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.     

Transient fluid flow and superheat transport in continuous casting of steel slabs

The turbulent flow of molten steel and the superheat transport in the mold region of a continuous caster of thin steel slabs are investigated with transient large-eddy simulations and plant experiments. The predicted fluid velocities matched measurements taken from dye-injection experiments on full-scale water models of the process. The corresponding predicted temperatures matched measurements by thermocouples lowered into the molten steel during continuous casting. The classic double-roll flow pattern is confirmed for this 132×984 mm slab caster at a 1.52 m/min casting speed, with about 85 pct of the single-phase flow leaving the two side ports of the three-port nozzle. The temperature in the top portion of the molten pool dropped to about 30 pct of the superheat-temperature difference entering the mold of 58 °C. About 12 pct of the superheat is extracted at the narrow face, where the peak heat flux averages almost 750 kW/m² and the instantaneous peaks exceed 1500 kW/m². Two-thirds of the superheat is removed in the mold. The jets exiting the nozzle ports exhibit chaotic variations, producing temperature fluctuations in the upper liquid pool of ±4 °C and peak heat-flux variations of±350 kW/m². Employing a static-k subgrid-scale (SGS) model into the three-dimensional (3-D) finite-volume code had little effect on the solution.     

多孔水口对轴承钢280 mm x325 mm铸坯结晶器钢液流场和温度场的影响

采用数值模拟的方法对比分析了直通式、四孔式以及五孔式水口对GCr15轴承钢280 mm×325 mm坯连铸结晶器内钢液流场和温度场的影响。结果表明,当前常用的直通式水口对坯壳无冲刷,利于坯壳均匀生长,但钢液冲击深度大,在弯月面处速度小,不利于大方坯质量的提高。当采用四孔水口时,钢液热中心上移,钢液面处温度可提高8℃,钢液向上漩流增强,有利于降低结晶器内钢水过热及保护渣的熔化,但由于钢液对结晶器宽、窄面坯壳的冲刷致使冲击区域附近坯壳出现不同程度的零增长区域。当采用五孔水口时,除了钢液热中心上移,钢液向上漩流增强,由于侧孔钢液流速减小,对坯壳的冲刷减小,有利于保护渣的快速熔化、过热度的快速降低,坯壳的均匀生长,显著提高大方坯的质量。     

Mold behavior and its influence on quality in the continuous casting of steel slabs: Part II. Mold heat transfer,mold flux behavior,formation of oscillation marks,longitudinal off-corner depressions,and subsurface cracks

Axial heat-flux profiles have been determined quantitatively from temperature measurements conducted on a slab mold under routine operating conditions. As in earlier studies, the heat flux was observed to have a maximum value at the meniscus and to decline with increasing distance down the mold. The mold heat flux increased with increasing casting speed and was greater with a mold powder having lower viscosity and melting point being applied as lubricant. The heat extraction was largest while casting 0.29 pet carbon steel and least for a 0.09 pet carbon grade; reducing the depth of the submerged entry nozzle increased the heat flux slightly in the upper region of the mold. Most significant was the higher heat flux observed at the meniscus of the outside-radius face, attributable to the locally greater copper plate thickness compared to that of the opposite broad face. All of the measurements can be explained straightforwardly by heat flow in the vicinity of the meniscus and the resulting behavior of the so-called slag rim adjacent to the mold wall. It is postulated that the difference in copper plate thickness between the two broad faces at the meniscus causes the slag rim to be smaller on the outside-radius face which gives rise to shallower oscillation marks, as observed, higher heat transfer, and a slightly thicker solid shell. The dissimilar behavior has implications for quality because the inside-radius shell, experiencing reduced heat extraction, cools and shrinks less than the outside-radius shell. Thus, for a given end-plate taper, the narrow face of the slab adjacent to the inside radius can push against the end plate, accelerating copper wear, and, owing to squeezing of the broad face, cause an off-corner depression and subsurface crack toward the mold exit. If this is correct, maintenance of the same copper plate thickness at the meniscus is fundamental to preventing such an occurrence. Moreover, adjustment of the heat extraction at the meniscus should be achievable by changing copper plate thickness, mold coating thickness/conductivity, cooling water velocity, cooling channel configuration, and mold flux composition for a given steel grade. Formerly Graduate Student, Centre for Metallurgical Process Engineering, The University of British Columbia,     

Thermal and mechanical behavior of copper molds during thin-slab casting (I): Plant trial and mathematical modeling

Three-dimensional (3-D) finite-element thermal-stress models have been developed to predict temperature, distortion, and residual stress in the mold of continuous casters of thin steel slabs, comparing both funnel-shaped and parallel molds. The mold shape and high casting speed leads to higher mold temperatures and shorter mold life than in conventional slab casters. This study investigates heat flux and the effects of mold shape on distortion and cracking of the thin-slab mold. In Part I of this two-part article, mold wall temperatures measured in the plant were analyzed to determine the corresponding heat-flux profiles in thin-slab molds. This data was then used in an elastic-visco-plastic analysis to investigate the deformation of the molds in service for the two different mold shapes. The model predictions of temperature and distortion during operation match plant observations. During operation, the hot-face temperature reaches 580 °C and heat flux varies from 7 to 4.5 MW/m² when casting at 3.6 m/min. The copper plates bend toward the steel, with a maximum outward distortion of about 0.3 mm. This occurs just above the center of the wide faces and is smaller than the distortion of a conventional slab mold.     

An asymptotic model of the mold region in a continuous steel caster

A model is developed to simulate the solidification of the steel shell in the mold region of the continuous casting process. Conduction-dominated temperature fields in the mold, mold flux, steel shell, and molten steel regions are determined through the development of an evolution equation for the solidifying front. This equation is derived in the limit of small aspect ratio, mold width to height, using asymptotic methods. These results are coupled with a lubrication-theory model for the mold flux region. This model assumes a temperature-dependent viscosity for the mold flux and allows for solidification of the flux at temperatures below a critical value. System response to changing casting speeds, superheat, mold wall temperatures, and mold flux properties is investigated.     

Mold behavior and its influence on quality in the continuous casting of steel slabs: Part i. Industrial trials,mold temperature measurements,and mathematical modeling

An extensive study has been conducted to elucidate mold behavior and its influence on quality during the continuous casting of slabs. The study combined industrial measurements, mathe matical modeling, and metallographic examination of cast slab samples. The industrial mea surements involved instrumenting an operating slab mold with 114 thermocouples in order to determine the axial mold wall temperature profiles for a wide range of casting conditions. A three-dimensional (3-D) heat-flow model of the mold wall was developed to characterize the heat fluxes in the mold quantitatively from the measured mold temperature data. Furthermore, heat-flow models were developed to examine steel solidification phenomena and mold flux behavior at the meniscus. Slab samples collected during the industrial trials were examined metallographically to evaluate the cast structure and defects. Owing to the length of the study, it is presented in two parts, the first of which describes the experimental techniques employed in the instrumentation of the mold together with the details of the industrial trials and mold temperature measurements. Also, the mathematical modeling technique applied to determine the axial heat-flux profiles from the measured mold temperature data is presented. It is shown that a fully 3-D model of the mold wall is needed to convert the measured temperatures to heat-flux profiles properly. Formerly Graduate Student, Centre for Metallurgical Process Engineering, The University of British Columbia Formerly with Research and Development, Stelco Inc.     

连铸圆坯结晶器的热流分析

笔者采用专门设计的热流传感器对弧形连铸圆坯结晶器的热流进行在线检测.结果表明:沿结晶器的高度和周向热流的分布是瞬间变化且不均匀的.温度的在线检测不能代替热流的在线检测,后者可更准确和直接地反映结晶器传热和坯壳厚度的均匀性;同时在线检测结晶器的温度和热流有可能对结晶器的设备状态(如结晶器的安装状况和水垢状况)实现在线预测.     

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。     

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...     

A Study for Initial Solidification of Sn-Pb Alloy During Continuous Casting: Part II. Effects of Casting Parameters on Initial Solidification and Shell Surface

The initial shell solidification of liquid steel in the mold has significant influence on both surface and internal quality of the final slab, and it is mainly determined by the high transient high temperature thermodynamics occurring in the mold. This study investigated the effects of casting parameters like casting temperature, mold oscillation frequency, and stroke on the initial solidification of a Sn-Pb alloy through the use of a mold simulator to allow the clear understanding of the inter-relationship between irregular shell solidification, heat transfer, negative strip time (NST), and casting conditions. Results suggested that the shell surface oscillation marks (OMs) are strongly depending upon the fluctuations of meniscus responding temperatures and heat flux. An abrupt sudden fluctuation of high frequency temperature and heat flux at the meniscus during the NST would deteriorate the shell surface and leads to deep OMs. The fluctuations of responding temperature and heat flux are determined by the NST, meniscus solidification, and oil infiltration, which in turn are influenced by casting conditions, like casting temperature, oscillation frequency, stroke, etc.     

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。      

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.     

Thermomechanical finite-element model of shell behavior in continuous casting of steel

A coupled finite-element model, CON2D, has been developed to simulate temperature, stress, and shape development during the continuous casting of steel, both in and below the mold. The model simulates a transverse section of the strand in generalized plane strain as it moves down at the casting speed. It includes the effects of heat conduction, solidification, nonuniform superheat dissipation due to turbulent fluid flow, mutual dependence of the heat transfer and shrinkage on the size of the interfacial gap, the taper of the mold wall, and the thermal distortion of the mold. The stress model features an elastic-viscoplastic creep constitutive equation that accounts for the different responses of the liquid, semisolid, delta-ferrite, and austenite phases. Functions depending on temperature and composition are employed for properties such as thermal linear expansion. A contact algorithm is used to prevent penetration of the shell into the mold wall due to the internal liquid pressure. An efficient two-step algorithm is used to integrate these highly nonlinear equations. The model is validated with an analytical solution for both temperature and stress in a solidifying slab. It is applied to simulate continuous casting of a 120 mm billet and compares favorably with plant measurements of mold wall temperature, total heat removal, and shell thickness, including thinning of the corner. The model is ready to investigate issues in continuous casting such as mold taper optimization, minimum shell thickness to avoid breakouts, and maximum casting speed to avoid hot-tear crack formation due to submold bulging.     

Effects of Mold Powder Chemistry on Shell Growth,Momentum and Heat Transfer in a Billet Mold

Effects of mold powder chemistry on shell growth and thinning have been studied using Computer Fluid Dynamic techniques under conditions of constant casting speed and steel superheat for a peritectic steel in a billet caster. Two mold powders were considered; a basic powder suitable for peritectic steels and an acid powder not recommendable for this steel in order to emphasize the importance of chemistry on shell stability. Numerical results indicate a strong interaction between powder composition and steel flow‐heat transfer phenomena. The acid powder creates recirculating flows at both sides of the entry jet that transport sensible heat to the shell inducing its remelting and thinning leading, eventually, to a strand breakout. Meanwhile, the basic powder induces a single recirculating flow in the internal radius side of the mold without severe shell thinning. A colder meniscus is predicted using the acid powder which is in agreement with the casting practice experience. Powder infiltration of the basic powder in between the mold hot wall and the strand provides a powder shell with a macroscopically smooth surface while the acid powder yields irregular infiltration. Buoyancy forces along the mold working height and mold curvature play a fundamental role on the generation of the recirculating flows. Interaction between powder chemistry and fluid flow‐heat transfer are two‐way coupled phenomena that must be considered for powder design purposes.     

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.     

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.     

Flow and thermal behavior of the top surface flux/powder layers in continuous casting molds

Steady-state finite-element models have been formulated to investigate the coupled fluid flow and thermal behavior of the top-surface flux layers in continuous casting of steel slabs. The three-dimensional (3-D) FIDAP model includes the shear stresses imposed on the flux/steel interface by flow velocities calculated in the molten steel pool. It also includes different temperature-dependent powder properties for solidification and melting. Good agreement between the 3-D model and experimental measurements was obtained. The shear forces, imposed by the steel surface motion toward the submerged entry nozzle (SEN), create a large recirculation zone in the liquid flux pool. Its depth increases with increasing casting speed, increasing liquid flux conductivity, and decreasing flux viscosity. For typical conditions, this zone contains almost 4 kg of flux, which contributes to an average residence time of about 2 minutes. Additionally, because the shear forces produced by the narrowface consumption and the steel flow oppose each other, the flow in the liquid flux layer separates at a location centered 200 mm from the narrowface wall. This flow separation depletes the liquid flux pool at this location and may contribute to generically poor feeding of the mold-strand gap there. As a further consequence, a relatively cold spot develops at the wideface mold wall near the separation point. This nonuniformity in the temperature distribution may result in nonuniform heat removal, and possibly nonuniform initial shell growth in the meniscus region along the wideface off-corner region. In this way, potential steel quality problems may be linked to flow in the liquid flux pool.     

Analytical,numerical, and experimental analysis of inverse macrosegregation during upward unidirectional solidification of Al-Cu alloys

The present work focuses on the influence of alloy solute content, melt superheat, and metal/mold heat transfer on inverse segregation during upward solidification of Al-Cu alloys. The experimental segregation profiles of Al 4.5 wt pct Cu, 6.2 wt pct Cu, and 8.1 wt pct Cu alloys are compared with theoretical predictions furnished by analytical and numerical models, with transient h _i profiles being determined in each experiment. The analytical model is based on an analytical heat-transfer model coupled with the classical local solute redistribution equation proposed by Flemings and Nereo. The numerical model is that proposed by Voller, with some changes introduced to take into account different thermophysical properties for the liquid and solid phases, time variable metal/mold interface heat-transfer coefficient, and a variable space grid to assure the accuracy of results without raising the number of nodes. It was observed that the numerical predictions generally conform with the experimental segregation measurements and that the predicted analytical segregation, despite its simplicity, also compares favorably with the experimental scatter except for high melt superheat.