Mathematical modeling of coupled turbulent flow and solidification in a single belt caster with electromagnetic brake

A mathematical model has been developed to simulate turbulent fluid flow and solidification in the presence of a DC magnetic field in an extended nozzle for metal delivery to a single belt caster. This paper reports on predicted effects of DC magnetic field conditions in modifying flows and solidification behavior in the metal delivery system. It is shown that the application of a DC magnetic brake to the proposed system can result in a reasonably uniform feeding of melt onto the cooled moving belt. This, in turn, optimises the rate of even shell growth along the chilled substrate. In order to account for the effects of turbulence, a revised low-Reynolds k–ε turbulent model was employed. A Darcy-porosity approach was used to simulate fluid flow within the mushy solidification region. Simulations were carried out for plain carbon steel strip casting. The fully coupled transport equations were numerically solved using the finite volume method. The computed flow patterns were compared with those reported in the literature. The performance of the magnetic flow control device proposed in this work is evaluated and compared with flow modifications obtained by inserting a ceramic filter within the reservoir.     

Mathematical and physical modeling of systems for metal delivery in the continuous casting of steel and DC casting of aluminum

In the continuous casting of steel, various nozzles have been used (e.g., bifurcated nozzles with ports inclined at various angles to the horizontal) to deliver metal from the tundish into the caster. An even greater variety of devices is used in the case of semi-continuous (direct chill (DC) or electromagnetic (EM)) casting of aluminum, for example, nozzles delivering metal into bags of various designs. The paper describes a physical (water) model whereby particle image velocimetry has been used to measure velocities. These measured velocities are compared to ones predicted using computational fluid dynamics. Conclusions are reached concerning the validity of the computations and recommendations made about improvement in casting operations by modification of melt flow.     

A three-dimensional fluid flow model for puddle formation in the single-roll rapid solidification process

The single-roll rapid solidification process (SRRSP) is considered to be a process of perspective to produce a Fe-Si-B ribbon of amorphous microstructure and near net shape products such as thin strips of stainless steel. The condition of a melt puddle between the nozzle and rotating wheel in the single-roll rapid solidification process significantly affects the quality and dimensional uniformity of the products as well as the smoothness of the operation. The purpose of this study was to develop a three-dimensional fluid flow analysis system to model the formation of puddle and flow conditions of molten metal in the puddle for the single-roll rapid solidification processes which include the planar flow casting (PFC) process and the single-roll strip casting process. The model is based on a computational fluid dynamics technique called the SOLA-VOF scheme, which possesses the capability of treating transient fluid flow problems with the evolution of free boundaries. Furthermore, the SOLA-VOF scheme is extended from two dimensions to three dimensions. The simulated results reveal how the melt puddle is formed between the nozzle and the rotating substrate and its corresponding fluid flow behavior for the PFC process as well as the single-roll strip casting process. The test results also demonstrate that two-dimensional analysis cannot properly consider the actual flow condition in the puddle.     

Strand straightening in the continuous casting of steel

In the continuous casting of steel, a strand with a solidifiededge is produced by pouring molten steel through a water-cooledmould. The strand is curved below the mould to travel horizontallyby a series of roll pairs. In this paper, the forces actingon these rolls and the stress and strain/strain rates withinthe steel are predicted. The mathematical model considers rigid-plasticand elastoplastic behaviour. A numerical solution procedurebased on computational fluid dynamics has been adapted to solvethe equations governing the material deformation. Algorithmsfor determining the location of the strand free surface andthe contact or noncontact of rolls are described.     

Influence of electromagnetic stirrer position on fluid flow and solidification in continuous casting mold

A computational study of the effect of stirrer position on fluid flow and solidification in a continuous casting billet mold with in-mold electromagnetic stirring has been carried out. The numerical investigation uses a full coupling method in which alternating magnetic field equations are solved simultaneously with the governing equations of fluid flow and heat transfer. An enthalpy-porosity technique is used for the solidification analysis while the magnetohydrodynamics technique is used for studying the fluid flow behavior under the electromagnetic field. The streamline, liquid fraction, and solid shell thickness at the mold wall have been predicted with and without EMS application at different positions along the length of the mold. Recirculation loops are seen to be formed above and below the stirrer position when fluid flow and electromagnetic field equations were solved, without incorporating the solidification model. Application of the solidification model interestingly resulted in the reduction of the size of the recirculation loops formed. The tangential component of velocity of the fluid near the solidification front, stirring intensity and the effective length of stirring below the stirrer decrease as the stirrer position is moved downwards. Significant changes in characteristics of solid shell formation like delay in initiation of solidification at the mold wall and formation of a gap in the re-solidified shell have been observed with change in stirrer position.     

Verified reduction of a model for a continuous casting process

The casting of metals is known to involve the complex interaction of turbulent momentum and heat transfer in the presence of solidification, and it is believed that computational fluid dynamical (CFD) techniques are required to model it correctly. Here, using asymptotic methods, we demonstrate that the key quantities obtained in an earlier CFD model for a particular continuous casting process – ostensibly for a pure metal, but equally for an alloy of eutectic composition – can be recovered using a much simpler model that takes into account just the heat transfer, requiring the numerical solution of a two-phase Stefan problem. Combining this with a more recent asymptotic thermomechanical model for the same continuous casting process, we postulate that it should be possible, with the additional help of algebraic manipulation, to reduce a model that takes into account turbulent momentum and heat transfer in the melt and the thermomechanics in the solid shell to one formulated in terms of only heat transfer, without adversely affecting model predictions.     

Boundary condition difficulties encountered in the simulation of bulging during the continuous casting of steel

In modelling the continuous casting of steel it is required to simulate the movement of the solidifying steel (containing liquid steel) through the guide rolls. This paper outlines some of the difficulties involved in forcing a modelled ‘single roll pitch’ to pass underneath the exit roll and describes a practical solution.     

Oscillation of Confined Jets in Continuous Casting Mold Flow

In continuous slab casting, the liquid steel is introduced into the mould via a submergered entry nozzle. This nozzle usually has two opposed orifices on its side walls, generating two diametrically opposed turbulent jets that are declined about 20° to the horizontal axis. These jets interact with the surrounding walls of the mould, which leads to an unstable flow situation and a self induced oscillation of the jets. Although both mould and nozzle geometry have two perpendicular symmetry planes, the oscillations are asymmetric. The fluid flow inside the mold is calculated with a 3D finite volume solver using turbulence models based on Reynolds-averaging. The massflow of the jets and the mould extensions are varied, and the numerical results are partially compared with PIV-measurements at a 1:1 scaled watermodel of the mould. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Short shots and industrial case studies: Understanding fluid flow and solidification in high pressure die casting

The geometric complexity and high fluid speeds involved in high pressure die casting (HPDC) combine to give strongly three dimensional fluid flow with significant free surface fragmentation and splashing. A simulation method that has proved particularly suited to modelling HPDC is Smoothed Particle Hydrodynamics (SPH). Materials are approximated by particles that are free to move around rather than by fixed grids, enabling more accurate prediction of fluid flows involving complex free surface motion. Three practical industrial case studies of SPH simulated HPDC flows are presented; aluminium casting of a differential cover (automotive), an electronic housing and zinc casting of a door lock plate. These show significant detail in the fragmented fluid free surfaces and allow us to understand the predisposition to create defects such as porosity in the castings. The validation of flow predictions coupled with heat transfer and solidification is an important area for such modelling. One powerful approach is to use short shots, where insufficient metal is used in the casting or the casting shot is halted part way through, to leave the die cavity only partially filled. The frozen partial castings capture significant detail about the order of fill and the flow structures occurring during different stages of filling. Validation can occur by matching experimental and simulated short shots. Here we explore the effect of die temperature, metal super-heat and volume fill on the short shots for the casting of a simple coaster. The bulk features of the final solid castings are found to be in good agreement with the predictions, but the fine details appear to depend on surface behaviour of the solidifying metals. This potentially has significant implications for modelling HPDC.     

Efficiency of a DC magnetic field used for braking the flow within a continuous casting mould

The continuous casting technology provides about 90 percent of the world steel production. The application of DC magnetic fields in form of so-called electromagnetic brakes is considered for an effective flow control with substantial capabilities to improve the product quality or to enhance the productivity of the process. The main effect of the DC magnetic field is supposed to result in a uniform reduction of the maximum velocities in the discharging jet from the submerged entry nozzle and to damp violent turbulent fluctuations. However, the electromagnetic braking of such highly turbulent and complex flows is complicated phenomenon and has not been understood fully until now. We present numerical and experimental investigations focusing on the fluid flow in the continuous casting mould under the influence of a transverse magnetic field. Numerical calculations were performed using the software package CFX with an implemented RANS-SST turbulence model. the non-isotropic nature of the MHD turbulence was taken into account by specific modifications of the turbulence model. Corresponding experimental investigations were carried out at the mock-up LIMMCAST at HZDR. The comparison between our numerical calculations and the experimental results display a very well agreement. An important outcome of this study is the feature that the magnetic field does not provide a continuous reduction of the velocity fluctuations at the nozzle port. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of a heuristic search technique for the improvement of spray zones cooling conditions in continuously cast steel billets

The process of casting occupies an important place in the metallurgical industry, and the entire world of the metal user. In the past, the ingot casting–rolling (slabbing, blooming, or billeting) process was commonly used. The continuous casting process has largely replaced this earlier method because of the inherent advantages of energy savings, enhanced productivity, higher yield and reduced costs. However, continuous casting process is not without of its problems. Considerable effort has been made by many researches to establish adequate design, operation and maintenance of continuous casting machine to ensure metallurgical quality of the final product. One of the most severe defects in continuous casting products is concerned with the cracks provoked by improper design of the spray cooling system. The aim of this work is to develop a two dimensional heat transfer model based on the finite difference method in order to calculate the strand temperatures and the solid shell profile along the machine. An Artificial Intelligence heuristic search procedure interacts with the numerical model to determine the improved cooling conditions for the sprays zones of a real continuous caster for the production of quality billets.     

Modelling of heat affected zone in cylindrical steel elements surfaced by welding

Computational models of a temperature field in cylindrical steel elements surfaced by the following methods: controlled pitch, spiral welding sequence and spiral welding sequence with swinging motion of the welding head are presented in the paper. The lateral surface of regenerated cylindrical object, subjected to the welding heat source, has been treated as a plane rolled on cylinder and temperature field of repeatedly surfaced plain massive body was solved. Temperature rises, caused by overlaying consecutive welding sequences and self-cooling of areas previously heated, were taken into consideration in the solution. The computations of the temperature field for continuous casting steel machine roll made of 13CrMo4 steel were carried out.     

Transient thermal model for the hot chamber injection system in the pressure die casting process

This paper describes a three-dimensional numerical model that is used to predict the transient thermal behaviour of the metal injection system of a hot chamber pressure die casting machine. The behaviour of the injection system is considered in conjunction with that of the die. The Boundary Element Method (BEM) is used to model the transient thermal behaviour of the injection system elements and the die blocks. A perturbation approach is adopted. By adopting this approach, only those surfaces over which a significant transient variation in temperature occurs need be considered. The model assumes that a corresponding steady-state analysis has first been performed so that time-averaged thermal information is available. A finite element based technique is used to model the phase change of the liquid metal in the die cavity and in the injection system. At injection the nozzle and die are assumed to be instantly filled with liquid metal, however, a procedure is presented that attempts to model the heat transfer associated with the flow through the nozzle, gate, and runner regions during injection. Model predictions are compared against thermocouple readings and thermal images obtained from experimental tests. Good agreement is obtained between predicted and measured temperatures. The transient thermal behaviour of an existing hot chamber injection system is investigated in detail and recommendations for improved performance are made. In an attempt to improve the solidification pattern of the casting and the thermal behaviour of the injection system, a redesign of the experimental die is considered. The numerical predictions indicate that the redesign will have a beneficial effect on the solidification pattern of the casting, and on the performance of the injection system.     

Discretisation procedures for multi-physics phenomena

Procedures are described for solving the equations governing a multi-physics process. Finite volume techniques are used to discretise, using the same unstructured mesh, the equations of fluid flow, heat transfer with solidification, and solid deformation. These discretised equations ofe then solved in an integrated manner. The computational mechanics environment, PHYSICA, which facilitates the building of multi-physics models, is described. Comparisons between model predictions and experimental data are presented for the casting of metal components.     

An adaptive level set method for shock-driven fluid-structure interaction

The fluid-structure interaction simulation of shock- and detonation-loaded structures requires numerical methods that can cope with large deformations as well as local topology changes. A robust, level-set-based shock-capturing fluid solver is described that allows coupling to any solid mechanics solver. As computational example, the elastic response of a thin steel panel, modeled with both shell and beam theory, to a shock wave in air is considered. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computed oscillations of a confined submerged liquid jet

The jet oscillation observed in thin slab continuous casting is studied numerically by modelling the flow of liquid injected through a submerged entry nozzle and into a cavity. The oscillation relies on the exchange of fluid between recirculation cells on each side of the jet via a cross-flow through the gap between the nozzle shaft and the broad face of the cavity wall. Features of the oscillating jet are investigated by varying the resistance to cross-flow. This resistance occurs naturally since the nozzle obstructs cross-flow. The predicted oscillation can be manipulated by altering the cross-flow (through the use of an effective resistance force in the model) or stopped altogether to form a static asymmetrical flow pattern. Flow calculations are performed using a transient, two-dimensional, turbulent, fluid flow model.     

连续铸钢保护渣热传递三维数值模拟

本文讨论了连续铸钢保护渣层热过程的物理 ,数学模型 ,采用三维有限元方法进行了数值计算 ,较成功地模拟了保护渣的热传递过程     

MHD analysis in hydromagnetic casting process of clad steel slabs

A novel continuous casting process for clad steel slabs has been developed by suppressing the mixing of molten steels in the mold pool of continuous casting strand with a level DC magnetic field (LMF) installed in the mold. In this process, two molten steels of different chemical composition are discharged by two nozzles into the upper and the lower pools respectively to solidify in the outer and the inner layers as a clad steel slabs. The mechanism of separation into two layers has been elucidated by using a three dimensional MHD analysis. The numerical prediction employing Maxwell's equation, Ohm's law, and the turbulent flow model shows that the mixing of the different type of steels is suppressed by the electromagnetic dividing of the upper and the lower recirculating flows. The principle of the new process has also been verified by steel casting trials of the stainless-steel clad steel slabs with an 8-ton scale pilot continuous casting machine.     

Stochastic optimization for blending problem in brass casting industry

A critical process in brass casting is blending of the raw materials in a furnace so that the specified metal ratios are satisfied. The uncertainties in raw material compositions may cause violations of the specification limits and extra cost. In this study, we proposed a chance-constrained stochastic programming approach for blending problem in brass casting industry to handle the statistical variations in raw material compositions. The proposed approach is a non-linear mathematical model that is solved global optimally by using GAMS/BARON solver. An application has been performed in MKEK brass factory in Kırıkkale, Turkey and the solution of the application has been compared with alternative solution approaches based on cost and specification violation risk conditions. This comparison demonstrates that the proposed model is the most effective solution approach for managing stochastic uncertainties in blending problems and successfully can be used other industries such as alloy steel or secondary aluminum production.     

The use of artificial intelligence technique for the optimisation of process parameters used in the continuous casting of steel

The productivity and quality of a continuous caster depend mainly on process parameters, i.e. casting speed, casting temperature, steel composition and cleanliness of the melt, water flow rates in the different cooling zones, etc. This work presents the development of an algorithm, which incorporates heuristic search techniques for direct application in metallurgical industries, particularly those using continuous casting process for the production of steel billets and slabs. This is done to determine the casting objectives of maximum casting rate as a function of casting constraints. These constraints are evaluated with the aid of a heat transfer and solidification model based on the finite difference technique, which has been developed and integrated with a genetic algorithm. The essential parts of continuous casting equipment, which must be subjected to monitoring, as well as a methodology of mathematical model and physical settlements in each cooling region, are presented. The efficiency of the intelligent system is assured by the optimisation of the continuous casting operation by maximum casting rate and defect-free products. This approach is applied to the real dimension of a steel continuous caster, in real conditions of operation, demonstrating that good results can be attained by using heuristic search, such as: smaller temperature gradients between sprays zones, reduction in water consumption and an increase in casting speed.