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.     

A Study about the Influence of Carbon Content in the Steel on the Casting Behavior

In the casting process of steels with a C‐content ranging from 0.09 to 0.53 mass%, austenite is formed as secondary crystal phase by peritectic reaction between crystal of δ ferrite and residual melt. For unalloyed or micro‐alloyed steels the C‐content or C‐equivalent influences the casting behavior of steel in the mould, such as strand shell growth, crack formation, heat transfer, temperature fluctuation in the copper plate, mould level fluctuation and oscillation marks formation. The negative casting behavior like the uneven strand shell growth, the deep oscillation mark formation, the high mould level fluctuation, the crack formation on the strand surface were found mostly for steel with C‐content or Cp between 0.10–0.13 mass%. The strand shell structure (strand shell growth, mushy zone, δ + γ phase transformation) and shrinkage of the strand shell were simulated depending on the C‐content by means of mathematical simulation. On the basis of the simulation results and of the measured high temperature strength of steel the dependence of stiffness and the irregularity of the shrinkage of strand shell on the C‐content was investigated. It was found that the stiffness and irregularity of the shrinkage of the strand shell reach the maximum value at a C‐content of about 0.12 mass%.     

Challenge to control mould heat transfer during thin slab casting

Abstract

At the thin slab caster of Tata Steel, IJmuiden, mild cooling mould powders were introduced with the aim to control the mould heat transfer during casting. These mild cooling mould powders are characterised by specific values of basicity, solidification point and chemical composition. Application of these mould powders resulted in a redistribution of mould heat transfer during casting, i.e. a reduced and more stable mould heat transfer in the critical upper part of the mould and an increased mould heat transfer in the lower part of the mould. The average mould heat transfer and hence the shell thickness at mould exit are comparable to the standard powder. The application of mild cooling mould powders also resulted in improved solidification behaviour of the steel shell. A thinner chill zone with smaller thickness variations was observed. Furthermore, it was found that the mould taper required optimisation to match the changes in shrinkage behaviour to ensure uniform solidification. The use of mild cooling powders was observed to give an increase in mould friction. Mould thermal monitoring indicated that the solid slag films fractured (sheeting) in the upper part of the mould. However, no operational problems were reported, which indicate that the first 200 mm under the steel meniscus is essential for initial solidification and for the formation of a homogeneous steel shell. All these findings can be understood by considering the crystallisation properties of the mould slag, which include the cooling rate. Mild cooling has been shown to provide uniform heat transfer and adequate lubrication for high speed thin slab casting.     

板坯结晶器钢液流动传热和摩擦行为的数值模拟

结晶器摩擦力对连铸顺行非常重要,而钢液流动行为会影响铸坯温度场和保护渣分布,可能对铸坯摩擦力产生一定的影响.利用Fluent软件建立结晶器内钢液流动、传热三维数学模型,并将温度场数据导入Ansys计算铸坯应变,然后根据铸坯-保护渣-结晶器摩擦行为数学模型讨论了渣膜润滑情况,对比了不同水口底部形状下结晶器内液态、固态和总摩擦力.结果表明:不考虑水口射流时结晶器总摩擦力比考虑水口时增大约29.4％;浸入式水口底部形状分别为凸底、平底和凹底3种情况下铸坯窄面中心温度依次降低,凝固壳厚度依次增大,固态摩擦力依次增大,总摩擦力依次增大,液态摩擦力相差较小.     

Solidification and Particle Entrapment during Continuous Casting of Steel

Avoiding particle entrapment into the solidifying shell of a steel continuous caster is important to improve the quality of the continuous cast product. Therefore, the fluid flow dynamics in the steel melt and mushy zone, heat transfer and solidification of the steel shell, as well as the motion and entrapment of inclusion particles during the casting process were investigated using computational models. Solidification of the strand shell is modelled with an enthalpy‐formulation by assuming a columnar morphology in the mushy zone. The motion of particles is tracked with a Lagrangian approach. When the particles reach the solidification front, they can be entrapped/engulfed into the solid shell or pushed away from the solidification front, depending on the mushy zone morphology and the forces acting on them. The current paper focuses on the mould region at a steel continuous caster, including the submerged entry nozzle (SEN) and 1.2 m length of the strand. The results are validated with plant measurements and demonstrate the potential of the model to predict fluid flow, shell growth and the positions and the amount of entrapped/engulfed particles in the solidifying strand.     

小方坯连铸机结晶器的研究

建立了铸坯固传热数学模型，模拟计算了铸坯温度场，坯壳厚度，热流场，坯壳热收缩应力场，坯壳与铜壁间气隙厚度，计算坯壳厚度与实测坯壳厚度基本吻合，计算结果为连铸机生产，连铸机设计提供参考。     

Combination of inverse problem and neural network for thermal behaviour calculation of mould process based on temperature measurements in plant trial

Abstract

Heat transfer between mould and strand has a critical influence on billet quality, caster productivity and operating safety. It is very important to obtain the correct distributions of temperature and heat flux, and many studies are made on the calculation methods of heat transfer between strand and mould, aiming to reduce the computation time and improve the calculation accuracy. In the present paper, based on measured data of temperature and heat flux during round billet continuous casting, the calculation method which combines the online measurement data and numerical simulation was investigated. Through identifying the local thermal resistance and its distribution between the mould and the strand by an inverse heat transfer model, the heat flux and shell thickness profiles were calculated. To avoid the iterative solution by inverse model, a faster alternative model using an artificial neural network was developed to predict the thermal resistance from the measured temperature. After training, there is an exact correspondence between the observed temperature values and the thermal resistance. The calculation results obtained by the combination of neural network and numerical simulation can correctly reflect the characteristics of non-uniform heat transfer around the mould circumference, which provides a worthwhile and applicable method for online calculation and visual technology of heat transfer and solidification in continuous casting mould.     

方坯结晶器多锥度分析

基于坯壳应力遗传特性建立铸坯热力耦合模型,利用ANSYS对结晶器内铸坯进行铸坯传热及应力分析。依据最小气隙原则对结晶器锥度进行优化,分析了单锥度和多锥度对坯壳凝固行为的影响。结果表明:采用两种锥度形式的结晶器,铸坯角部凝固行为存在明显差异,而表面中心区域基本一致。单锥度结晶器内气隙分布较广,角部热流明显降低,在偏离角部12～22 mm处存在"热点"。多锥度结晶器内气隙宽度和存在范围显著减少,"热点"消失,多锥度结晶器更符合坯壳凝固收缩规律。     

Analysis of thermomechanical behaviour in billet casting with different mould corner radii

Abstract

A finite element thermal stress model to compute the thermomechanical state of the solidifying shell during continuous casting of steel in a square billet casting mould has been applied to investigate longitudinal cracks. A two-dimensional thermoelastoviscoplastic analysis was carried out within a horizontal slice of the solidifying strand which moves vertically within and just below the mould. The model calculates the temperature distributions, the stresses, the strains in the solidifying shell, and the intermittent air gap between the casting mould and the solidifying strand. Model predictions were verified with both an analytical solution and a plant trial. The model was then applied to study the effect of mould corner radius on longitudinal crack formation for casting in a typical 0·75%/m tapered mould with both oil and mould powder lubrication. With this inadequate linear taper, a gap forms between the shell and the mould in the corner region. As the corner radius of the billet increases from 4 to 15 mm, this gap spreads further around the corner towards the centre of the strand and becomes larger. This leads to more temperature non-uniformity around the billet perimeter as solidification proceeds. Longitudinal corner surface cracks are predicted to form only in the large corner radius billet, owing to tension in the hotter and thinner shell along the corner during solidification in the mould. Off corner internal cracks form more readily in the small corner radius billet. They are caused by bulging below the mould, which bends the thin, weak shell around the corner, creating tensile strain on the solidification front where these longitudinal cracks are ultimately observed.     

On the Formation of Centreline Segregation in Continuous Slab Casting of Steel due to Bulging and/or Feeding

Centreline macrosegregation is often observed in continuous slab casting of steel. Two of the main macrosegregation formation mechanisms are bulging and feeding. Both were studied and compared in the current work by using a two‐phase volume averaging model considering only columnar solidification. The casting of the strand itself is modelled by applying a predefined velocity following the casting speed and solid shell deformation (e.g. bulging). Three different cases are simulated and discussed. (i) The first case considers the influence of the feeding flow during solidification without taking bulging into account. Negative macrosegregation is observed in the centre of the casting in this case. (ii) The second case takes the flow caused by series of bulging along the solidifying strand shell into account, and is, therefore, representative for an ideal situation where bulging takes place without solidification shrinkage. In this case positive centreline segregation is found. (iii) The last case shows the results of a simulation which combines both shrinkage‐ and bulging‐induced flows. It is found that under the current casting conditions the bulging effect dominates over the shrinkage effect, and so positive centreline segregation is predicted.     

Analytical model for continuous caster profile optimisation

Abstract

As a partial solution of the differential equation of the continuous caster pass line, the analytical relationship between the basic radius and the lengths of the radial and unbending zones was derived. Choosing rationally the length of the unbending zone at a given unbending strain rate, it is possible to reduce the height of a high productivity caster and the ferrostatic pressure within the strand shape to eliminate internal cracking. The software developed allows the temperature, stress, and strain distribution in the strand shell to be determined and, for assumed allowable strains due to bulging and unbending, the caster profile and the positioning of support and unbending rollers to be optimised. For the case of a continuous caster with a vertical mould, the same technique for its profile optimisation was proposed.     

Numerical simulation of fluid flow and solidification in continuous slab casting mould based on inverse heat transfer calculation

Abstract

A mathematical model based on an inverse heat transfer calculation was built to determine the heat flux between the mould and slab based on the measured mould temperatures. With K–? turbulence model, a mathematical model of three-dimensional heat transfer and solidification of molten steel in continuous slab casting mould is developed. Solidification has been taken into consideration, and flow in the mushy zone is modelled according to Darcy’s law as is the case of flow in the porous media. The heat flux prescribed on the boundaries is obtained in the inverse heat conduction calculation; thus, the effect of heat transfer in the mould has been taken into consideration. Results show that the calculated values of mould temperature coincide with the measured ones. Results also reveal that the temperature distribution and shell thickness are affected by the fluid flow and heat transfer of slab which is governed by the heat flux on the mould/slab interface.     

Investigation of mould thermal behaviour by means of mould instrumentation

Abstract

The thermal behaviour of the continuous casting mould has a critical influence on strand surface quality, casting productivity and operating safety. voestalpine Stahl GmbH has long been interested in the field of research into mould behaviour, and began with the investigation of heat flux in 1995, and then of thermal variability in 1999. Since 2000, an online mould thermal monitoring system for heat flux density, thermal variability and friction has been installed. The heat flow density in the mould is determined by measuring the inflow and outflow temperatures and the throughflow volume of the primary cooling water. Temperature as measured by a thermocouple based breakout detection system in the mould copper plate is used to investigate the thermal variability. These online measured values have been employed to examine the influence of casting parameters, steel analysis and casting powder on the heat flux and thermal variability, and the relationship between these variables and cracking. The knowledge gained through these wide ranging plant based investigations has been used as a major tool in the diagnosis of problems (such as breakout and sticking), for optimisation of the process, particularly in the field of casting powders, and for control of slab quality. In particular, this knowledge has been incorporated into online mould thermal monitoring.     

Optimisation of cutting length of continuously cast strands

Abstract

Weight per metre and strand circumference were measured, using sensitive methods, on 177 mm round strands, with particular attention being paid to phase transformation and thermal shrinkage in the vicinity of the peritectic. The following results were achieved for a broad range of steel grades. With constant mould dimensions, the weight per metre of round continuously cast strand increases as casting speed rises. Soft steels, such as grade S35 containing 0·10%C, have a low weight per metre, whereas harder grades, such as C60 with 0·60%C, have the highest weight per metre. Low alloyed steels and oilfield tubular grades occupy rankings between these extremes. Martensitic and more highly resulphurised round billets have a conspicuously low weight per metre. The following definitive influencing factors on weight per metre became apparent: expansion of the mould tube under exposure to heat; shrinkage as a result of δ - γ transformation; creep processes under exposure to ferrostatic pressure; density of the compact steel; and porosity in the strand centre. These influences lessen in the order in which they are listed; they are, in some cases, contradictory, and balance one another out.     

日本在软接触电磁连铸方面的最新研究进展

主要介绍了软接触电磁连铸的原理和日本最近几年来在软接触电磁连铸方面的研究进展,分析了电流强度、焦耳热、结晶器形状和早期凝固壳形态对铸坯表面质量的影响,提出了该技术还需进一步研究的关键问题.分析认为：感应线圈产生的焦耳热是决定铸坯表面质量的首要因素;电流强度存在一个最佳值,过大或者过小均会对铸坯表面质量产生不利影响;连铸条件相同时,角部形状为圆角的结晶器所生产出来的铸坯表面质量要好于角部形状为直角的结晶器.     

高速方坯连铸结晶器冶金理论问题探讨

提出并论述了高速方坯连铸结晶器冶金中结晶器热流、钢的凝固收缩、结晶器变形、锥度设计和圆角半径等问题,重点讨论了拉速、碳含量及润滑剂对热流的影响,不同碳含量的钢凝固收缩和相变特征以及结晶器热变形规律,提出了不同钢种的凝固收缩和相变收缩的计算方法和结晶器锥度、圆角半径的设计思路.     

凝固末端电磁搅拌和轻压下复合技术对大方坯高碳钢偏析和中心缩孔的影响

基于ANSYS软件建立了310 mm×360 mm断面大方坯连铸过程二维凝固传热数学模型,并采用窄面射钉试验及铸坯表面测温试验对模型的准确性进行了验证.通过模型研究了过热度、拉速和二冷比水量对铸坯中心固相率以及凝固坯壳分布的影响,并结合高碳耐磨球钢BU的高温拉伸试验结果,确定了最佳的拉速以及最优轻压下压下区间要求.通过工业试验对理论模型进行了验证,并分析研究了拉速对采用凝固末端电磁搅拌(F-EMS)以及凝固末端17 mm大压下量的轻压下技术生产310 mm×360 mm断面大方坯高碳耐磨球钢BU铸坯的偏析和中心缩孔的影响.结果表明:采用凝固末端电磁搅拌和轻压下复合技术,通过调整拉速优先满足轻压下压下区间要求,可显著降低中心偏析、V型偏析及中心缩孔,但如果仅达到凝固末端电磁搅拌位置要求时,则铸坯中心质量不会得到明显改善.拉速为0.52 m·min-1且轻压下压下区间铸坯中心固相率为0.30~0.75时,偏析和中心缩孔有很大程度的改善,不合理的压下量分配会引起铸坯出现内裂纹以及中心负偏析.      

Numerical Investigation of Shell Formation in Thin Slab Casting of Funnel-Type Mold

The key issue for modeling thin slab casting (TSC) process is to consider the evolution of the solid shell including fully solidified strand and partially solidified dendritic mushy zone, which strongly interacts with the turbulent flow and in the meantime is subject to continuous deformation due to the funnel-type mold. Here an enthalpy-based mixture solidification model that considers turbulent flow [Prescott and Incropera, ASME HTD, 1994, vol. 280, pp. 59–69] is employed and further enhanced by including the motion of the solidifying and deforming solid shell. The motion of the solid phase is calculated with an incompressible rigid viscoplastic model on the basis of an assumed moving boundary velocity condition. In the first part, a 2D benchmark is simulated to mimic the solidification and motion of the solid shell. The importance of numerical treatment of the advection of latent heat in the deforming solid shell (mushy zone) is specially addressed, and some interesting phenomena of interaction between the turbulent flow and the growing mushy zone are presented. In the second part, an example of 3D TSC is presented to demonstrate the model suitability. Finally, techniques for the improvement of calculation accuracy and computation efficiency as well as experimental evaluations are also discussed.     

Microstructure and cooling conditions of steel solidified in the continuous casting mould

Importance of uniform shell growth and fine microstructure on breakout safety and strand surface quality. Analysis of heat flow and shell growth in the mould for a 0.62 wt% C-steel, and correlation with the microstructure by comparison of calculated with measured dendrite arm spacing. Proposal of metallographic standards for the subsurface microstructure in order to check the intensity and uniformity of solidification conditions in the mould.     

Water model study on fluid flow in slab continuous casting mould with solidified shell

Abstract

A water modelling experiment was conducted to study the fluid flow in a continuous slab casting mould with solidified shell. The level fluctuation, residence time distribution and velocity of free surface have been varied in the water model to study the differences of flow behaviour between the mould with a shell and without a shell. The results show that the mould with a solidified shell has higher level fluctuations, higher surface velocities and worse liquid slag distribution. The tapering of the shell in the mould enabled downward flow to facilitate more fluid being ‘pushed’ into the upper recirculation zone, yielding higher velocities and greater turbulence at the top surface. With the consideration of the solidified shell, the fluid flow in the mould is more representative of real casters, and the physical modelling results will be more accurate and reliable. It may cause unrealistic lower surface level fluctuations and surface velocities in the water model when the solidified shell is neglected in the mould.