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.     

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.     

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.     

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.     

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。      

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.     

Influence of Billet Size on Flow, Solidification and Solute Transport in Continuous Casting

ListofSymbol　　B———Buoyancy ,m·s- 2 ;　　c———Concentrationofsoluteelement ;　　Cμ———Turbulentconstant;　　D———Diffusivityofsoluteelement ,m2 ·s- 1 ;　　fl,fs———Liquidandsolidfraction ;　　fμ———Turbulentcoefficient ;　　h———Enthalpy ,J·kg- 1 ;　　k———Turbulentkineticenergy ,m2 ·s- 2 ;　　kp———Equilibriumpartitioncoefficient;　　Kp———Permeabilityofmushyzone ,m2 ;　　K0 ———Permeabilitycoefficient;　　p———Pressure ,Pa ;　　Pr———Prandtlnumber ;…     

Heat Transfer and Deformation Behavior of Shell Solidification in Wide and Thick Slab Continuous Casting Mold

With the considerations of the behaviors of shell deformation, mold flux film and air gap dynamic distribution in shell/mold gap, a two dimensional slice-travel transient thermo-mechanical coupled model of simulation shell solidification in wide and thick slab continuous casting mold was developed by using the commercial program ANSYS. The evolutions of strand-mold system thermal behaviors, including the air gap formation and the mold flux film dynamical distribution in shell/mold gap and shell temperature field, and the evolutions of shell deformation and stress distribution of peritectic steel solidified in a 2120 mm wide and 266 mm thick slab continuous casting mold were analyzed. The results show that the air gap formation and the thick mold flux film distribution mainly concentrate in the regions 0–21 mm and 0–7 mm, 0–120 mm and 0–100 mm off the shell wide and narrow faces corners, and thus the hot spots are given rise to form in the regions 15–55 mm and 15–50 mm off the shell wide and narrow face corners. The shell server deformation occurs in the off-corners in the middle and lower parts of the mold. The stress evolution in shell surface is tensile stress, while that in shell solidification front is compressive stress.     

连铸结晶器内铸坯温度场和应力场耦合过程数值模拟

针对碳钢在连铸结晶器内的凝固过程,考虑铸坯和铜板间接触状态,建立了完全热力耦合的二维热-弹塑性有限元模型.利用MARC商用软件包在微机上求解,模拟出了连铸结晶器区域热和力学状态,特别是铸坯和结晶器壁界面状态,包括铸坯表面温度、界面热流和气隙分布规律等.本模拟工作可以为优化结晶器锥度,开发高拉速曲面结晶器提供理论依据和技术基础.     

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.     

Analysis of thin-slab casting by the compact-strip process: Part II. Effect of operating and design parameters on solidification and bulging

The mathematical model to compute the thermal evolution and solidification of thin slabs, previously presented in Part I of this article, was used in combination with a three-dimensional (3-D) finite-element thermomechanical model to analyze how actual operation conditions can lead to excessive deflection and jamming of the slab shell at the pinch rolls. The models suggest that these phenomena arise from a sudden loss of control of the metallurgical length stemming from the coupling of inappropriate steel superheats and casting velocities to deficient heat-extraction conditions at the mold or secondary cooling system. The bulging deformation was calculated with an elastic and creep model that takes into account the temperature distribution across the shell thickness and the different times that shell elements have to creep exposure, i.e., according to the time that rows of elements require to reach their current position in the casting direction at a given casting speed. The last point was simulated by varying the duration of application of the ferrostatic load to the inside surface of each row of elements. The conditions forecast by the models as being responsible for excessive bulging agree very well with those present during the occurrence of these events in the plant. Since bulging after the last containment roll is a major limitation to productivity, this article also presents a parametric evaluation of the casting-speed limits that two compact-strip process (CSP) casters with different supported lengths may have as a function of steel superheat, mold heat-extraction level, water flow rate of the spray and air-mist nozzles, and slab thickness.     

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.     

漏斗形薄板坯结晶器内铸坯传热分析

 为了更好地研究FTSC结晶器内铸坯的凝固过程,基于节点温度传递方法建立薄板坯结晶器内铸坯三维瞬态传热数值模型,采用有限元软件ANSYS模拟结晶器内铸坯三维稳态温度场。对比分析平板形及漏斗形结晶器内铸坯传热规律,探讨了漏斗区传热特点。结果表明,漏斗区内钢水存储空间增大,总热容量增加,漏斗区铸坯宽面表面中心温度升高,坯壳厚度减薄。FTSC结晶器宽面出口温度、坯壳厚度连续变化,与漏斗形布置一致。     

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...     

The Effect of Basicity on the Radiative Heat Transfer and Interfacial Thermal Resistance in Continuous Casting

The basicity of mold flux has been recognized to have a significant influence on the mold flux crystallization in continuous casting, which would in turn affect the heat-transfer rate between the solidified shell and mold. The research regarding the mold flux crystallization as well as its effect on the heat transfer has been conducted intensively. However, few studies have been developed to specify the effect of basicity introduced mold flux crystallization on the radiative heat transfer and interfacial thermal resistance in continuous casting. By using an infrared radiation emitter, a radiative heat flux was applied to a copper mold covered with a solid mold flux disk to simulate the heat-transfer phenomena in continuous casting. The crystallization behaviors of mold fluxes with different basicities and their impact on the radiative heat transfer were investigated dynamically. The interfacial thermal resistance between the solid mold flux and copper mold was also studied in this article. The results suggested that the basicity tends to enhance the mold flux crystallization, leading to the reduction of radiative heat-transfer rate and enlargement of interfacial thermal resistance.     

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%。     

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.      

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.