Measurement and Modeling of Heat Transfer Across Interfacial Mold Flux Layers

Abstract

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 Wm K and appear to evolve with time. Contact resistances at both interfaces are significant and average about 0.0015 m². KW. 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. © 2000 Canadian Institute of Mining and Metallurgy. Published by Elsevier Science Ltd. All rights reserved.

Résumé

Les problèmes de qualité de surface de l'acier de coulée continue sont grandement affectés parle transfert de chaleur à travers les couches interfaciales dans l'intervalle entre la gaine d'acier en train de se solidifier et le moule. On a construit un appareil expérimental afin de mesurer la température de l'acier, des couches d'écoulement du moule et du cuivre sous des conditions appro chant celles de la coulée continue. L'écoulement s'est solidifié en couches multiples similaires à celles observees dans les moules de coulée continue et celles-ci contenaient plusieurs bulles de gaz. La moyenne de conductivité de l'écoulement est d'environ 1.0 Wm K et semble évoluer avec le temps. La résistance de contact aux deux interfaces est importante et atteint en moyenne environ 0.0015 m².kw. La cristallisation de l'écoulement parait etre le seul effet important de la composition du flux. Le seul écoulement vitreux évalué avait une conductivité thermique beaucoup plus élevée, vraisemblablement dil au transport parradiation. La température et la largeur de l'intervalle avaient un effet négligeable sur les propriétés. Ces propriétés dépendent du modèle utilisé pour les extraire. On est en train de les développer en un modéle mathématique afin de simuler le transfert de chaleur dans le moule, à l'interface et dans la gaine de solidification d'un appareil de coulée continue de brame. © 2000 Canadian Institute of Mining and Metallurgy.Published by Elsevier Science Ltd. All rights reserved.     

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.     

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。      

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.     

Multiphase Flow and Thermo-Mechanical Behaviors of Solidifying Shell in Continuous Casting Mold

 The metallurgical phenomena occurring in the continuous casting mold have a significant influence on the performance and the quality of steel product. The multiphase flow phenomena of molten steel, steel/slag interface and gas bubbles in the slab continuous casting mold were described by numerical simulation, and the effect of electromagnetic brake (EMBR) and argon gas blowing on the process were investigated. The relationship between wavy fluctuation height near meniscus and the level fluctuation index F, which reflects the situation of mold flux entrapment, was clarified. Moreover, based on a microsegregation model of solute elements in mushy zone with δ/γ transformation and a thermo-mechanical coupling finite element model of shell solidification, the thermal and mechanical behaviors of solidifying shell including the dynamic distribution laws of air gap and mold flux, temperature and stress of shell in slab continuous casting mold were described.     

Improvement of Castability and Surface Quality of Continuously Cast TWIP Slabs by Molten Mold Flux Feeding Technology

An innovative continuous casting process named POCAST (POSCO’s advanced CASting Technology) was developed based on molten mold flux feeding technology to improve both the productivity and the surface quality of cast slabs. In this process, molten mold flux is fed into the casting mold to enhance the thermal insulation of the meniscus and, hence, the lubrication between the solidifying steel shell and the copper mold. Enhancement of both the castability and the surface quality of high-aluminum advanced high-strength steel (AHSS) slabs is one of the most important advantages when the new process has been applied into the commercial continuous casting process. A trial cast of TWIP steel has been carried out using a 10-ton scale pilot caster and 100-ton scale and 250-ton scale commercial casters. The amount of mold flux consumption was more than 0.2 kg/m² in the new process, which is much larger than that in the conventional powder casting. Trial TWIP castings at both the pilot and the plant caster showed stable mold performances such as mold heat transfer. Also, cast slabs showed periodic/sound oscillation marks and little defects. The successful casting of TWIP steel has been attributed to the following characteristics of POCAST: dilution of the reactant by increasing the slag pool depth, enlargement of channel for slag film infiltration at meniscus by elimination of the slag bear, and decrease of apparent viscosity of the mold slag at meniscus by increasing the slag temperature.     

Heat Withdrawal in the Mold in Continuous Casting of Steel. Review and Analysis

Two principal methods are used to investigate the heat transfer in the continuous casting mold. The direct way is to measure cooling water temperatures, mold wall temperatures, strand temperatures and shell thickness in actual operation, and then deduce from these data the correlations for heat flux densities. The other way is to investigate the “unit operations” of heat transfer theoretically or experimentally in the laboratory, viz. heat transfer through a layer of casting flux or of gas, and heat transfer in a copper wall cooled on one side by water. The results obtained in this approach can then be used to explain the data determined with the direct method and to optimize the heat transfer behaviour of the mold in the machine. In the first part of this paper some unit operations are discussed and engineering formulae are given for computation of the heat resistances of the gap and the copper/water system. In the second part of the paper the available operational data on heat flux density are analysed. Algorithms are presented for computation of local and average heat flux density as functions of casting speed, carbon content of the steel and composition of the casting flux. Finally, values of shell thickness are computed with the correlation for heat flux density and are compared with the measured data.     

Heat-Transfer Measurements in the Primary Cooling Phase of the Direct-Chill Casting Process

Thermal modeling of the direct-chill casting process requires accurate knowledge of (1) the different boundary conditions in the primary mold and secondary direct water-spray cooling regimes and (2) their variability with respect to process parameters. In this study, heat transfer in the primary cooling zone was investigated by using temperature measurements made with subsurface thermocouples in the mold as input to an inverse heat conduction algorithm. Laboratory-scale experiments were performed to investigate the primary cooling of AA3003 and AA4045 aluminum alloy ingots cast at speeds ranging between 1.58 and 2.10 mm/s. The average heat flux values were calculated for the steady-state phase of the casting process, and an effective heat-transfer coefficient for the global primary cooling process was derived that included convection at the mold surfaces and conduction through the mold wall. Effective heat-transfer coefficients were evaluated at different points along the mold height and compared with values from a previously derived computational fluid dynamics model of the direct-chill casting process that were based on predictions of the air gap thickness between the mold and ingot. The current experimental results closely matched the values previously predicted by the air gap models. The effective heat-transfer coefficient for primary cooling was also found to increase slightly with the casting speed and was higher near the mold top (up to 824 W/m²·K) where the molten aluminum first comes in contact with the mold than near the bottom (as low as 242 W/m²·K) where an air gap forms between the ingot and mold because of thermal contraction of the ingot. These results are consistent with previous studies.     

Analysis of Non-uniform Mechanical Behavior for a Continuous Casting Mold Based on Heat Flux from Inverse Problem

The distortion of mold plates plays an important role in the formation of surface cracks on continuously cast steel products.To investigate the non-uniform distortion of a mold,a full-scale stress model of the mold was de-veloped.An inverse algorithm was applied to calculate the heat flux using the temperatures measured by the thermo-couples buried inside the mold plates.Based on this,a full-scale,finite-element stress model,including four copper plates,a nickel layer and water slots in different depths,was built to determine the complex mechanical behavior of the continuous casting mold used to produce steel slabs.The heat flux calculated by the inverse algorithm was applied to the stress model to analyze the non-uniform mechanical behavior.The results showed that the stress and distortion distributions of the four copper plates were not symmetrical,which reflected the non-uniform distortion behaviors of copper plates,water slots,nickel layer and the corner region of the mold.The gap between the mold and the slab was increased because of the corner distortion,which was very important for the heat transfer of initial solidifying shell,and it may be a major reason for the slow cooling of the slab corner.     

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     

An Investigation of the Mold-Flux Performance for the Casting of Cr12MoV Steel Using a Mold Simulator Technique

Mold flux plays important roles in the process of continuous casting. In this article, the performance of mold flux for the casting of Cr12MoV steel was investigated by using a mold simulator. The results showed that the slag film formed in the gap between the initial shell and mold hot surface is thin and discontinuous during the casting process with the Flux BM, due to the absorption of chromic oxide inclusions into the liquid slag, while the slag film formed in the case of the optimized Flux NEW casting process is uniform. The main precipitated crystals in Flux BM slag film are cuspidine (Ca₄Si₂O₇F₂) and Cr₃O₄, but only Ca₄Si₂O₇F₂ precipitated in the Flux NEW case. Besides, both the responding temperature and heat flux in the case of Flux BM are relatively higher and fluctuate in a larger amplitude. The surface of the shell obtained in the case of the Flux BM experiment is quite uneven, and many severe depressions, cracks, and entrapped slags are observed in the surface due to the lack of lubrication. However, the obtained shell surface in the case of the Flux NEW shows good surface quality due to the addition of B₂O₃ and the adjustment of basicity, which can compensate for the negative effects of the mold-flux properties caused by the absorption of chromic oxide during the casting process.     

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.     

连铸结晶器内渣膜形成及传热的研究现状

介绍了模拟结晶器内渣膜形成的实验方法, 综述了国内外学者在保护渣传热方面所做的研究工作, 包括固态渣膜的界面热阻、保护渣的导热系数、辐射传热以及渣膜的光学性质, 并提出了今后在渣膜形成及传热研究中有待进一步完善的内容和方向.现有的研究结果表明利用热丝法可以对渣膜的形成过程进行原位观察, 采用水冷铜探头法可以获取用于研究渣膜微观组织的固态渣膜样品.渣膜的界面热阻在0.0002~0.002 m2·K·W-1之间.在800℃以下, 保护渣的导热系数在1.0~2.0 W·m-1·K-1范围内, 且随温度的升高而逐渐增加.渣膜中的晶体一方面可以增加渣膜的界面热阻, 另一方面可以提高固态渣膜的反射率, 起到降低辐射热流的作用.此外, 过渡族金属氧化物的加入以及固态渣膜中弥散分布的微小颗粒也能改变渣膜的光学性质, 从而影响通过渣膜的辐射传热.      

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.     

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.     

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。     

小方坯结晶器水温水速对传热过程影响

通过建立结晶器内钢液和水的二维对流-传热耦合模型过程,研究了小方坯结晶器冷却水入口温度和流速对铜管温度和结晶器内平均热流的影响.该模型使用Fluent进行求解,模拟了钢液和冷却水的流动和传热,凝固坯壳的生长,以及热量以辐射和导热两种通过保护渣和气隙.通过将坯壳厚度和铜管温度与其他研究的结果进行对比来验证模型准确性.研究结果表明,结晶器冷却水的温度显著影响铜管的冷面温度,水温超过313 K会导致铜管冷面最高温度超过水的沸点.水流速升高0.49 m·s-1能够消除水温升高4 K带来的不利影响.      

Crystallization Characteristics of CaO-Al2O3-Based Mold Flux and Their Effects on In-Mold Performance during High-Aluminum TRIP Steels Continuous Casting

Crystallization behaviors of the newly developed lime-alumina-based mold fluxes for high-aluminum transformation induced plasticity (TRIP) steels casting were experimentally studied, and compared with those of lime-silica-based mold fluxes. The effects of mold flux crystallization characteristics on heat transfer and lubrication performance in casting high-Al TRIP steels were also evaluated. The results show that the crystallization temperatures of lime-alumina-based mold fluxes are much lower than those of lime-silica-based mold fluxes. Increasing B₂O₃ addition suppresses the crystallization of lime-alumina-based mold fluxes, while Na₂O exhibits an opposite effect. In continuous cooling of lime-alumina-based mold fluxes with high B₂O₃ contents and a CaO/Al₂O₃ ratio of 3.3, faceted cuspidine precipitates first, followed by needle-like CaO·B₂O₃ or 9CaO·3B₂O₃·CaF₂. In lime-alumina-based mold flux with low B₂O₃ content (5.4 mass pct) and a CaO/Al₂O₃ ratio of 1.2, the formation of fine CaF₂ takes place first, followed by blocky interconnected CaO·2Al₂O₃ as the dominant crystalline phase, and rod-like 2CaO·B₂O₃ precipitates at lower temperature during continuous cooling of the mold flux. In B₂O₃-free mold flux, blocky interconnected 3CaO·Al₂O₃ precipitates after CaF₂ and 3CaO·2SiO₂ formation, and takes up almost the whole crystalline fraction. The casting trials show that the mold heat transfer rate significantly decreases near the meniscus during the continuous casting using lime-alumina-mold fluxes with higher crystallinity, which brings a great reduction of surface depressions on cast slabs. However, excessive crystallinity of mold flux causes poor lubrication between mold and solidifying steel shell, which induces various defects such as drag marks on cast slab. Among the studied mold fluxes, lime-alumina-based mold fluxes with higher B₂O₃ contents and a CaO/Al₂O₃ ratio of 3.3 show comparatively improved performance.     

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.     

大方坯径向水口旋流效应及其对凝固的影响

通过改变水口侧孔钢水流动方向可以控制结晶器内钢水流动与换热。采用流体动力学与凝固模拟方法对比研究了浸入式四分径向水口不同出流方向对大方坯连铸结晶器内流动、传热和凝固行为的影响。结果表明,侧孔方向对浇注过程结晶器内钢水的流动与凝固行为有显著影响。当水口侧孔水平旋转角度为30°时,结晶器内形成较好的水平旋流,可以有效降低侧孔出流钢水对坯壳的冲刷作用,并有利于结晶器内自由液面过热度的提高。比较不同侧孔出流角度发现,利用普通径向四分水口在一定安装角度下的旋流效应不仅对于初生坯壳的均匀生长以及自由液面的冶金效果产生有利影响,还可能在不改变水口结构条件下获得类似结晶器电磁搅拌的旋流效应。