Transient Thermo-fluid Model of Meniscus Behavior and Slag Consumption in Steel Continuous Casting

The behavior of the slag layer between the oscillating mold wall, the slag rim, the slag/liquid steel interface, and the solidifying steel shell, is of immense importance for the surface quality of continuous-cast steel. A computational model of the meniscus region has been developed, that includes transient heat transfer, multi-phase fluid flow, solidification of the slag, and movement of the mold during an oscillation cycle. First, the model is applied to a lab experiment done with a “mold simulator” to verify the transient temperature-field predictions. Next, the model is verified by matching with available literature and plant measurements of slag consumption. A reasonable agreement has been observed for both temperature and flow-field. The predictions show that transient temperature behavior depends on the location of the thermocouple during the oscillation relative to the meniscus. During an oscillation cycle, heat transfer variations in a laboratory frame of reference are more severe than experienced by the moving mold thermocouples, and the local heat transfer rate is increased greatly when steel overflows the meniscus. Finally, the model is applied to conduct a parametric study on the effect of casting speed, stroke, frequency, and modification ratio on slag consumption. Slag consumption per unit area increases with increase of stroke and modification ratio, and decreases with increase of casting speed while the relation with frequency is not straightforward. The match between model predictions and literature trends suggests that this methodology can be used for further investigations.     

Large Eddy Simulations of Double-Ruler Electromagnetic Field Effect on Transient Flow During Continuous Casting

Transient flow during nominally steady conditions is responsible for many intermittent defects during the continuous casting of steel. The double-ruler electromagnetic field configuration, or “FC-Mold EMBr,” is popular in commercial slab casting as it provides independent control of the applied static field near the jet and free surface regions of the mold. In the current study, transient flow in a typical commercial caster is simulated in the absence and in the presence of a double-ruler magnetic field, with rulers of equal strengths. Large eddy simulations with the in-house code CU-FLOW resolve the important transient behavior, using grids of over five million cells with a fast parallel solver. In the absence of a magnetic field, a double-roll pattern is observed, with transient unbalanced behavior, high surface velocities (~0.5 m/s), surface vortex formation, and very large surface-level fluctuations (~±12 mm). Applying the magnetic field suppresses the unbalanced behavior, producing a more complex mold flow pattern, but with much lower surface velocities (~0.1 m/s), and a flat surface level with small level fluctuations (<±1 mm). Nail board measurements taken at this commercial caster, in the absence of the field, matched reasonably well with the calculated results, both quantitatively and qualitatively.     

Hydrostatic, Temperature, Time-Displacement Model for Concrete Dams

This paper presents frequency domain solution algorithms of the one-dimensional transient heat transfer equation that describes temperature variations in arch dam cross sections. Algorithms are developed to compute the temperature T(x,t), spatial distribution, and time evolution for the “direct” problem, where the temperature variations are specified at the upstream and downstream faces, and for the “inverse” problem, where temperatures have been measured at thermometers located inside instrumented dam sections. The resulting nonlinear temperature field is decomposed in an effective average temperature, Tm(t), and a linear temperature difference, Tg(x,t), from which the dam thermal displacement response can be deducted. The proposed frequency domain solution procedures are able to reproduce an arbitrary transient heat response by appending trailing temperatures at the end of thermal signals, thus transforming a periodic heat transfer problem in a transient one. The frequency domain solution procedures are used to develop the HTT (hydrostatic, temperature, time) statistical model to interpret concrete dam-recorded pendulum displacements. In the HTT model, the thermal loads are arbitrary and can contain temperature drift or unusual temperature conditions. The explicit use of Tm(t) and Tg(x,t) in the HTT dam displacement model allows extrapolation for temperature conditions that have never been experienced by the dam before (within the assumption of elastic behavior). The HTT model is applied to the 131-m-high Schlegeis arch dam, and the results are compared with the HST (hydrostatic, seasonal, time) displacement model that is widely used in practice.     

Multiscale Modeling and Simulation of Directional Solidification Process of Turbine Blade Casting with MCA Method

Nickel-based superalloy turbine blade castings are widely used as a key part in aero engines. However, due to the complex manufacturing processes, the complicated internal structure, and the interaction between different parts of the turbine blade, casting defects, such as stray grains, often happen during the directional solidification of turbine blade castings, which causes low production yield and high production cost. To improve the quality of the directionally solidified turbine blade castings, modeling and simulation technique has been employed to study the microstructure evolution as well as to optimize the casting process. In this article, a modified cellular automaton (MCA) method was used to simulate the directional solidification of turbine blade casting. The MCA method was coupled with macro heat transfer and micro grain growth kinetics to simulate the microstructure evolution during the directional solidification. In addition, a ray tracing method was proposed to calculate the heat transfer, especially the heat radiation of multiple blade castings in a Bridgman furnace. A competitive mechanism was incorporated into the grain growth model to describe the grain selection behavior phenomena of multiple columnar grains in the grain selector. With the proposed models, the microstructure evolution and related defects could be simulated, while the processing parameters optimized and the blade casting quality guaranteed as well. Several experiments were carried out to validate the proposed models, and good agreement between the simulated and experimental results was achieved.     

Modeling of Electromagnetic Field and Liquid Metal Pool Shape in an Electroslag Remelting Process with Two Series-Connected Electrodes

A three-dimensional finite-element model has been developed to understand the electromagnetic field and liquid metal pool shape in an electroslag remelting (ESR) process with two series-connected electrodes. The magnetic vector potential is introduced into the Maxwell’s equations, and the nodal-based method is used to solve a three-dimensional harmonic electromagnetic field. The heat transfer of the solidifying processes of ingot is modeled by a source-based enthalpy method, and the Joule heating is included in an inner source. The results show the main part of the current flows through the slag cap and a little enters into ingot in a two-series-connected electrode ESR system. As the interaction of self-induced and mutual-induced of two electrodes occurs, the skin effect is significantly suppressed by the neighbor effect. A symmetrical pattern of magnetic flux density in a two-series-connected electrode ESR system is displayed. The magnetic flux density between two electrodes is reinforced and reduced at the outside of two electrodes. The maximum Joule heat power density is located at the interface of slag and electrodes, and it decreases with an increase of the electrode immersion depth. The averaged Joule heat power density increases when slag cap thickness is reduced. With the increase of ingot height, the liquid metal pool shape changes from arc shaped to “V” shaped. When the ingot height is more than the diameter in the ESR processes, the liquid metal pool shape is constant.     

Tree-ring formation during vacuum arc remelting of INCONEL 718: Part II. Mathematical modeling

Tree-ring grain formations, a common microstructural feature found in vacuum arc remelted (VAR) ingots of nickel-based superalloys, were characterized experimentally in Part I. The experimental observations led to the conclusion that tree rings are chains of fine-equiaxed grains interrupting a predominately columnar-dendritic structure. Several possible mechanisms for their formation were considered, and their implications correlated with experimental observations. The most likely mechanism was determined to be that process perturbations cause changes in the thermal (or solutal) fields ahead of the columnar-dendrite tips, temporarily altering the conditions to increase grain nucleation and, hence, forming fine-equiaxed grains. In this article, Part II, a multiscale mathematical model of the VAR process is presented that simulates the macroscopic heat and momentum transport and combines it with a mesoscopic model of the nucleation and growth of grains. Using this multiscale model, the transient development of the VAR grain structure was simulated with varying levels and durations of fluctuations in the principal process parameters: power supply, arc focus, melt rate, and the ingot-crucible heat-transfer coefficient. The simulations were shown to agree with optical and electron back-scattered diffraction (EBSD) measurements of grain morphology and crystallographic orientation. The model results predict that tree-ring structures (consistent with those observed experimentally) can be formed by process perturbations that alter the thermal field conditions at the solidification front. A sensitivity study of the effect of the different process fluctuations on the microstructure formation was performed, providing process maps predicting the range of conditions where tree rings will not form.     

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.     

圆坯凝固末端电磁搅拌作用下的流动与传热行为

以特殊钢圆坯连铸为研究对象, 建立了研究凝固末端电磁搅拌作用效果的三维耦合数值模型.利用分段计算模型获得末端电磁搅拌区域钢液流动与凝固的实际状态, 并采用达西源项法处理凝固末端钢液在糊状区的流动, 研究了不同电磁搅拌工艺参数下的电磁场分布及钢液的流动与传热特征.通过测量搅拌器中心线磁感应强度和铸坯表面温度验证了模型的准确性.研究结果表明: 电流强度每增加100 A, 搅拌器中心磁感应强度增加19.05 mT, 电磁力随着电流强度的增加显著增大.在20~40 Hz范围, 随着电流频率的提高, 中心磁感应强度略微下降, 但电磁力仍有所增加.在搅拌器区域, 液相穴内的钢液在切向电磁力的作用下旋转流动, 其切向速度随着电流强度和频率的增加而变大.末端电磁搅拌可促进钢液在圆坯径向的换热, 随着电流强度和频率的提高, 铸坯中心轴线上的钢液温度降低, 同时末端搅拌位置处的中心固相分率增加.      

430不锈钢凝固显微组织模拟的3D CAFE模型

在同时考虑传热、流动和溶质扩散基础上建立了预测铁素体不锈钢多元合金凝固组织的3D CAFE模型,揭示了430不锈钢凝固过程中温度、固相率及晶粒形貌的变化规律.模型中采用高斯分布描述形核密度与过冷度的关系,应用KGT模型描述枝晶的生长过程.根据Fe-C-17% Cr平衡相图确定了430不锈钢的凝固路径,在考虑凝固收缩的基础上预测了铸锭的疏松和缩孔分布.组织模拟结果与实际铸锭基本一致,二者的温度变化和组织结构特征也基本吻合.     

高频磁场下连铸保护渣润滑行为数学模型

摘要：为了研究高频磁场下连铸保护渣在结晶器内的润滑状况，建立了高频磁场下连铸保护渣润滑行为数学模型，并应用该数学模型研究了初始凝固时磁场作用下渣道宽度、弯月面高度、渣道动压、渣耗、摩擦力等因素对保护渣润滑行为的影响。结果发现，磁场的作用拓宽了保护渣渣道宽度，增大了弯月面高度，使保护渣渣道入口及出口宽度增加，使初始凝固点下移，改善了传热条件有利于铸坯表面质量提升；磁场的作用减小了因结晶器振动而产生的正压和负压，并且正、负压都是随着磁场强度的增大而减小，但磁场强度存在一个最佳值；磁场的作用增大了渣耗量，改善了铸坯与结晶器之间的润滑；铸坯与结晶器之间摩擦力随着磁场强度的增大而减小，当磁场强度为40mT时，总摩擦力减小趋于平缓，因此磁场强度为40mT左右时对减小摩擦力的作用效果较好。     

Three-dimensional transient model for arc welding process

A direct computer simulation technique, discrete element analysis (DEA), was utilized in the development of a transient multidimensional (2-D and 3-D) mathematical model for investi-gating coupled conduction and convection heat transfer problems associated with stationary and moving arc welding processes. The mathematical formulation considers buoyancy, electro-magnetic, and surface tension driving forces in the solution of the overall heat transfer conditions in the specimen. Furthermore, the formulation of the model allows realistic consideration of the geometrical variations in the workpiece. The model treats the -weld pool surface as a truly deformable free surface, allowing for the prediction of the weld surface deformations such as the “weld crown.≓ A marked element formulation was employed to monitor the transient de-velopment of the weld pool as determined by the latent heat considerations and the calculated velocities in the weld pool. The model was utilized to simulate the heat and fluid flows in the weld pool that occur during stationary (spot) and moving (linear) gas tungsten-arc welding. Also, the present analysis considers a simple rectangular specimen and a geometrically complex specimen to demonstrate the capability of the model to simulate realistic 3-D arc welding prob-lems. The results of the present investigation clearly demonstrate the significant influence of the heat and fluid flows and the specimen geometry on the development of the weld. Comparison of the predicted and the experimentally observed fusion zone and heat-affected zone (HAZ) geometries indicate good agreement.     

Arc Distribution During the Vacuum Arc Remelting of Ti-6Al-4V

Currently, the temporal distribution of electric arcs across the ingot during vacuum arc remelting (VAR) is not a known or monitored process parameter. Previous studies indicate that the distribution of arcs can be neither diffuse nor axisymmetric about the center of the furnace. Correct accounting for the heat flux, electric current flux, and mass flux into the ingot is critical to achieving realistic solidification models of the VAR process. The National Energy Technology Laboratory has developed an arc position measurement system capable of locating arcs and determining the arc distribution within an industrial VAR furnace. The system is based on noninvasive magnetic field measurements and a VAR specific form of the Biot–Savart law. The system was installed on a coaxial industrial VAR furnace at ATI Albany Operations in Albany, OR. This article reports on the different arc distributions observed during production of Ti-6Al-4V. It is shown that several characteristic arc distribution modes can develop. This behavior is not apparent in the existing signals used to control the furnace, indicating the measurement system is providing new information. It is also shown that the different arc distribution modes observed may impact local solidification times, particularly at the side wall.     

Modeling macro-and microstructures of Gas-Metal-Arc Welded HSLA-100 steel

Fluid flow and heat transfer during gas-metal-arc welding (GMAW) of HSLA-100 steel were studied using a transient, three-dimensional, turbulent heat transfer and fluid flow model. The temperature and velocity fields, cooling rates, and shape and size of the fusion and heat-affected zones (HAZs) were calculated. A continuous-cooling-transformation (CCT) diagram was computed to aid in the understanding of the observed weld metal microstructure. The computed results demonstrate that the dissipation of heat and momentum in the weld pool is significantly aided by turbulence, thus suggesting that previous modeling results based on laminar flow need to be re-examined. A comparison of the calculated fusion and HAZ geometries with their corresponding measured values showed good agreement. Furthermore, “finger” penetration, a unique geometric characteristic of gas-metal-arc weld pools, could be satisfactorily predicted from the model. The ability to predict these geometric variables and the agreement between the calculated and the measured cooling rates indicate the appropriateness of using a turbulence model for accurate calculations. The microstructure of the weld metal consisted mainly of acicular ferrite with small amounts of bainite. At high heat inputs, small amounts of allotriomorphic and Widmanstätten ferrite were also observed. The observed microstructures are consistent with those expected from the computed CCT diagram and the cooling rates. The results presented here demonstrate significant promise for understanding both macro-and microstructures of steel welds from the combination of the fundamental principles from both transport phenomena and phase transformation theory.     

Macrosegregation in Rotated Remelted Ingots

A computer model is presented for predicting macrosegregation in rotated electroslag or vacuum arc remelted ingots. Sample calculations of segregation are carried out for ingots of the model alloy Sn-12 pet Pb in which the liquid density increases during solidification and for two hypothetical alloys; in one, the liquid density decreases during solidification, and in the other, liquid density first increases and then decreases during solidification. In alloys such as Sn-Pb in which liquid density increases during solidification, segregation is positive at the ingot centerline and if solidification is sufficiently slow, “freckles” form near the centerline. Positive segregation and freckles are found at the outer periphery of the ingot when liquid density decreases during solidification. Positive segregation and freckles are found at midradius when liquid density first increases and then decreases during solidification, and when the solidus isotherm changes shape abruptly at midradius (with density increasing during solidification). Ingot rotation, by introducing a radial component to the force field, alters interdendritic flow behavior and therefore macrosegregation. Modest rotation speeds eliminate “freckles” and reduce macrosegregation in all modeling studies conducted. Greater rotational speeds can accentuate the segregation. Experiments were conducted on simulated remelted ingots of Sn-Pb alloy. The ingots were 8 cm diam, rotated at speeds up to 119 rpm and solidified at rates from 5.3 × 10^?3 to 1.36 × 10^?2 cm/s. Segregation behavior obtained agrees qualitatively and quantitatively with theory.     

Modeling of transient flow phenomena in continuous casting of steel

This paper describes initial efforts to develop and apply 3D finite-difference models to simulate transient flow in the mold. These transient flow phenomena include flow pattern oscillations caused by sudden changes in nozzle inlet conditions and rapid fluctuations in the molten steel⧹flux interface level at the top surface of the mold. The flow model incorporates interactions with other transport phenomena, including turbulence, superheat removal and argon gas bubble injection. Predictions are shown for the oscillatory evolution of the flow pattern from biased steady flow to symmetrical steady flow after a sudden change in inlet conditions. In addition, the predicted turbulent kinetic energy levels at steady state are shown to correlate with measured surface level fluctuations. The effect of processing conditions are consistent with experimental findings. Without argon, the greatest level fluctuations are found near the narrow face, while increased argon moves the maximum towards the center. Fluctuations decrease with deeper submergence and lower casting speed. These transient phenomena are important because they may lead to defects in the final steel product from entrainment of slag, disruption of solidification at the meniscus and non-uniform heat transfer.     

Effect of Solidification Texture on the Magnetostrictive Behavior of Galfenol

This study investigates the magnetostrictive functionality of crystallographic textures developed by directional solidification of a vacuum-melted galfenol cast button. A polycrystalline Fe_82.4Ga_17.6 alloy was melted using vacuum arc melting and solidified in a water-cooled copper mold. Optical metallography confirmed the development of large columnar grains in the solidification microstructure. Phase constitution and magnetic domain structures of sample were studied by X-ray diffraction (XRD) and magnetic force microscopy (MFM). The results showed that the cast button has a disordered body-centered cubic (bcc) (A2) single-phase structure that consisted of a combination of well-aligned stripe-like and maze-like magnetic domains. To investigate the magnetostriction behavior, a couple of pins were cut along columnar grains as well as in the transverse direction. Magnetostriction was measured in the presence of an externally applied magnetic field. It was found that pins cut along the columnar grains comprised very high magnetostriction, whereas transverse pins had lower magnetostriction against the applied field.     

小方坯连铸末端电磁搅拌综合控制模型

 为解决连铸生产过程中因拉速、过热度等工艺条件频繁波动而导致铸坯凝固末端发生变化,使得末端电磁搅拌(FEMS)难以产生稳定良好的搅拌效果的问题,提出一种FEMS综合控制模型。此模型通过在线凝固传热模型计算得到FEMS安装处的坯壳厚度SF,然后采用基于目标坯壳厚度控制的二冷模型调节二冷水量使SF保持稳定,并根据不同的SF调节FEMS的电流和频率,使FEMS的使用效果达到最优值。采用射钉试验验证了数学模型的计算精度。计算机模拟及现场应用的结果表明,在160mm×160mm小方坯连铸机上,此综合控制模型能够使FEMS安装处的坯壳厚度保持稳定,目标坯壳厚度设定为52mm时,有效提高铸坯的内部质量。     

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。      

电磁搅拌对电渣重熔钢锭温度场的影响

建立了电磁搅拌条件下电渣重熔钢锭凝固过程数学模型。利用Visual Basic编程模拟分析了旋转电磁搅拌下15Mn钢的电渣重熔凝固过程,结果表明:未施加磁场时,模拟结果与实验结果较吻合;施加磁场时,电磁搅拌加强了钢液内部传热,熔池变平坦,有利于消除电渣锭宏观偏析和缩孔等缺陷,同时有利于晶核发展成等轴晶组织。     

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.