats, densities, and so on. This lack of information seriously limits the development and application of low-melting-point multi-component eutectic alloys. In this paper, the low-melting-point multi-component eutectic alloys composed of Bi, Cd, Sn, Pb, and In elements synthesized by high vacuum induction melting and fundamental data were investigated by scanning electron microscopy (SEM), energy dispersive spectrometry (EDS), X-ray diffraction (XRD), differential scanning calorimetry (DSC), and density analysis instrument. Most of the LMP-MCEAs with complex eutectic morphology structures and XRD diffraction patterns could be explained with the fact that they were three-phase eutectic alloys with mixed growth way. Generally, LMP-MCEAs present an extremely low melting point between 48.3 and 124 °C and high density between 8 and 10 g/cm3.

Simulation of slab formation in a continuous-casting machine

A discrete analog of the differential heat-conduction equation permits the use of nonuniform calculation grids in the simulation of continuous casting. That allows the distribution of the temperature gradients in the model to be taken into account, with corresponding increase in the accuracy of the approximation and the results. A mathematical model is developed for the solidification and shrinkage of continuous-cast slab in the mold. The adoption of a nonuniform grid permits the use of elements measuring 1–2 mm in the simulation. This model is used to study the distortion of the slab cross section at the mold walls. Calculation of the geometric profile permits refinement of the thermal and mechanical interaction of the solidifying shell and the mold walls and determination of the optimal mold taper so as to reduce the risk of surface and subsurface cracking in the slabs.

DEVELOPMENT OF THE STUDY OF MECHANISM OF “HEALING” DEFECTS OF CONTINUOUS CAST BILLET AXIAL ZONE ON A PHYSICAL MODEL

The concept of metal construction minimization of finished products requires an increasing set of requirements for steels as structural materials. In this context, issues related to the study of the continuous casting defects macrostructure behavior (shrinkage, gas holes, axial porosity) during deformation are very actual. This work presents further development of metal forming processes research methods with layered physical models use. Layered models usage in conjunction with the proposed method of defects application on the surface of n -th layer and processing information method concerning the nature of its forming allows to evaluate the rate deformation influence during the process of “healing”. The initial adaptation of the proposed method applying to the conditions of the deformation process simulation of continuous casting in the first three rectangular breakdown stand calibers of linear mill 500/370 of PJSC “DMPZ” has been performed. Obtained experimental data allow to clarify the existing mechanism of “healing” of axial discontinuities defects in metal depending on the overall elongation and schemes of deformation application.

Continuous Casting of a Multi-Crystalline Silicon Billet

In order to improve the production efficiency, numerical simulation and experiments of continuous casting of a multi-crystalline silicon (mc-silicon) billet were carried out. Modeling works were done firstly to optimize casting recipe and predict billet cooling behaviors, a three-dimensional finite element model for the simulation of thermal field and fluid flow was built. The continuous casting of cylindrical silicon billet was studied considering different casting parameters such as withdrawal speed and heat transfer ability of mold. The simulation results indicate that lower casting speed and lower heat transfer coefficient of mold are beneficial to acquire better morphology. Experimental works were practiced lying on the modeling results, using the self-designed mc-silicon continuous casting apparatus, mc-silicon billet with a diameter of 100 mm was obtained.

Improving Steel Processing Through Thermo-Mechanical Simulation Studies

Thermo-mechanical simulation studies can be effectively utilized for optimization of processing parameters apart from development of new alloys, quality/yield improvement and material characterization. Physical simulation, being very close to the real world process, can be very helpful in near exact reproduction of the process, and in turn, better results. Thermo-mechanical simulation studies using Gleeble System found extensive applications in steel research and its processing. It can help in careful design of alloy chemistry, proper continuous casting operation to produce defect-free casting, and optimization of hot rolling and post-cooling parameters to produce the desired microstructure and annealing process after cold rolling to achieve the desired microstructure and properties, welding for easy fabrication, etc. Each of these steps needs to be fine-tuned and optimized to achieve the maximum benefit towards reduction in alloy additions, as well as quality and yield improvement during steel processing. A number of studies like continuous casting simulation for production of Cr-alloyed rail steel, hot deformation simulation and phase transformation behavior to optimize hot rolling of difficult to process high boron steel, and hot deformation simulation to bring down the rolling load and annealing simulation to achieve the desired hardness in low nickel stainless steel, etc. undertaken, helped to improve the processing of these steels. Details of these studies, results obtained, and the way to improve processing were discussed.

Numerical simulation of continuous casting of steel alloy for different cooling ambiences and casting speeds using immersed boundary method

This article demonstrates implementation of immersed boundary method in continuous casting simulation involving boundary movement. In this methodology, the immersed boundary method is coupled with the second-order accurate finite difference solution of unsteady three-dimensional heat conduction equation. The moving molten metal front is modelled using the immersed boundary method in a Cartesian mesh framework that provides simplicity in its implementation and reduces the computational time as compared to the adaptive mesh solutions. A parallel programming paradigm using message passing interface has been implemented to obtain enhanced computational efficiency. This study has focused on capturing moving boundary during continuous casting and predicts the temperature distribution and shell thickness under different cooling ambiences and casting function. Good agreements with published data and correlations are obtained through numerical analysis. Mould-region shell thickness agrees well with Chipman–Fondersmith correlations. A new correlation has been further proposed for the delay constant at different heat extraction rates. The effects of key parameters like casting speed, convection and radiation from the continuous casting are also quantified in attempt to avail the data for optimal design of continuous caster.

Application of Thermal Analysis Tests Results in the Numerical Simulations of Continuous Casting Process

Abstract Measurement of thermophysical properties of steel is possible by using different thermal analysis techniques. In the field of metallurgy the most relevant methods are Differential Thermal Analysis (DTA) and Differential Scanning Calorimetry (DSC). The paper presents the results of thermophysical properties which are necessary to carry out numerical simulation of continuous casting of steel. The study was performed for two steel grades S320GD and S235JR. The main aim of the research was to determine the dependence of specific heat on temperature. On the basis of obtained results the thermal effects of phase transformations and characteristic transition temperatures were also identified. Both the specific heat of steel and thermal effects of phase transformations are included in the Fourier-Kirchhoff equation, as the material properties necessary to obtain the numerical solution. The paper presents the research methodology, analysis of results and method of determining the specific heat of steel based on the results of DSC analysis.

Simulation of low carbon steel solidification and mold flux crystallization in continuous casting using a multi-mold simulator

An inverted water-cooled multi-mold continuous casting simulator was used to investigate initial solidification of low-carbon steels and crystallization of mold flux. Embedded mold thermocouples showed characteristic temperature profiles dependent on parameters including casting speed, oscillation frequency, and stroke. Higher maximum temperatures for thermocouples at higher casting speeds, higher frequencies, and lower stroke lengths were observed. The surface of the as-cast steel strips showed oscillation marks similar to those of industrially cast slabs and higher casting speeds resulted in shallower oscillation marks. The measured pitch agreed well with the theoretical pitch suggesting the multi-mold simulator to be a cost-effective alternative to pursue fundamental studies on initial solidification in the mold. Analysis of the mold flux taken between the copper mold and solidified steel shell showed highly dendritic uni-directional crystallization occurring within the flux film suggesting that the heat transfer direction is dominantly horizontal towards the water-cooled copper mold. In addition, the solidified flux located at the upper to lower part of the mold suggested morphological differences in the size and shape of the crystalline phases indicating that crystallization ratio can increase depending upon the retention in the mold and subsequently decrease radiative heat transfer as the flux traverses down the mold.

High Manganese TWIP Steel - Technological Plasticity and Selected Properties

Over the last few years national as well as international research centres conducting research on the development of high-manganese steels. Some of these materials belong to the group of AHS steels, are characterized by the twinning induced plasticity (TWIP) effect which is a new type of steel possessing together with high strength a great plastic elongation, and an ideal uniform work hardening behavior. It is therefore a good candidate for deep drawing applications in the automobile and railway industry. The article presents the results of researches of TWIP-type austenitic steel in case of determination some of the more important parameters for continuous casting simulation process and the results of tests regarding the influence of strain parameters on sensitivity to plastic forming and deformation strengthening. It has been shown that the researched steel reaches a zero plasticity temperature at 1250°C. The deformation tests indicate its good workability of hot processing within the temperature range of 1100 ÷ 800°C. The relation between yield stress and strain during the hot deformation is typical for the presence of dynamic recrystallization processes. The tested steel has good formability and high mechanical properties, especially when being deformed at a high strain rate. Analysis of the substructure of researched steel was indicate presence of mechanical twinning.

New Continuous Casting and Slab Tracking Simulators for Steel Industry

Research group of Metallurgy at Aalto University has been developing simulation models and tools for continuous casting since from the early 80s. The main models developed are the heat transfer model, DYN3D, and the solidification and microstructure model IDS. The models have been further developed and integrated to a continuous casting simulator and to a slab simulator. The continuous casting simulator calculates the important phenomena taking place in the strand during casting and the slab simulator calculates the phenomena taking place in the slabs when they are transferred from caster to reheating furnace. The numerical solution algorithms in the simulators are so fast that they can be used in on-line applications. The simulators have today many new options as hydrogen removal and quality prediction modules. In this paper, the simulators and their modules are presented.

Effect of Forced Convection on Grain Refinement of S32205 Duplex Stainless Steel

The effects of forced convection on grain refinement of S32205 duplex stainless steel (DSS) were investigated using a continuous casting simulation setup. The sample, which was called slab simulating unit here, was solidified in the continuous casting simulation setup, whose temperature was controlled according to the cooling curve of a DSS slab center, with the bottom cooled by running water to simulate the solidification process of slab. Forced convection was generated by square-wave mechanical stirring. The CET (columnar to equiaxed transition) was gradually promoted by forced convection when the rotation of the crucible speeded up, the microstructure was refined significantly. The average columnar zone length was reduced from 8.2 cm to 4.8 cm, the equiaxed grain average size decreased from 9.5 mm to 1.7 mm, and the microstructure was refined from Widmänstatten plates to island-shaped pieces.

Modeling and Control of Temperature Field of the Secondary Cooling Zone in Continuous Casting of Steel as Distributed Parameter System

This paper presents some results on modeling and control of temperature field in a steel continuous casting, demonstrating the possibilities of using engineering methods for control of distributed parameter systems along with virtual engineering environments. A system to be controlled is considered as lumped-input and distributed-parameter-output system. Dynamics and control synthesis are decomposed into time and space components, respectively. Demonstrations of PID and adaptive model-based predictive control are being presented via cosimulation, utilizing virtual software environments for continuous casting simulation and distributed parameter control systems, respectively.

Application of particle method to the casting process simulation

Casting processes involve many significant phenomena such as fluid flow, solidification, and deformation, and it is known that casting defects are strongly influenced by the phenomena. However the phenomena complexly interacts each other and it is difficult to observe them directly because the temperature of the melt and other apparatus components are quite high, and they are generally opaque; therefore, a computer simulation is expected to serve a lot of benefits to consider what happens in the processes. Recently, a particle method, which is one of fully Lagrangian methods, has attracted considerable attention. The particle methods based on Lagrangian methods involving no calculation lattice have been developed rapidly because of their applicability to multi-physics problems. In this study, we combined the fluid flow, heat transfer and solidification simulation programs, and tried to simulate various casting processes such as continuous casting, centrifugal casting and ingot making. As a result of continuous casting simulation, the powder flow could be calculated as well as the melt flow, and the subsequent shape of interface between the melt and the powder was calculated. In the centrifugal casting simulation, the mold was smoothly modeled along the shape of the real mold, and the fluid flow and the rotating mold are simulated directly. As a result, the flow of the melt dragged by the rotating mold was calculated well. The eccentric rotation and the influence of Coriolis force were also reproduced directly and naturally. For ingot making simulation, a shrinkage formation behavior was calculated and the shape of the shrinkage agreed well with the experimental result.

Simulation of continuous casting of steel by a meshless technique

A recently developed local radial basis function collocation method is used for the solution of the transient convective–diffusive heat transport in continuous casting of steel. The solution of the thermal field with moving boundaries due to phase-change and the growing computational domain is based on the mixture continuum formulation. The growth of the domain and the movement of the starting block are described by activation of additional nodes and by the movement of the boundary nodes through the computational domain, respectively. Time-stepping is performed in an explicit way by a simple characteristic procedure. A two-dimensional transient test case solution is shown at different times and its accuracy is verified by comparison with the reference finite volume method results. The method is very attractive in the present context due to its trivial implementation of curved geometry for two and three dimensions, accuracy and stability of the results.