Transport and Entrapment of Particles in Steel Continuous Casting

A particle-capture model based on local force balances has been developed, implemented into computational models of turbulent fluid flow and particle transport, and applied to simulate the entrapment of slag inclusions and bubbles during the continuous casting of steel slabs. Turbulent flow of molten steel is computed in the nozzle and mold using transient computational fluid flow models, both with and without the effects of argon gas injection. Next, the transport and capture of many particles are simulated using a Lagrangian approach. Particles touching the dendritic interface may be pushed away, dragged away by the transverse flow, or captured into the solidifying shell according to the results of a local balance of ten different forces. This criterion was validated by reproducing experimental results in two different systems. The implications of this criterion are discussed quantitatively. Finally, the fluid flow/particle transport model results and capture criterion are applied together to predict the entrapment distributions of different sized particles in a typical slab caster. More large particles are safely removed than small ones, but the entrapment rate into the solidifying shell as defects is still very high.     

Numerical Investigation of Shell Formation in Thin Slab Casting of Funnel-Type Mold

The key issue for modeling thin slab casting (TSC) process is to consider the evolution of the solid shell including fully solidified strand and partially solidified dendritic mushy zone, which strongly interacts with the turbulent flow and in the meantime is subject to continuous deformation due to the funnel-type mold. Here an enthalpy-based mixture solidification model that considers turbulent flow [Prescott and Incropera, ASME HTD, 1994, vol. 280, pp. 59–69] is employed and further enhanced by including the motion of the solidifying and deforming solid shell. The motion of the solid phase is calculated with an incompressible rigid viscoplastic model on the basis of an assumed moving boundary velocity condition. In the first part, a 2D benchmark is simulated to mimic the solidification and motion of the solid shell. The importance of numerical treatment of the advection of latent heat in the deforming solid shell (mushy zone) is specially addressed, and some interesting phenomena of interaction between the turbulent flow and the growing mushy zone are presented. In the second part, an example of 3D TSC is presented to demonstrate the model suitability. Finally, techniques for the improvement of calculation accuracy and computation efficiency as well as experimental evaluations are also discussed.     

Multiphase Flow and Thermo-Mechanical Behaviors of Solidifying Shell in Continuous Casting Mold

 The metallurgical phenomena occurring in the continuous casting mold have a significant influence on the performance and the quality of steel product. The multiphase flow phenomena of molten steel, steel/slag interface and gas bubbles in the slab continuous casting mold were described by numerical simulation, and the effect of electromagnetic brake (EMBR) and argon gas blowing on the process were investigated. The relationship between wavy fluctuation height near meniscus and the level fluctuation index F, which reflects the situation of mold flux entrapment, was clarified. Moreover, based on a microsegregation model of solute elements in mushy zone with δ/γ transformation and a thermo-mechanical coupling finite element model of shell solidification, the thermal and mechanical behaviors of solidifying shell including the dynamic distribution laws of air gap and mold flux, temperature and stress of shell in slab continuous casting mold were described.     

Modelling of Melt Flow and Solidification in the Twin‐Roll Strip Casting Process

A three‐dimensional mathematical model has been developed to simulate turbulent fluid flow, heat transfer and solidification in the pool of a twin‐roll strip caster. A Darcy‐porosity approach was used to study the fluid flow within the mushy solidification zone in the pool. The effect of the heat transfer coefficient and permeability constant on the flow and solidification was also predicted. It was shown that an even flow and temperature distribution of the pool can be obtained by using a suitable feeding system. The heat transfer between the rolls and the solidifying metal has a big influence on the location of the solidification end point. The permeability of the mushy zone is a key factor which affects the flow and solidification in the twin‐roll strip casting process.     

Numerical Prediction on the Flow Field of Molten Steel and the Trajectory of Inclusion in Continuous Casting Mold Effected by Electromagnetic Field

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Modeling of solute redistribution in the mushy zone during solidification of aluminum-copper alloys

A mathematical model has been established to predict the formation of macrosegregation for a unidirectional solidification of aluminum-copper alloys cooled from the bottom. The model, based on the continuum formulation, allows the calculation of transient distributions of temperature, velocity, and species in the solidifying alloy caused by thermosolutal convection and shrinkage-induced fluid flow. Positive segregation in the casting near the bottom (inverse segregation) is found, which is accompanied by a moving negative-segregated mushy zone. The effects of shrinkage-induced fluid flow and solute diffusion on the formation of macrosegregation are examined. It is found that the redistribution of solute in the solidifying alloy is caused by the flow of solute-rich liquid in the mushy zone due to solidification shrinkage. A higher heat-extraction rate at the bottom increases the solidification rate, decreasing the size of the mushy zone, reducing the flow of solute-rich liquid in the mushy zone and, as a result, lessening the severity of inverse segregation. Comparisons between the theoretical predictions from the present study and previous modeling results and available experimental data are made, and good agreements are obtained.     

Prediction of cracks in continuously cast steel beam blank through fully coupled analysis of fluid flow, heat transfer, and deformation behavior of a solidifying shell

A mathematical model has been developed for the prediction of cracks in the continuously cast steel beam blank through the fully coupled analysis of fluid flow, heat transfer, and deformation behavior of a solidifying shell. Fluid flow and heat transfer in the strand mold were analyzed with a three-dimensional (3-D) finite-volume method (FVM). For the complex geometry of the beam blank, a body-fitted coordinate (BFC) system was employed. Thermo-elastic-plastic deformation behavior in the strand was analyzed using the finite-element method (FEM) based on the two-dimensional (2-D) slice model. The thermal fields of the strand calculated with the FVM were used in the analysis of the deformation behavior of the strand. Through the iterative analysis of the fluid flow, heat-transfer, and deformation behavior, the coupling parameter of the heat-transfer coefficient between the strand and the mold was obtained. In order to describe the thermophysical properties and thermomechanical behavior of steel in the mushy zone, the microsegregation of solute elements was assessed. Consequently, some characteristic temperatures of steel as well as variations of phase fractions with temperature were determined. The probability of cracking in the strand, originating from an interdendritic liquid film, was quantified as a crack susceptibility coefficient. Recirculating flows were developed in the web and flange-tip regions. The development of a solidifying shell in the flange-center region was retarded by the inlet flow from a submerged entry nozzle (SEN). An air gap was formed mainly near the flange-tip corner. Surface cracks in the web and fillet regions and internal cracks in the flange-tip region were predicted.     

水口类型对大方坯结晶器内钢水流动与凝固行为的影响

采用数值计算方法对比研究了直通式、4分径向以及新型4分切向水口对大方坯连铸结晶器内钢水流动与凝固行为的影响.结果表明,当前常用的直通式水口对坯壳无冲击,利于坯壳均匀生长,但钢水冲击深度大,易在弯月面处形成死区,不利于大方坯内部及表面质量的提高;改用4分水口浇铸时,结晶器宽、窄面冲击区附近都会出现不同程度的坯壳厚度零增长...     

Bubble Entrapment on Solidified Shell caused by Unsteady Steel Flow in Mold

The molten steel flow in the continuous casting mold and entrapment of inclusions and bubbles on the inner surface of the solidified shell are examined to clarify the mechanism of internal defects in steel products. Defects on steel sheets are caused by bubbles and inclusions entrapped on the solidified shell during casting. It was found that bubbles penetrate deeply due to an unbalanced time‐dependent flow. This phenomenon can be explained by the Large Eddy Simulation model, which can predict the time‐dependent flow. The number of inclusions increases as the bubble diameter and the distance of the position of entrapment from the top free surface increase. This indicates that bubbles collect inclusions while traveling in the molten steel in the continuous caster. A simple mathematical model is presented to explain the mechanism by which inclusions become attached to bubbles.     

Simulation of thermal behavior during peritectic steel solidification in slab continuous casting mold

Thermal behavior of the solidifying shell in continuous casting mold is very important to final steel products.In the present work,one two-dimension transient thermal-mechanical finite element model was developed to simulate the thermal behavior of peritectic steel solidifying in slab continuous casting mold by using the sequential coupling method.In this model,the steel physical properties at high temperature was gotten from the micro-segregation model withδ/γtransformation in mushy zone,and the heat flux was obtained according to the displacement between the surface of solidifying shell and the hot face of mold as solidification contraction,the liquid-solid structure and distribution of mold flux,and the temperature distribution of slab surface and mold hot face,in addition,the rate-dependent elastic-viscoplastic constitutive equation was applied to account for the evolution of shell stress in the mold.With this model,the variation characteristics of surface temperature,heat flux, and growth of the solidifying shell corner,as well as the thickness distribution of the liquid flux,solidified flux,air gap and the corresponding thermal resistance were described.     

连铸流动与凝固耦合模拟中糊状区系数的表征及影响

分析提出了连铸流动与凝固耦合数值模拟中, 钢液在两相区流动时的糊状区系数(A_mush)与渗透率的关系; 通过建立大方坯连铸结晶器三维耦合数值模型, 揭示了不同糊状区系数对钢液流动、传热与凝固进程的影响, 以及早期相关研究结果差异的源头.结果表明: 糊状区系数越大, 钢液在糊状区内的流动阻力越强, 凝固时钢液流动速度降低越快.采用较大的糊状区系数时, 糊状区呈较窄的"带状"分布在固液相之间; 当糊状区系数较小时, 糊状区范围变大, 钢液在结晶器内温降过快, 自由液面处出现过冷现象, 凝固坯壳局部发生重熔.结合实验数据验证与模型分析, 认为糊状区系数取值1×108~5×108 kg·m-3·s-1可以较可靠地揭示连铸结晶器内的实际凝固现象.      

Using a Two-Phase Columnar Solidification Model to Study the Principle of Mechanical Soft Reduction in Slab Casting

A two-phase columnar solidification model is used to study the principle of mechanical soft reduction (MSR) for the reduction of centerline segregation in slab casting. The two phases treated in the model are the bulk/interdendritic melt and the columnar dendrite trunk. The morphology of the columnar dendrite trunk is simplified as stepwise growing cylinders, with growth kinetics governed by the solute diffusion in the interdendritic melt around the growing cylindrical columnar trunk. The solidifying strand shell moves with a predefined velocity and the shell deforms as a result of bulging and MSR. The motion and deformation of the columnar trunks in response to bulging and MSR is modeled following the work of Miyazawa and Schwerdtfeger from the 1980s. Melt flow, driven by feeding of solidification shrinkage and by deformation of the strand shell and columnar trunks, as well as the induced macrosegregation are solved in the Eulerian frame of reference. A benchmark slab casting (9-m long, 0.215-m thick) of plain carbon steel is simulated. The MSR parameters influencing the centerline segregation are studied to gain a better understanding of the MSR process. Two mechanisms in MSR modify the centerline segregation in a slab casting: one establishes a favorable interdendritic flow field, whereas the other creates a non-divergence-free deformation of the solid dendritic skeleton in the mushy region. The MSR efficiency depends not only on the reduction amount in the slab thickness direction but also strongly on the deformation behavior in the longitudinal (casting) direction. With enhanced computation power the current model can be applied for a parameter study on the MSR efficiency of realistic continuous casting processes.     

The Influence of Support Rollers of Continuous Casting Machines on Heat Transfer and on Stress‐Strain of Slabs in Secondary Cooling

The processes of solidification and heat extraction are important for the continuous casting of steel. In this work, investigations on the influence of support roller contact on solidification in a strand of a slab caster, such as surface temperature and strand shell growth, and on thermal strain and stress in the slab have been carried out. The results show that roller contact has an influence on the solidification of steel and on the thermo‐mechanical behaviour of the strand.     

Inclusions in continuously cast steel slabs - numerical model and validation

A numerical model for liquid steel flow and inclusion transport and separation in continuous casting moulds is presented, which covers several features simultaneously. The free surface at the meniscus is computed; the submerged entry nozzle is discretised in detail to resolve the outlet geometry; gas injection through the SEN and its effect on liquid steel flow are considered; capture of inclusions within gas bubbles is covered in a simplified approach; the solidifying shell and the process of inclusion entrapment by the growing shell are simulated. Computed flow profiles are compared to experimental results on water and to measurements on liquid steel in a slab caster. Predicted inclusion profiles in solid slabs are compared to empirical findings from literature. Results of the model for various cases will be presented in a subsequent publication.     

A 3-D numerical prediction of turbulent flow,heat transfer and solidification in a continuous slab caster for steel

This study describes the numerical modeling of three-dimensional coupled turbulent flow, heat transfer, and solidification in a continuous slab caster for stainless steel. The model uses generalized transport equations which are applicable to the liquid, mushy and solid regions within the caster. The turbulent characteristics in the melt pool and mushy region are accounted for using the low-Reynolds number k–ε turbulence model by Launder and Sharma. This version of the low-Reynolds number turbulence model is found to be more easily adaptable to the coupled flow and mushy region solidification caster problem compared to the standard high-Reynolds number and other low-Reynolds number turbulence models. The macroscopic solidification process itself is based on the enthalpy-porosity scheme. The governing transport equations are solved employing the primitive variables and using the control volume based finite-difference scheme on a staggered grid. The process variables considered are the casting speed and the inlet superheat of the melt. The effects of these process variables on the velocity and temperature distributions and on the extent of the solidification and mushy regions are reported and discussed. The numerical predictions of solidification profile are compared with the limited experimental data available in the literature, and very good agreement was found.     

Analysis of thermomechanical behaviour in billet casting with different mould corner radii

Abstract

A finite element thermal stress model to compute the thermomechanical state of the solidifying shell during continuous casting of steel in a square billet casting mould has been applied to investigate longitudinal cracks. A two-dimensional thermoelastoviscoplastic analysis was carried out within a horizontal slice of the solidifying strand which moves vertically within and just below the mould. The model calculates the temperature distributions, the stresses, the strains in the solidifying shell, and the intermittent air gap between the casting mould and the solidifying strand. Model predictions were verified with both an analytical solution and a plant trial. The model was then applied to study the effect of mould corner radius on longitudinal crack formation for casting in a typical 0·75%/m tapered mould with both oil and mould powder lubrication. With this inadequate linear taper, a gap forms between the shell and the mould in the corner region. As the corner radius of the billet increases from 4 to 15 mm, this gap spreads further around the corner towards the centre of the strand and becomes larger. This leads to more temperature non-uniformity around the billet perimeter as solidification proceeds. Longitudinal corner surface cracks are predicted to form only in the large corner radius billet, owing to tension in the hotter and thinner shell along the corner during solidification in the mould. Off corner internal cracks form more readily in the small corner radius billet. They are caused by bulging below the mould, which bends the thin, weak shell around the corner, creating tensile strain on the solidification front where these longitudinal cracks are ultimately observed.     

Engulfment Behavior of Inclusions in High-Carbon Steel: Theoretical and Experimental Investigation

Previous studies on inclusions behavior at the front of the solidifying steel shell have mainly focused on low-carbon steels. However, with the increasing applications of high-carbon steel in recent years because of its superior properties, it is crucial to understand this behavior in high-carbon steel. Most of the high-carbon steels are deoxidized by silicon, calcium treated, and contain higher sulfur percentage. Also, higher carbon content has a determining influence on the viscosity and surface tension, which will affect the inclusion behavior. In this study, we have investigated the engulfment behaviors of inclusions in front of the solidifying interface in high-carbon steels using concentric solidification method. The critical velocity of the growing shell, at which the particle is engulfed in the solidifying shell, instead of being pushed by this shell, was determined. The inclusion identified in this study is a bi-component form of CaO-SiO₂-based oxide and CaS. It was revealed that engulfment behavior is strongly affected by convection of liquid steel that originates from carbon push out in high-carbon steels. This study provides new crucial information to produce high-carbon steel with fewer inclusions, which opens new application pathways for this emerging grade of steel.     

Influence of Forced/Natural Convection on Segregation During the Directional Solidification of Al-Based Binary Alloys

We analyzed the columnar solidification of a binary alloy under the influence of an electromagnetic forced convection of various types and investigated the influence of a rotating magnetic field on segregation during directional solidification of Al-Si alloy as well as the influence of a travelling magnetic field on segregation during solidification of Al-Ni alloy through directional solidification experiments and numerical modeling of macrosegregation. The numerical model is capable of predicting fluid flow, heat transfer, solute concentration field, and columnar solidification and takes into account the existence of a mushy zone. Fluid flows are created by both natural convection as well as electromagnetic body forces. Both the experiments and the numerical modeling, which were achieved in axisymmetric geometry, show that the forced-flow configuration changes the segregation pattern. The change is a result of the coupling between the liquid flow and the top of the mushy zone via the pressure distribution along the solidification front. In a forced flow, the pressure difference along the front drives a mush flow that transports the solute within the mushy region. The channel forms at the junction of two meridional vortices in the liquid zone where the fluid leaves the front. The latter phenomenon is observed for both the rotating magnetic field (RMF) and traveling magnetic field (TMF) cases. The liquid enrichment in the segregated channel is strong enough that the local solute concentration may reach the eutectic composition.     

Analysis on Initial Defects Based on Mechanical State of Meniscus Shell

The meniscus shell plays an important role in slab quality and process operation for continuously cast steel.One decisive reason is initial solidifying shell and growing dendrite under the mechanical stress caused by mold oscillation and liquid steel flow to generate disturbance of casting.The mechanical state of meniscus shell was analyzed using mathematical models in combination with thermo-physical properties and flow rate of steel to shed light on the formation of initial defects.The results show that the mold oscillation is a critical factor on the initial crack formation because the periodic stress makes the shell bending.The formed crack may also expand and propagate due to the following secondary cooling and straightening behavior.The primary dendrite has high possibility to be broken by fluid flow in the solidification front to lead to the non-uniform thickness of solidifying shell.The inter-dendrite bridging is also likely to be formed to produce other internal defects,such as air hole and solute enrichment in the residual molten steel located in the bridging area.     

薄板坯连铸结晶器内流动传热行为的研究

基于珠钢CSP薄板坯连铸机设备工艺条件和所采用扁平浸入式水口结构,结合铜板测温导出的热流密度分布进行了漏斗形结晶器内钢水流动、自由液面以及传热凝固等冶金现象的综合描述和数值分析.结晶器熔池中以两个上旋涡为主的钢水循环流动局限在漏斗形结晶器内,上旋涡流股冲击和离开熔池液面分别对液面起伏波动有所贡献,弯月面下距窄边100 mm范围内有二次涡形成.除水口下方两侧存在两个具有明显过热的高温区外,熔池中绝大部分钢水的温度在液相线附近保持恒定,铸坯表面温度分布和坯壳发育过程均反映出水口高温射流的影响,铸坯表面最高温区位于熔池液面下方靠近结晶器窄边的地方.