Modelling of crystal growth during the ribbon formation in planar flow casting

The crystalline solidification during rapid substrate quenching in planar-flow casting was simulated by using a numerical model based on a rapid solidification algorithm and the infinite viscosity approximation. The calculation shows that the existence of a real melt puddle shape suppresses undercooling and recalescence on the melt surface as well as on the solidifying ribbon. The melt puddle length is mainly determined by the heat-transfer coefficient. With increasing heat transfer across the melt – substrate interface the melt puddle length decreases. If the formation rate of critical nuclei on the substrate surface is low compared to the present cooling rate a large undercooling may occur. The performed calculations reveal that an undercooling of up to 600 K does neither affect the temperature distribution on the surface of the melt nor the melt puddle length, perceptibly. Therefore, investigations on microstructural features of rapidly quenched metals might give detailed information on the amount of undercooling present at the beginning of solidification.     

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.     

Issues on Puddle Formation During Rapid Solidification of Fe–Si–B–Nb–Cu Alloy Using Planar Flow Melt Spinning Process

The present investigation deals with the processing of rapidly solidified 10?C40?mm wide, 30?C50???m thick and 10?C30?m long continuous amorphous ribbons of Fe?CSi?CB?CNb?CCu alloy using a planar flow melt spinning (PFMS) equipment. As the formation of quality amorphous ribbon depends on the melt puddle formed between the nozzle and the rotating copper wheel, the effect of different processing parameters such as nozzle wheel gap, ejection pressure etc. on the shape and stability of puddle has been studied using a high-speed imaging system and correlated with ribbon formation. Simultaneously, a two-dimensional numerical model has been developed to simulate the puddle formation during the PFMS process. The model is based on a computational fluid dynamics technique, called volume of fluid using transient heat transfer and fluid flow equations with the evolution of free boundaries. Different simulations have been performed to study the effect of process parameters on the puddle formation. The simulated results have been verified with the experimental observations considering same set of process parameters. It has been observed that the present simulations have produced exact replica of the experimental observations. Further parametric analysis as well as analysis of simulated result has been carried out to understand how the different process parameters affect the formation of quality amorphous ribbons during PFMS process.     

A mathematical model of the planar flow melt spinning process

The Planar Flow Melt Spinning Process for the Rapid Solidification of metallic materials is analyzed using a mathematical model based on the principles of capillary fluid dynamics and solidification heat transfer. The results suggest the existence of a region of slowly recirculating flow inside the melt puddle which acts as a lubricant between the nozzle and the wheel. Markedly different thermal conditions across the ribbon thickness are also predicted by the model, as are the resultant microstructural variations across such thickness. The results of the model compare well with the available experimental evidence. The model is sufficiently general as to be immediately applicable to the study of other meniscus controlled continuous casting processes.     

Effect of Nozzle Angle on Flow Field and Temperature Distribution in a Billet Mould when using Swirl Flow

Recently, interesting effects have been noted in studies of swirl flow, particularly regarding billet moulds when considering a specific divergent angle of the immersion nozzle. Therefore, in the present work a numerical analysis and water model study of the mould region of a continuous casting apparatus are performed with changing the outlet divergent angles of the immersion nozzle using swirling flow in the pouring tube, to control the heat and mass transfer in the continuous casting mould. To make our studies consistent with the previous research, which was done based on a square billet, this time we investigate round billets. The results show that the distance from the meniscus of the centres of both the lower and upper circulation loops decreases systematically with increasing the divergent angle. This, in turn, leads to: (i) a more active heat and mass transport near the meniscus (particularly over 100°); (ii) a gradual change from a concentric circulation to a more clearly logarithmic spiral from the mould wall to the nozzle on the meniscus, which leads to more active heat and mass transfer; (iii) a decreased penetration depth of nozzle outlet flow (even at a comparatively small divergent angle such as 20°) and a superheat dissipation in the melt.     

圆坯结晶器水口优化的模拟研究

以大圆坯结晶器为原型,采用数值模拟与物理模拟相结合的方法,分别研究了使用直通式水口和4孔旋转水口时该圆坯结晶器内钢液流场和温度场的分布情况,对比分析了2种水口的优劣。数值模拟和物理模拟结果表明,使用目前常用的直通型水口时钢水冲击深度大,易在弯月面处形成死区,不利于圆坯内部及表面质量的提高;4孔旋转水口比直通水口的钢液冲击深度浅,回旋区位置明显比直通水口更靠近自由液面,这将有利于夹杂物的上浮去除和热区中心的上移。温度场模拟结果显示,使用旋转水口时自由液面温度比直通型水口高14℃,更有利于结晶器内钢水过热耗散及保护渣的熔化,可防止液面结壳。     

Heat Flow Model for Surface Melting and Solidification of an Alloy

The heat flow model previously developed for a pure metal is extended to the solidification of an alloy over a range of temperatures. The equations are then applied to rapid surface melting and solidification of an alloy substrate. The substrate is subjected to a pulse of stationary high intensity heat flux over a circular region on its bounding surface. The finite difference form of the heat transfer equation is written in terms of dimensionless nodal temperature and enthalpy in an oblate spheroidal coordinate system. A numerical solution technique is developed for an alloy which precipitates a eutectic at the end of solidification. Generalized solutions are presented for an Al-4.5 wt pct Cu alloy subjected to a uniform heat flux distribution over the circular region. Dimensionless temperature distributions, size and location of the “mushy” zone, and average cooling rate during solidification are calculated as a function of the product of absorbed heat flux,q, the radius of the circular region, a, and time. General trends established show that for a given product ofqa all isotherms are located at the same dimensionless distance for identical Fourier numbers. The results show that loss of superheat and shallower temperature gradients during solidification result in significantly larger “mushy” zone sizes than during melting. Furthermore, for a given set of process parameters, the average cooling rate increases with distance solidified from the bottom to the top of the melt pool.     

A 3D Mathematical Modeling on Meniscus Solidification and Heat Transfer in Continuous Casting Chamfered Mold of Slab

Herein, a 3D mathematical model is established to elucidate the meniscus solidification and heat transfer in the chamfered mold. The fluid flow, heat transfer, the solidification of steel, the oscillation of the mold, and the steel–slag interfacial tension are considered, and the meniscus behavior on different longitudinal sections and cross sections is discussed. Under the influence of the upper roll flow, the height of the steel level increases from submerged entry nozzle to narrow face, which affects the distribution of the oscillation mark on the surface of the shell. With the mold chamfer and two new corners, the thickness of the slag film at the corner 1 with angle of 123.7° is the largest, and the shell thickness is the smallest, which is related to the 3D profile of the meniscus near the corner. The largest heat flux is located at 10–14 mm below the initial level of liquid steel and is below 3.0 MW m⁻². The heat flux at the corner 1 with small obtuse angle is the smallest on the same cross section, indicating that small obtuse angle near the corner resulted in the low heat transfer.     

Effect of holding time and surface cover in ladles on liquid steel flow in continuous casting tundishes

Mathematical modeling of fluid flow and heat transfer of melt in a typical two-strand slab caster tundish has been done for a complete casting sequence. The complete casting sequence consists of 1 minute of tundish emptying period during the ladle transfer operation followed by 1 minute of tundish filling period by the new ladle and pouring at the normal operating level of the tundish for 46 minutes. The effect of varying ladle stream temperature conditions on the melt flow and heat transfer in the continuous casting tundish has been studied. When the ladle stream temperature decreases appreciably over the casting period, corresponding to heat loss of the melt in the ladle from the top free surface, the incoming melt temperature becomes lower than that of the melt in the bulk of the tundish after about 30 minutes from the start of teeming. This results in melt flow along the bottom of the tundish instead of the normal free surface directed flow. The ladle melt stream temperature shows little variability when the ladle has an insulated top. Corresponding to this situation, the temperature of the incoming melt remains higher than that of the melt in the bulk of the tundish and the normal free surface directed flow is maintained throughout the casting period. The product cast under such condition is expected to have a uniformly low inclusion content. The heat loss condition from the top of the ladle has been shown to be the dominant factor in determining fluid flow and heat-transfer characteristics of the melt in the tundish rather than the holding time of the melt in the ladle. Formerly Graduate Student, Department of Materials Science and Engineering, Ohio State University     

Mathematical Modeling of Multi-sized Argon Gas Bubbles Motion and Its Impact on Melt Flow in Continuous Casting Mold of Steel

The 3D turbulence k-ε model flow of the steel melt(continuous phase)and the trajectories of individual gas bubbles(dispersed phase)in a continuous casting mold were simulated using an Eulerian-Lagrangian approach.In order to investigate the effect of bubble size distribution,the radii of bubbles are set with an initial value of 0.1-2.5mm which follows the normal distribution.The presented results indicate that,in the submerged entry nozzle(SEN),the distribution of void fraction is only near the wall.Due to the fact that the bubbles motion is only limited to the wall,the deoxidization products have no access to contacting the wall,which prevents clogging.In the mold,the bubbles with a radius of 0.25-2.5mm will move to the top surface.Larger bubbles issuing out of the ports will attack the meniscus and induce the fluid flows upwards in the top surface near the nozzle.It may induce mold powder entrapment into the mold.The bubbles with a radius of 0.1-0.25mm will move to the zone near the narrow surface and the wide surface.These small bubbles will probably be trapped by the solidification front.Most of the bubbles moving to the narrow surface will flow with the ascending flow,while others will flow with the descending flow.     

狭缝射流冲击柱状凸形表面流动换热特性

采用数值方法研究了狭缝射流冲击柱状凸形表面的流动换热特性,通过四种湍流模型计算结果与实验数据对比,确定了湍流模型适用性.以压力梯度分布为依据,重点分析了狭缝射流沿柱状凸形表面的流动结构和边界层分离特点及柱状凸形表面的强化换热特性.结果表明:RNG k-ε和Realizable k-ε模型具有预测适应性;狭缝射流冲击至柱状凸形表面,气体沿表面运动,速度降低,并在流动下游发生边界层分离;量纲一的逆压梯度随量纲一的曲率半径(D/B)的减小而增大,使得边界层分离更早出现;驻点区域换热Nu随量纲一的曲率半径(D/B)的减小而获得增强,但流动进入下游后,D/B对换热基本无影响;压力梯度是影响狭缝射流冲击柱状凸形表面换热分布的重要因素.      

Heat Transfer and Cooling Rate Model of Flow Melt on Vibration Wall

In this paper, a model of heat transfer of melt flow on a vibration wall has been established. Calculation results show that the temperature boundary layer thickness decreases with the increase of vibration frequency and amplitude. As the vibration frequency and amplitude increase, the heat transfer coefficient between alloy melt and slope and between cooling water and slope increase. Cooling rate of melt can reach 400-600 K/s which belong to the sub-rapid solidification regime. The heat transfer mode doesn’t change during the flow process, so vibration not only strengthens the cooling rate of melt, but also stabilizes heat transfer between melt and slope. The grain size of solidification microstructure decreases with increasing vibration intensity, which indicates that vibration increases cooling rate and accelerates nucleation rate. So, the established model agrees with verification experiment, and can relatively well explain the heat transfer and cooling rate of melt flow on vibration plate.     

旋流水口对圆管坯连铸结晶器内钢水流场的影响

借助于流体力学分析软件Fluent,在圆管坯连铸浸入式水口上施加电磁力,对结晶器内钢水产生电磁搅拌作用使模型水口出流成螺旋状态的钢水流场进行了数值模拟。结果表明:旋流式水口有利于改善结晶器内的流场,有效降低冲击深度,增大液流向弯月面区域的回流和热流上传,提高了液面的活跃程度,增强钢水表面融渣的效果。     

大钢锭凝固界面换热系数的数值模拟

基于热-黏弹塑性本构方程建立了大钢锭凝固时热-流-力耦合的3D有限元模型,并对8.5t钢锭浇注过程中不同位置处热流密度、气隙宽度和界面换热系数的变化规律进行了模拟分析。结果表明,钢水与钢锭模刚刚接触时的热流密度和换热系数最大,二者随后迅速下降,且角部区域的下降趋势略大于面部。凝固初期时热流密度和换热系数的最大值位置并非位于面部中心,而是在1/4宽度处;由于宽面对钢水静压力的抵抗作用小于窄面,其界面热流密度和换热系数也略大于窄面。凝固中后期时,换热系数的区域差异逐渐趋于不明显。同时,建立了基于凝固时间和界面温度的平均换热系数的反算模型。应用2个模型所求结果计算的钢锭和钢锭模温度变化与实测值及热-流-力耦合模型结果基本一致。进一步研究发现,界面换热系数随温度的变化规律可推广应用到3~30t钢锭的模拟研究中,计算结果与实际更为符合。     

High-speed temperature measurements during rapid solidification of iron-silicon ribbons,produced by planar flow casting

In order to investigate the melt undercooling and the non-equilibrium solidification of crystalline Fe 5 wt.% Si melt spun ribbons, produced by planar flow casting (PFC), high speed temperature measurements and appropriate process simulations have been performed. Using a rotating fibre optical system with a fast response double pyrometer, the temperature radiation of the solidifying ribbon during the casting process has been recorded with a measuring frequency of 50 kHz. The obtained cooling curves have been interpreted by computer simulations. It is shown that with increasing wheel temperature the overall cooling becomes more efficient. This is caused by an improved wetting behaviour of the melt-wheel system and an increase in the heat transfer coefficient at the interface of the solidifying ribbon and the wheel from 6 · 10⁴ to about 2 · 10⁵ W/(m²K). The solidification of 100 to 200 μm thick ribbons takes place in a time interval of 2 to 5 ms. The average growth rate varies between 10 and 60 mm/s. The high cooling rate results in a fine dendritic solidification morphology with diminishing microsegregations.     

Rapid melting and solidification of surface due to stationary heat flux

A general two-dimensional computer heat flow model is developed in an oblate spheroidal coordinate system for rapid melting and subsequent solidification of the surface of a semiinfinite solid subjected to a high intensity heat flux over a circular region on its bounding surface. Generalized numerical solutions are presented for an aluminum substrate subjected to both uniform and Gaussian heat flux distributions. Temperature distributions, melt depth and geometry, and melting and solidification interface velocities are calculated as a function of applied heat flux, radius of the circular region, and time. It is shown that the important melting and solidification parameters are a function of the product of the absorbed heat flux, q, and the radius of the circular region, a. General trends established show that melt depth perpendicular to the surface is inversely proportional to the absorbed heat flux for a given temperature at the center of the circular region. Dimensionless temperature distributions and the ratio of liquid-solid interface velocity to absorbed heat flux,R/q, as a function of dimensionless melt depth remain the same if the productqa is kept constant, whileq anda are varied. For a given total power absorbed melting and solidification parameters are compared for uniform and Gaussian heat flux distributions. For a given temperature at the center of the circular region both melt depth and width are smaller for the Gaussian distribution while temperature gradients and interface velocities are larger. Formerly Graduate Research Assistant, Department of Mechanical and Industrial Engineering, University of Illinois. Formerly Research Associate, Department of Metallurgy and Mining Engineering,University of Illinois. Formerly Professor at the University of Illinois, Urban, IL.     

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

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连铸结晶器内钢液流动、凝固和夹杂物的分布

 建立并求解动量、热量和质量传输耦合模型,研究了连铸结晶器内钢液流动、传热、凝固、溶质输送和夹杂碰撞长大行为。数值结果表明,受钢液流动的影响,在连铸机内钢液温度、碳浓度和夹杂物的空间分布与钢水流动特征相似,也可分为上下两个循环区。但是其分布具有各自的特点。在涡心处,钢液温度较低,碳浓度较高,夹杂物体积浓度和数量密度较低。在弯月面处,钢液温度较低,碳浓度较高,夹杂物的体积浓度和数量密度较低。在结晶器出口处的凝固坯壳内,夹杂物的浓度和数量密度分布极不均匀,存在阶跃现象,这与冲击点处凝固坯壳的重熔有关。     

Mechanisms of initial melt/substrate heat transfer pertinent to strip casting

An experimental study of initial solidification of 304 stainless steel melts in direct contact with copper substrates under conditions approximating the meniscus region of a strip caster has highlighted the importance of interfacial heat transfer during the first 30 ms of contact. The mechanisms governing initial heat transfer are strongly influenced by dynamic wetting phenomena. This has been illustrated experimentally by the effects of the buildup and melting of oxide films such as manganese silicates at the interface during successive immersions, by the role of surface active agents such as tellurium in the melt, and by the use of specially designed substrate textures to control contact areas. This article is based on a presentation made in the “Geoffrey Belton Memorial Symposium,” held in January 2000, in Sydney, Australia, under the joint sponsorship of ISS and TMS.