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.     

Oscillating Jet Flows in a Thin Slab Mold and their Influence on Meniscus Stability

Sustainability of oscillating liquid steel jets discharging from a submerged, two‐port entry nozzle in thin slab molds has been studied through a water model and mathematically simulated using the Reynolds Stress Model of turbulence combined with the Volume of Fluid model to capture dynamics of the water‐air interface. At casting speeds of 5 and 7 m/min, both jets yield long range time‐dependent Reynolds stresses with high gradients which induce oscillating upper roll flows in the mold providing permanent flow asymmetry. Intermittent vortexes at the water‐air interface are generated by the interaction between the flow arising from the upper roll toward the SEN and a high velocity flow which goes through the gap between the SEN shaft and mold wall oriented toward the narrow wall. These flows gather at expansion of the mold funnel generating intermittent vortexes. Meniscus oscillation decreases in narrower molds even at high casting speeds. At lower casting speed like 5 m/min meniscus oscillation decreases considerably in wide and narrow molds. Turbulence understanding in thin slab molds would help to design submerged entry nozzles for higher steel casting speeds through wide molds with better meniscus stability.     

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.     

Study of the Effects of the Mold Surface and Solid Mold Flux Crystallization on Radiative Heat Transfer Rates in Continuous Casting

Radiative heat transfer plays a crucial role in the meniscus area of a steel continuous casting machine. However, the study of radiation across the mold flux and copper molds is very difficult due to the harsh environment and highly transient nature of the phenomena in continuous casting molds. By using an infrared radiation emitter, a radiative heat flux was able to be applied to a copper mold with different top surfaces to observe their effects on the radiative heat transfer. The mold surface was covered with solid slag disk subjected to the radiative heat flux to simulate the radiative heat transfer phenomena in continuous casting. The solid slag disk could either be glass or a mixture of glass and precipitated crystals. The effect of full crystallization of a slag disk was to reduce the heat transfer rate by 20.5%, as compared with a completely glassy sample.     

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.     

The thermal distortion of continuous-casting billet molds

Preliminary mathematical analyses involving plate bending theory and two-dimensional elastic calculations have revealed that the dominant component contributing to the distortion of continuous-casting billet molds is thermal expansion in the transverse directions. A three-dimensional, elasto-plastic, finite-element analysis of the mold wall has then shown that localized yielding initiates in a region close to the meniscus. The plastic flow is a result of the high thermal stresses induced by the geometric restraint to bending coupled with the locally high temperatures. The resultant distortion profile of the mold down the centerline of a face exhibits a maximum outward bulge of 0.1 to 0.3 mm, which is bounded above by a region of negative taper (1∼2 pct/m) and below by a region of positive taper (∼0.4 pct/m). Measurements of mold wall movement in an operating billet caster using linear displacement transducers compare favorably with model predictions, except in the meniscus region. Case studies of several industrial billet molds have shown that lowering the meniscus level with respect to the location of constraints, or modifying the method of support of the mold tube within its housing so as to reduce the restraint to thermal expansion in the meniscus region, may minimize the extent of permanent distortion. Also, wall thickness can have a significant effect on thermal distortion. Increasing wall thickness results in an increase in both peak wall temperatures and thermal gradients. The former increases the local distortion while the latter causes higher thermal stress levels and possibly permanent distortion. Of the casting variables that can be manipulated to major advantage, cooling water flow rate is the most important. Increasing the water velocity reduces mold wall temperatures, as well as both the total and permanent distortion of the wall.     

宽厚板坯连铸结晶器流场、温度场及应力场的耦合数值模拟

利用Pro CAST软件对2400 mm×400 mm宽厚板坯结晶器建立三维动态模型,采用移动边界法实现结晶器内流场、温度场及应力场的耦合模拟.结果表明:考虑凝固坯壳的影响,下回流区位置向铸坯中心靠拢,真实反映了钢液在连铸结晶器内的流动情况.自由液面的钢液从窄面流向水口,速度先增大后减小,距水口约0.7 m处,出现最大表面流速,约为0.21 m·s-1.结晶器出口坯壳窄面中心厚度最小且由中心向两侧逐渐增大,最小厚度约为10.4 mm;受流股冲击影响较弱的宽面坯壳与窄面相比生长更均匀,宽面偏角部和中心的坯壳厚度分别为18.9 mm和27.6 mm.铸坯坯壳应力变化趋势与温度基本保持一致,表明初凝坯壳应力主要是热应力.结晶器内铸坯宽窄面上的等效应力均沿着结晶器高度下降方向呈增大趋势,铸坯角部、宽面中心及窄面中心位置的最大应力各约为200、100和25 MPa.      

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     

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.     

连铸机结晶器铜板失效分析及改进措施

为了提高结晶器的使用寿命,从分析铜板及表面涂镀层失效原因出发,对结晶器的设计、铜板材质的选择和表面强化技术等方面进行了研究和总结,针对结晶器铜板在使用中出现的问题提出了改进措施。对比银铜和铬锆铜金相组织并通过实验发现：铜晶界之间析出的富铬金属化合物是铬锆铜基体结晶器的热裂纹来源。研究各种合金电镀层、热喷涂层以及纳米复合镀层的内应力分布特点,优化了铜板涂镀层的生产技术,不依靠任何有机添加剂生成压应力的涂镀层,在国内外多个钢厂实际应用并取得良好效果。     

Efficiency of continuous-caster-mold walls with cylindrical and slit-like channels

One way of improving the durability of the working walls of continuous-caster molds is to increase the rate at which heat is removed from the melt. New designs of mold walls have been developed for this specific purpose. This article compares the thermal state and temperatures of molds having drilled and slit-type channels for coolant water. An algorithm is developed to design bolts for securing the working slabs of the mold. The algorithm was developed with allowance for the nonuniformity of temperature over the surface of the mold walls and with the assumption that the joints between the walls remains intact during service. __________ Translated from Metallurg, No. 6, pp. 40–42, June, 2007.     

Determination of interface heat transfer coefficient between aluminum casting and graphite mold

To produce castings of titanium, nickel, copper, aluminum, and zinc alloys, graphite molds can be used, which makes it possible to provide a high cooling rate. No die coating and lubricant are required in this case. Computer simulation of casting into graphite molds requires knowledge of the thermal properties of the poured alloy and graphite. In addition, in order to attain adequate simulation results, a series of boundary conditions such as heat transfer coefficients should be determined. The most important ones are the interface heat transfer coefficient between the casting and the mold, the heat transfer coefficient between the mold parts, and the interface heat transfer coefficient into the environment. In this study, the interface heat transfer coefficient h between the cylindrical aluminum (99.99%) casting and the mold made of block graphite of the GMZ (low ash graphite) grade was determined. The mold was produced by milling using a CNC milling machine. The interface heat transfer coefficient was found by minimizing the error function reflecting the difference between the experimental and simulated temperatures in a mold and in a casting during pouring, solidification, and cooling of the casting. The dependences of the interface heat transfer coefficient between aluminum and graphite on the casting surface temperature and time passed from the beginning of pouring are obtained. It is established that, at temperatures of the metal surface contacting with a mold of 1000, 660, 619, and 190°C, the h is 1100, 4700, 700, and 100 W/(m² K), respectively; i.e., when cooling the melt from 1000°C (pouring temperature) to 660°C (aluminum melting point), the h rises from 1100 to 4700 W/(m² K), and after forming the metal solid skin on the mold surface and decreasing its temperature, the h decreases. In our opinion, a decrease in the interface heat transfer coefficient at casting surface temperatures lower than 660°C is associated with the air gap formation between the surfaces of the mold and the casting because of the linear shrinkage of the latter. The heat transfer coefficient between mold parts (graphite–graphite) is constant, being 1000 W/(m² K). The heat transfer coefficient of graphite into air is 12 W/(m² K) at a mold surface temperature up to 600°C.     

Thermal and mechanical behavior of copper molds during thin-slab casting (II): Mold crack formation

The formation of cracks in a funnel mold of thin-slab casting is investigated using metallographic studies and mathematical models. In Part II of this two-part article on thin-slab casting molds, short longitudinal cracks near the meniscus region of a thin-slab funnel mold are studied metallurgically. X-ray analyses revealed the formation of Cu-Zn brass on the copper matrix at high temperature where the crack initiated. Heat-transfer and thermal-elastic-viscoplastic stress models described in Part I are applied to investigate the temperature and stress fields associated with the cracks. Large cyclic inelastic strains were found in the funnel transition region just below the meniscus due to the slightly higher temperature at that location. The cracks then appear to have propagated by thermal fatigue caused by major level fluctuations at transitions. The stress and strain predictions suggest cycles to failure for molds for various hot-face temperatures.     

The use of water cooling during the continuous casting of steel and aluminum alloys

In both continuous casting of steel slabs and direct chill (DC) casting of aluminum alloy ingots, water is used to cool the mold in the initial stages of solidification, and then below the mold, where it is in direct contact with the newly solidified surface of the metal. Water cooling affects the product quality by (1) controlling the heat removal rate that creates and cools the solid shell and (2) generating thermal stresses and strains inside the solidified metal. This work reviews the current state-of-the-art in water cooling for both processes, and draws insights by comparing and contrasting the different practices used in each process. The heat extraction coefficient during secondary cooling depends greatly on the surface temperature of the ingot, as represented by boiling water-cooling curves. Thus, the heat extraction rate varies dramatically with time, as the slab/ingot surface temperature changes. Sudden fluctuations in the temperature gradients within the solidifying metal cause thermal stresses, which often lead to cracks, especially near the solidification front, where even small tensile stresses can form hot tears. Hence, a tight control of spray cooling for steel, and practices such as CO₂ injection/pulse water cooling for aluminum, are now used to avoid sudden changes in the strand surface temperature. The goal in each process is to match the rate of heat removal at the surface with the internal supply of latent and sensible heat, in order to lower the metal surface temperature monotonically, until cooling is complete.     

延长铜冶炼阳极模服役寿命的工业实践

针对大冶有色冶炼厂铜阳极板浇铸工序铸模平均服役寿命较短问题,本文研究分析了浇铸过程铜水温度、脱模剂喷涂效果、喷淋系统冷却能力等因素对服役寿命的影响,提出了阳极模结构改进、浇铸铜水温度控制、喷涂管结构改进、圆盘冷却系统优化等措施,技术改造后,阳极模平均服役使用寿命由 240t·Cu/ 块延长至 350t·Cu/ 块。     

不同角部形状特厚矩形坯凝固传热及应变数值模拟

 为了更加有效控制和减少连铸坯的角部横裂纹质量缺陷,根据其形成的机制,针对两种新型铸坯模型,即圆角和倒角模型进行研究。通过建立特厚连铸矩形坯在凝固过程的传热模型并进行数值模拟,得到铸坯在凝固过程沿拉速方向上温度场和坯壳厚度的分布规律,并在此基础上建立热力耦合模型,分析铸坯的应力变化,讨论了产生裂纹的可能性。研究结果表明,通过对比传统直角模型,得出圆角和倒角模型对铸坯角部温度场和应力场两个方面的分布状况都有改善,即新铸坯模型角部温度在连铸矫直段有效避开了钢的高温脆性区,同时降低了铸坯角部的应力值,减小了角部裂纹产生的可能性。     

延长铜冶炼阳极模服役寿命的工业实践

针对大冶有色冶炼厂铜阳极板浇铸工序铸模平均服役寿命较短问题,本文研究分析了浇铸过程铜水温度、脱模剂喷涂效果、喷淋系统冷却能力等因素对服役寿命的影响,提出了阳极模结构改进、浇铸铜水温度控制、喷涂管结构改进、圆盘冷却系统优化等措施,技术改造后,阳极模平均服役使用寿命由240t·Cu/块延长至350t·Cu/块。     

A Mathematical model of the closed mold (Watts) horizontal continuous casting process

A mathematical model is presented for the closed mold, horizontal (Watts) continuous casting system. A particular feature of the system is that molten metal is fed, from a tundish, through a pipe formed by the solidified shell, to a closed mold which is made to move away from the tundish as casting proceeds. A major practical problem in the technical assessment of the process is to estimate the maximum length that may be cast before the supply of metal to the mold is restricted by the solidification of the shell downstream from the tundish nozzle. The model described in the paper is based on a two-dimensional transient heat balance written for both the solidified shell and the molten metal (+ slurry) stream and the resultant differential equations are solved numerically. It was found that both the maximum length that may be cast and the actual location of the freezing blockage are markedly affected by the melt-shell heat transfer coefficient, the spray-shell heat transfer coefficient and the fraction of the mushy zone that is swept away by the melt. The maximum length may be cast when the melt-shell heat transfer coefficient is large and when much of the mushy zone is being swept away by the melt, which, in a physical sense would correspond to a fast casting rate. Freezing blockage would then occur some distance downstream from the inlet. For the range of operating conditions considered, for slab casting, the maximum length that could be cast corresponded to some 300 to 550 times the width of the slab. Formerly of the Department of Chemical Engineering, State University of New York at Buffalo, At this stage we shall not specify whether the thickness of the solidified shell will correspond to the solidus or the liquidus temperature at the inner surface, or to some intermediate value. This will be one of the parameters in subsequent calculations.     

Influence of mold length and mold heat transfer on horizontal continuous casting of nonferrous alloy rods

The influence of mold length and mold heat transfer on the conventional hot-top D.C. continuous casting process was studied through numerical simulations and experiments with horizontally cast 20 mm diameter lead and zinc rods. The minimum casting speed was found to be a nonlinear function of the mold length. For short molds, an inverse relationship between mold length and minimum casting speed was observed. However, the minimum casting speed for zinc cast from molds longer than 12 mm was constant at 2.5 mm/s. For lead cast in molds longer than 12 mm, the minimum observed casting speed was constant at 4.0 mm/s. The observed nonlinear relationship between minimum casting speed and mold length was predicted using a numerical model of the process. For this, an analytical expression for the mold boundary conditions was derived which included the influence of gas gap formation between the rod and the mold due to thermoelastic deformations of both the rod and the mold. Correlation between observed and predicted behavior was demonstrated for both the lead and zinc rods. Maximum casting speed was observed to increase with increased mold length; however, this speed was found to be critically dependent on process attributes such as mold and pinch wheel alignment and mold lubrication.