Metal cooling and solidification in a continuous-casting mold

A mathematical model is proposed for cooling a metal solidifying in a continuous-casting mold. In this model, heat exchange is related to solidification; therefore, the thermal resistance of the gap between the ingot and the work mold surface, which is the main component of the total thermal resistance to heat transfer from the ingot to cooling water, can be calculated. This mathematical model is applied to the cooling and solidification of an ingot in a continuous-casting mold, and some numerical-calculation results for the case of a medium-carbon steel are presented.     

Mathematical Modeling of Hot Tearing in the Solidification of Continuously Cast Round Billets

Billets produced by continuous casting sometimes show the presence of subsurface cracks that can compromise the quality of the final product. The presence of these cracks is revealed by Baumann prints of billet cross sections in which the chill zone is visible and the short radial cracks are located only where the chill zone thickness is thinner. This experimental finding induces the hypothesis that cracks are formed as a result of the presence of unevenness in the mold heat extraction around the billet perimeter. Cracks start to open in the dendritic front in regions where the shell growth in the mold is slower. The study presented in this article focused on steels with a sulfur content of about 300 ppm. The Baumann prints taken from billet samples of numerous different heats allowed detecting the presence of subsurface cracks and their location nearby visible chill zone thinning areas. To understand the mechanisms of crack formation and to define the possible corrections, a modeling activity has been carried out using the finite element technique on 148-mm diameter billets continuously cast at TenarisDalmine (Dalmine, Italy). The model performs a two-dimensional thermomechanical analysis of the solidification in the mold and within about 4 cm below the mold exit, along which the shell surface is cooled only by radiation to the environment, before the sprays of the first ring impact on the strand. The model includes the contact of the shell with the mold inner surface, which moves according to taper and distortion (this last part is calculated by means of a separate mold model); the steel creep behavior; the calculation of the heat transfer through the gap depending on the local mutual distance between the two surfaces; the effect of the liquid steel fluid dynamics on the solidification growth as a result of the temperature distribution; and the calculation of a hot tearing indicator represented by the porosity fraction caused by mechanical strains applied at the dendrite roots. From the simulation results, it is concluded that subsurface cracks are generated in the space between the mold exit and the first cooling ring; the involved mechanisms of formation also are withdrawn. Nucleation of MnS precipitates of large dimensions is an additional cause of defectiveness in controlled sulfur steels. As a final conclusion of this work, the most important actions to eliminate subsurface cracks are derived.     

Mathematical model for the unidirectional solidification of metals: I. cooled molds

This paper presents a new mathematical model that can be used to predict the solidification rate and the temperature distribution during the unidirectional solidification of metals n molds cooled by fluids such as air and water. The model differs from other analytical methods presented in the literature in the sense that it is more general in application and easier to manipulate, while retaining the advantage of convenience over numerical techniques. The proposed model permits the measurement of the Newtonian heat transfer coefficient at the metal/mold interface. In order to verify the applicability to air cooled molds, the model is compared with experimental results in the literature for the cases of lead, tin and lead-tin eutectic. Finally, the case of water cooled molds is examined, the model being compared with experimental results obtained in this work for lead and aluminum.     

Mathematical model for the unidirectional solidification of metals: I. cooled molds

This paper presents a new mathematical model that can be used to predict the solidification rate and the temperature distribution during the unidirectional solidification of metals n molds cooled by fluids such as air and water. The model differs from other analytical methods presented in the literature in the sense that it is more general in application and easier to manipulate, while retaining the advantage of convenience over numerical techniques. The proposed model permits the measurement of the Newtonian heat transfer coefficient at the metal/mold interface. In order to verify the applicability to air cooled molds, the model is compared with experimental results in the literature for the cases of lead, tin and lead-tin eutectic. Finally, the case of water cooled molds is examined, the model being compared with experimental results obtained in this work for lead and aluminum.     

Heat transfer-solidification kinetics modeling of solidification of castings

A close examination of the recent developments in the field of computer simulation of solidification process reveals that a combination of both macroscopic and microscopic models is necessary in order to accurately describe the solidification of castings. Currently available macroscopic models include models that describe heat transfer from metal to mold, fluid flow of liquid metal during mold filling, and stress field in the casting. At the microscopic level, the models should include more intricate issues such as solidification kinetics and fluid flow in the mushy zone. Although significant progress has been accomplished over the years in each field, the task of including all of these models into a comprehensive package is far from being complete. This paper describes the state of the art on coupling the macroscopic heat transfer (HT) and microscopic solidification kinetics (SK) models and introduces thelatent heat method as a more accurate method for solving the heat source term in the heat conduction equation. A new method for calculation of fraction of solid evolved during solidification based on computer-aided cooling curve analysis (CA-CCA), as well as a method based on nucleation and growth kinetics laws, is discussed. A new nucleation model based on the concept of instantaneous nucleation, which is used to describe equiaxed eutectic solidification of commercial alloys, has been introduced. It is demonstrated that the instantaneous nucleation model agrees well with the experimental results in terms of cooling curves and of evolution of the fraction of solid during solidification. Validation results are also shown for SK models that are based on CA-CCA coupled with HT models for eutectic Al-Si and gray cast iron alloys.     

基于无网格伽辽金法的连铸坯凝固计算方法

为考察无网格方法求解铸坯凝固过程的可行性,本文依据移动最小二乘和变分原理,推导并建立了基于无网格伽辽金法的结晶器内铸坯凝固过程二维非稳态传热/凝固数学模型。以小方坯凝固过程为对象,分别采用节点均匀布置、加密布置、随机布置方式,模拟分析了小方坯凝固过程的温度场变化,并将计算结果与参考解、有限元法数值解进行了对比,结果证实无网格伽辽金法在计算精度、自适应性、网格依赖性等方面均优于有限元法。研究结果为无网格方法应用于连铸过程的传热、凝固以及应力/应变行为的数值计算提供参考。      

Modeling of ingot development during the start-up phase of direct chill casting

Direct chill (DC) casting is a core primary process in the production of aluminum ingots. However, its operational optimization is still under investigation with regard to a number of features, one of which is the issue of curvature at the base of the ingot. Analysis of these features requires a computational model of the process that accounts for the fluid flow, heat transfer, solidification phase change, and thermomechanical anlaysis. This article describes an integrated approach to the modeling of all the preceding phenomena and their interactions     

基于反算热流的结晶器内流动--传热--凝固耦合模拟

基于Navier-Stokes动量方程和湍流低雷诺数k-ε方程,综合考虑能量守恒和钢液凝固与糊状区对流动过程的影响,建立了描述结晶器内钢液流动、传热及凝固过程的三维耦合数学模型.以实测温度和结晶器反问题模型计算出的热流为边界条件,模拟计算了结晶器内钢水的流动、传热和凝固行为.钢液流动决定结晶器内的温度和热流分布,铸坯凝固受钢液流动和结晶器热流双重因素的影响.建立的模型以及由此得到的铸坯凝固非均匀特征可为进一步考察浇铸过程中纵裂和其他表面缺陷提供借鉴和参考.      

异形坯连铸充型凝固过程数值模拟

利用CFD商用软件Flow-3d,对单双水口Q215钢750 mm×450 mm×120 mm异形坯连铸结晶器内钢水充型凝固过程进行数值模拟,得到了速度场、温度场的分布图和充填过程自由表面的位置和形状图。分析了单双水口模型对速度场及凝固的影响。结果表明,双水口模型可以减轻结晶器上部回流的强度,减小冲击深度,提高传热效率,加快结晶器内钢液的凝固速度,有助于提高铸坯的质量和提高拉速。     

Solidification in Soft-Contact Continuous Casting Mold with Alternating Electromagnetic Field

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结晶器内连铸坯的热和应力状态数值模拟

针对碳钢在连铸结晶器内的凝固过程,考虑铸坯和结晶器内的接触状态,利用ANSYS软件建立了完全热力耦合的三维稳态有限元模型,模拟出结晶器区域内的热和力学状态,包括铸坯应力场、气隙分布规律以及整个结晶器内钢液温度分布等。结果显示,铸坯出结晶器时坯壳外层处于压缩状态、内层处于拉伸状态,内外表面应力分别为279、311 MPa,凝固前沿处应力为3 MPa左右,处于材料的极限强度范围,有产生裂纹的可能。锥度结晶器有利于钢液凝固换热,采用0.7%/m的倒锥度设计后,气隙量较无锥度结晶器最多减少了42%。     

Determination of interface heat transfer coefficient between aluminum casting and graphite mold

To produce castings of titanium, nickel, copper, aluminum, and zinc alloys, graphite molds can be used, which makes it possible to provide a high cooling rate. No die coating and lubricant are required in this case. Computer simulation of casting into graphite molds requires knowledge of the thermal properties of the poured alloy and graphite. In addition, in order to attain adequate simulation results, a series of boundary conditions such as heat transfer coefficients should be determined. The most important ones are the interface heat transfer coefficient between the casting and the mold, the heat transfer coefficient between the mold parts, and the interface heat transfer coefficient into the environment. In this study, the interface heat transfer coefficient h between the cylindrical aluminum (99.99%) casting and the mold made of block graphite of the GMZ (low ash graphite) grade was determined. The mold was produced by milling using a CNC milling machine. The interface heat transfer coefficient was found by minimizing the error function reflecting the difference between the experimental and simulated temperatures in a mold and in a casting during pouring, solidification, and cooling of the casting. The dependences of the interface heat transfer coefficient between aluminum and graphite on the casting surface temperature and time passed from the beginning of pouring are obtained. It is established that, at temperatures of the metal surface contacting with a mold of 1000, 660, 619, and 190°C, the h is 1100, 4700, 700, and 100 W/(m² K), respectively; i.e., when cooling the melt from 1000°C (pouring temperature) to 660°C (aluminum melting point), the h rises from 1100 to 4700 W/(m² K), and after forming the metal solid skin on the mold surface and decreasing its temperature, the h decreases. In our opinion, a decrease in the interface heat transfer coefficient at casting surface temperatures lower than 660°C is associated with the air gap formation between the surfaces of the mold and the casting because of the linear shrinkage of the latter. The heat transfer coefficient between mold parts (graphite–graphite) is constant, being 1000 W/(m² K). The heat transfer coefficient of graphite into air is 12 W/(m² K) at a mold surface temperature up to 600°C.     

气隙对连铸坯凝固影响的有限元数值模拟

以连铸坯凝固传热有限元数学模型研究了铸坯角部形状和气隙对坯壳凝固行为的影响研究结果表明：采用有限元法离散铸坯圆角能更合理地反映铸坯角部的几何和换热条件，从而可以更准确地研究角部换热条件对铸坯凝固行为的影响。角部气隙显著地降低了坯壳表面的换热，使铸坯偏角区成为热节区。此热节区是铸坯凹陷、皮下裂纹等缺陷和漏钢事故发生的诱因。     

Effect of thermal conditions and alloying constituents (Ni,Cr) on macrosegregation in continuously cast high-carbon (0.8 Pct), low-alloy steel

The aim of this study was to investigate the influences of heat transfer, thermal gradient, solidification rate, and the addition of up to 1 pct Ni and 1 pct Cr on the solidification and macrosegregation of high-carbon (0.8 pct), low-alloy steel. Sixteen 13.6-kg laboratory ingots were horizontally and unidirectionally cast in a static moll, fitted on one face with a water-cooled copper chill to simulate a continuous casting mold. Thermocouples, placed in the chill and the mold, were used to calculate heat flux, thermal gradient, and solidification rate. The ingots were examined with respect to macro- and microstructures, distribution of phases, dendrite arm spacing, and solute element distribution. The extent of macrosegregation of carbon and sulfur was determined by wet chemical analysis of drillings, and a TANDEM VAN DE GRAAFF accelerator was used for A1, Si, P, V, S, C, Mn, Ni, and Cu. The extent of macrosegregation of these elements was correlated with heat transfer and thermodynamic distribution coefficient data.     

The effect of thermal contact resistance on the solidification process of a pure metal

The role of thermal contact resistance between a casting and a metal mold, as well as the effect of natural convection in the melt during solidification of a pure metal, is numerically studied. Numerical simulation is performed for a two-dimensional rectangular cavity using the coordinate transformation by boundary-fitted coordinate, and pure aluminum is used as the phase-change material. The influ-ences of thermal contact resistance on the interface shape and position, solidified volume fraction, streamlines, temperature field, and the local heat transfer are investigated.     

小方坯连铸机结晶器的研究

本文建立了铸坯凝固传热数学模型，模拟计算了铸坯温度场、坯壳厚度、热流场、坯壳热收缩应力场、坯壳与铜壁间气隙厚度；计算出的坯壳厚度与实测的坯壳厚度基本吻合，计算结果可为连铸机生产和连铸机设计提供参考。     

小方坯连铸机喷淋结晶器的研究

建立小方坯喷淋结晶器凝固传热数学模型，模拟计算了铸坯温度场、坯壳厚度、热流场，坯壳与铜壁间气隙厚度。计算坯壳厚度与实测坯壳厚度基本吻合；与普通水缝式结晶器相比，铸坯温度场均匀，坯壳厚度均匀，冷却强度有所提高。     

A study on heat source equations for the prediction of weld shape and thermal deformation in laser microwelding

In the area of laser welding, numerous studies have been performed in the past decades using either analytical or numerical approaches, or both combined. However, most of the previous studies were process oriented and modeled conduction and keyhold welding differently. In this research, various heat source equations that have been proposed in previous studies were calculated and compared with a new model. This is to address the problem of predicting, by numerical means, the thermomechanical behavior of laser spot welding for thin stainless steel plates. A finite-element model (FEM) code, ABAQUS, is used for the heat transfer and mechanical analysis with a three-dimensional plane assumption. Experimental studies of laser spot welding and measurement of thermal deformation have also been conducted to validate the numerical models presented. The results suggest that temperature profiels and weld deformation vary according to the heat source equation of the laser beam. For this reason, it is essential to incorporate an accurate model of the heat source.