Modeling transient slag-layer phenomena in the shell/mold gap in continuous casting of steel

Mold-slag friction and fracture may cause heat-transfer variations in continuous casting, which leads to steel shell temperature and stress variations, resulting in surface cracks. Analytical transient models of liquid slag flow and solid slag stress have been coupled with a finite-difference model of heat transfer in the mold, gap, and steel shell to predict transient shear stress, friction, slip, and fracture of the slag layers. The models are validated by comparing with numerical models and plant measurements of mold friction. Using reported slag-fracture strength and time-temperature-transformation (TTT) diagrams, the models are applied to study the effect of casting speed and mold-powder viscosity properties on slag-layer behavior between the oscillating mold wall and the solidifying steel shell. The study finds that liquid-slag lubrication would produce negligible stresses. A lower mold-slag consumption rate leads to high solid friction and results in solid-slag-layer fracture and movement below a critical value. Crystalline slag tends to fracture near the meniscus and glassy slag tends to fracture near the mold exit. A medium casting speed may be the safest to avoid slag fracture, due to its having the lowest critical lubrication consumption rate. The high measured friction force in operating casters could be due to three sources: an intermittent moving solid slag layer, excessive mold taper, or mold misalignment. Other symbols are defined in Table I     

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.     

Heat-transfer and solidification model of continuous slab casting: CON1D

A simple, but comprehensive model of heat transfer and solidification of the continuous casting of steel slabs is described, including phenomena in the mold and spray regions. The model includes a one-dimensional (1-D) transient finite-difference calculation of heat conduction within the solidifying steel shell coupled with two-dimensional (2-D) steady-state heat conduction within the mold wall. The model features a detailed treatment of the interfacial gap between the shell and mold, including mass and momentum balances on the solid and liquid interfacial slag layers, and the effect of oscillation marks. The model predicts the shell thickness, temperature distributions in the mold and shell, thickness of the resolidified and liquid powder layers, heat-flux profiles down the wide and narrow faces, mold water temperature rise, ideal taper of the mold walls, and other related phenomena. The important effect of the nonuniform distribution of superheat is incorporated using the results from previous three-dimensional (3-D) turbulent fluid-flow calculations within the liquid pool. The FORTRAN program CONID has a user-friendly interface and executes in less than 1 minute on a personal computer. Calibration of the model with several different experimental measurements on operating slab casters is presented along with several example applications. In particular, the model demonstrates that the increase in heat flux throughout the mold at higher casting speeds is caused by two combined effects: a thinner interfacial gap near the top of the mold and a thinner shell toward the bottom. This modeling tool can be applied to a wide range of practical problems in continuous casters.     

Modelling of steel shrinkage and optimisation of mould taper for high speed continuous casting

Abstract

In high speed continuous casting, optimisation of mould taper is key for intensifying heat transfer and for improving the quality of the cast products. Mathematical modelling has been carried out by combining heat transfer, steel shrinkage and parabolic continuous taper model in order to optimise the mould taper profile. These models have been assembled to a set of software, the inputs of which include the steel grade, casting speed, casting temperature, length and the cross-section of mould tube, while the outputs consist of surface temperature of the strand, thickness of solidified shell, thermal linear expansion coefficient, steel shrinkage, distortion of the mould tube wall, the actual air gap, total taper and the continuous taper profile. Optimum mould taper has a parabolic profile which is tapered inwards that changes continuously along the length of the strand in order to achieve reduction in air gap while avoiding distortion of the mould tube.     

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%。     

提高亚包晶钢板坯拉速对结晶器传热的影响

通过对提高亚包晶钢AQ钢种230 mm×1200 mm板坯拉速试验过程中结晶器冷却水参数、铜板测温等数据进行适时记录,并与数学模型及ANSYS商业软件相结合,研究了提高拉速对结晶器平均热流、局部热流、铜板温度场以及坯壳厚度的影响。结果表明,拉速由1.3m/min提高到1.5m/min时,平均热流增加0.1 MW/m²左右,宽边弯月面区域局部热流增加0.13 MW/m²,但均在合理范围内,这与采用高碱度高结晶温度的试验保护渣有关;结晶器窄/宽面平均热流比超过0.9,应适当减少结晶器锥度;宽面坯壳厚度平均减薄4 mm左右,应严格控制结晶器传热强度,以保证连铸工艺稳定和铸坯质量。     

高速连铸结晶器内凝固传热行为及其均匀性控制

从分析高拉速包晶钢板坯连铸结晶器内凝固传热行为特征入手,首先阐明拉速对结晶器内的界面热阻、凝固坯壳的温度与应力分布的影响规律,研究发现拉速超过1.6 m·min?1时,界面热阻明显增加,拉速由1.4 m·min?1提升至1.6 m·min?1和1.8m·min?1时,出结晶器坯壳厚度相应减少约10%,其发生漏钢的危险不断增加;在此基础上,阐述了结晶器的内腔结构、保护渣、振动与液面控制等控制结晶器内坯壳凝固均匀性的相关技术。要实现高速连铸,首要应考虑结晶器内腔结构的优化设计,使其能更好地迎合凝固坯壳的生长,研制适合包晶钢等凝固特点的专用连铸保护渣至关重要,铸坯鼓肚控制也是保障高拉速液面稳定的关键。      

连续铸钢过程中结晶器的传热研究

 为了研究结晶器内壁温度的分布,设计了模拟结晶器工作过程的实验装置,并进行了实验。实验结果表明,结晶器内壁温度趋近于冷却水温度。基于实验,推导了结晶器边界等效导热系数。该系数用于解决金属和冷却水之间的传热,即反映结晶器的传热能力。用等效导热系数处理结晶器的边界传热,对包括结晶器在内的连铸凝固进程温度场进行数值模拟既简单又方便,并且计算结果与实验结果符合。还讨论了拉坯速度和冷却水流量对结晶器温度场的影响。     

Analysis of the nonuniform slag film,mold friction,and the new cracking criterion for round billet continuous casting

A method predicting the thickness of solid and liquid slag films is presented to understand the complicated heat transfer from the strand to mold for round billet continuous casting. A mathematical model is also developed to calculate the liquid slag lubrication and solid slag friction on the basis of mechanics of viscous fluids and the contact state between the solidifying shell and mold. And a new criterion, based on the nonuniformity of mold heat transfer around the perimeter is proposed to predict the longitudinal crack. The results show that in the upper mold the distribution of the thickness of liquid slag film is similar with that of the solid one, and both of them are nonuniform around the mold perimeter, so does the mold friction. Increasing the casting speed could advance the time of crack formation for one casting process. By comparison, the sensitive area of the longitudinal crack predicted by the new criterion corresponds to that by a stress-based crack criterion. It may lay the theoretical foundation for the on-line detection of billet quality and the visualization of the continuous casting mold process.     

低碳钢和中碳钢连铸方坯初始凝固的对比研究

以低碳钢和中碳钢为研究对象,围绕不同连铸工艺参数对方坯初始凝固行为的影响,利用CA-FE耦合模型模拟实际连铸过程结晶器内方坯的初始凝固行为,考察拉速和过热度对方坯出结晶器坯壳厚度的影响,对比二者出结晶器横截面枝晶微观形貌.研究表明:过热度和拉速增加均能使出结晶器坯壳厚度下降,而拉速的影响更为显著.不同钢种在相同条件下出结晶器坯壳厚度下降梯度不同.过热度越低柱状晶越致密细小,利于提高连铸坯质量,拉速对柱状晶的影响相对较小.由于出结晶器坯壳安全厚度限制,过热度取15℃,低碳钢拉速不能超过2.2 m·min-1,中碳钢拉速不能超过2.5 m·min-1,据此针对不同钢种设计不同拉速可提高连铸效率.同时,模型结果显示低碳钢出结晶器时刻柱状晶更为发达.      

薄腹板近终形异形坯连铸温度场数值模拟

 薄腹板异形坯更体现了近终形的特点。采用有限元数值模拟计算了薄腹板异形坯连铸温度场,分析了不同拉速、比水量对连铸过程温度、坯壳厚度和液芯长度的影响。结果表明：异形坯不同位置的温度和坯壳厚度不均匀,当异形坯腹板较薄时,腹板处凝固传热较慢,腹板处和R角处坯壳最薄弱,比翼缘边部薄约4mm;拉速每提高0.1m/s,异形坯出结晶器时的表面温度会提高约80～100℃,坯壳厚度会减薄0.8～1.2mm,液芯长度增加1.2～1.6m;比水量每提高0.05L/kg,异形坯出二冷段时的表面温度会降低约8～16℃,液芯长度缩小0.13m。     

钢的连铸过程结晶器与铸坯之间的传热分析

针对连铸过程中的结晶器传热模型，分析总结了结晶器与坯壳之间的热阻构成，并研究了结晶器壁和坯壳界面热流的影响因素，为传热模型的求解和结晶器锥度的优化设计提供了理论依据。     

H型钢表面裂纹成因分析

 H型钢由异型坯轧制生产,异型坯形状独特,连铸生产中横向表面温度极不均匀,应力、应变状况复杂,对冶炼和连铸工艺均有较高要求。SS400异型坯生产中钢水未经精炼处理,部分炉次钢水碳含量处于包晶反应严重的碳含量范围,硫、磷含量较高,w(Mn)/w(S)较低,总氧和大型夹杂物含量较高;浸入式水口为直孔型,结晶器中上升流股较弱,坯壳生长不均匀;拉速较慢,并采用双水口浇铸,结晶器中上升流股更弱,弯月面处钢水供热不足,处于低温状态,保护渣也因温度低而熔融欠佳;二冷强度偏高,矫直辊前异型坯腹板表面温度处于低温脆性区,因此轧制成品H型钢的表面裂纹较多。     

H型钢表面裂纹成因分析

H型钢由异型坯轧制生产,异型坯形状独特,连铸生产中横向表面温度极不均匀,应力、应变状况复杂,对冶炼和连铸工艺均有较高要求。SS400异型坯生产中钢水未经精炼处理,部分炉次钢水碳含量处于包晶反应严重的碳含量范围,硫、磷含量较高,w（Mn）／w（S）较低,总氧和大型夹杂物含量较高;浸入式水口为直孔型,结晶器中上升流股较弱,坯壳生长不均匀;拉速较慢,并采用双水口浇铸,结晶器中上升流股更弱,弯月面处钢水供热不足,处于低温状态,保护渣也因温度低而熔融欠佳;二冷强度偏高,矫直辊前异型坯腹板表面温度处于低温脆性区,因此轧制成品H型钢的表面裂纹较多。     

Simulation of Thermal Insulation of Top-Surface Slag Layers in Continuous Casting Mold

 A computational model of thermal behavior of the top-surface slag layers in continuous casting mold was applied to interpret the thermal insulation of mold powder. The temperature drop of liquid steel caused by heat removal at the interface of molten steel and slag in mold was proposed to evaluate the thermal insulation of mold slag. The calculation results show that slag consumption is one of important factor influencing the temperature drop, while the casting speed has no obvious effect on it. With the increase of slag consumption, the temperature drop is increased.     

Measurement and modeling of heat transfer across interfacial mold flux layers

Surface quality problems in continuous cast steel are greatly affected by heat transfer across the interfacial layers in the gap between the solidifying steel shell and the mold. An experimental apparatus has been constructed to measure temperatures in the steel, mold flux layers, and copper under conditions approximating those in continuous casting. The flux solidified in multiple layers similar to those observed from continuous casting molds and contained many gas bubbles. Flux conductivities average about 1.0 W/m·K and appear to evolve with time. Contact resistances at both interfaces are significant and average about 0.0015 m²·K/W. Flux crystallization appears to be the only significant effect of flux composition. The one glassy flux tested had much greater thermal conductivities, presumably due to radiation transport. Temperature and gap thickness had a negligible effect on the properties. These properties depend on the model used to extract them. They are being implemented into a mathematical model to simulate heat transfer in the mold, interface, and solidifying shell of a continuous slab-casting machine.     

Modeling superheat removal during continuous casting of steel slabs

To investigate superheat dissipation in a continuous slab casting machine, mathematical models have been developed to compute fluid flow velocities, temperature distribution within the liquid pool, heat transfer to the inside of the solidifying shell, and its effect on growth of the shell. Three-dimensional (3-D) velocity and heat-transfer predictions compare reasonably with pre-vious experimental measurements and two-dimensional (2-D) calculations. The results indicate that the maximum heat input to the shell occurs near the impingement point on the narrow face and confirm that most of the superheat is dissipated in or just below the mold. Superheat tem-perature and casting speed have the most important and direct influence on heat flux. The effects of other variables, including mold width, nozzle jet angle, and submergence depth, are also investigated. Calculated heat flux profiles are then input to a one-dimensional (1-D) solidifi-cation model to calculate growth of the shell. Shell thickness profiles down the wide and narrow faces are compared with the predictions of conventional heat conduction models and available measurements.     

Initial development of thermal and stress fields in continuously cast steel billets

A mathematical model has been developed to compute the thermomechanical state of the shell of continuously cast steels in a round billet casting mold. The model determines the temperature distributions, the stresses in and the gap between the casting mold and the solidifying strand. The effect of variations in steel carbon content and mold taper on the thermal, displacement, and stress fields are examined. Comparisons with available experimental observations verify the predictions of the model. The model demonstrates that the thermal shrinkage associated with the phase change from delta-ferrite to austenite in 0.1 Pct C steel accounts for the decreased heat transfer observed in that alloy, as well as its susceptibility to cracking. Formerly Graduate Student, Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign.     

Mold Simulator Study of Heat Transfer Phenomenon During the Initial Solidification in Continuous Casting Mold

In this paper, mold simulator trials were firstly carried out to study the phenomena of the initial shell solidification of molten steel and the heat transfer across the initial shell to the infiltrated mold/shell slag film and mold. Second, a one-dimensional inverse heat transfer problem for solidification (1DITPS) was built to determine the temperature distribution and the heat transfer behavior through the solidifying shell from the measured shell thickness. Third, the mold wall temperature field was recovered by a 2DIHCP mathematical model from the measured in-mold wall temperatures. Finally, coupled with the measured slag film thickness and the calculations of 1DITPS and 2DIHCP, the thermal resistance and the thickness of liquid slag film in the vicinity of the meniscus were evaluated. The experiment results show that: the total mold/shell thermal resistance, the mold/slag interfacial thermal resistance, the liquid film thermal resistance, and the solid film thermal resistance is 8.0 to 14.9 × 10^?4, 2.7 to 4.8 × 10^?4, 1.5 to 4.6 × 10^?4, and 3.9 to 6.8 × 10^?4 m² K/W, respectively. The percentage of mold/slag interfacial thermal resistance, liquid film thermal resistance, and solid film thermal resistance over the total mold/shell thermal resistance is 27.5 to 34.4, 17.2 to 34.0, and 38.5 to 48.8 pct, respectively. The ratio of radiation heat flux is around 14.1 to 51.9 pct in the liquid slag film.     

The Thermal Distortion of a Funnel Mold

This article investigates the thermal distortion of a funnel mold for continuous casting of thin slabs and explores the implications on taper and solidification of the steel shell. The three-dimensional mold temperatures are calculated using shell-mold heat flux and cooling water profiles that were calibrated with plant measurements. The thermal stresses and distorted shape of the mold are calculated with a detailed finite-element model of a symmetric fourth of the entire mold and waterbox assembly, and they are validated with plant thermocouple data and measurements of the wear of the narrow-face copper mold plates. The narrow-face mold distorts into the typical parabolic arc, and the wide face distorts into a ??W?? shape owing to the large variation in bolt stiffnesses. The thermal expansion of the wide face works against the applied narrow-face taper and funnel effects, so the effect of thermal distortion must be considered to accurately predict the ideal mold taper.