待定系数法确定双辊薄带铸轧中的边界热流

熔池与铸轧辊接触的边界热流是进行双辊薄带铸轧数值模拟研究的重点,通过铸轧过程中金属凝固机制和传热过程的研究,提出结晶辊和熔池接触的边界热流分布函数形式,利用凝固初始位置、薄带坯出坯厚度,再结合能量守恒原理进行求解,确定函数中的待定参数,避开传统方法需要求解坯壳和铸轧辊间气隙热阻的难题;通过施加所提出的边界热流函数对某试验铸轧辊温度场进行求解,结果与实测结果相吻合,这表明文中提出的边界热流分布函数形式与实际相符合。     

Computational fluid dynamics applied to twin-roll casting

Near-net-shape casting technology is one of the most important research areas in the iron and steel industry today. Driving forces for the development of this technology include a reduction in the number of operations needed for conventionally produced strip. This is especially true of hot rolling operations. The consequent reduction in investment costs, when considering new industrial facilities, makes near-net-shape casting operations extremely attractive from a commercial standpoint.Various processes for near-net-shape casting of steel are currently being developed around the world. Of these processes, the twin-roll casting machines represent a major area of concentration. We believe that one of the main issues concerning the design of twin-roll casters is the metal delivery system and its effects on the homogeneity of solid shell formation, segregation and surface quality.In the present work, computational fluid dynamics has been used to study different metal delivery systems for twin-roll casting. The METFLO code has been adapted to simulate three dimensional turbulent fluid flow, heat transfer and solidification in this type of machine. The enthalpy-porosity technique was used to couple fluid flow and solidification phenomena. Two configurations for metal delivery system have been studied to date, one is a conventional tubular nozzle with horizontal outlets in the directions of the side dams. The other is a slot nozzle with a vertical inlet stream.These simulations have been applied to a pilot caster being studied in Canada, with a roll radius of 0.30 m, producing steel strips with thicknesses ranging from 4 to 7 mm, at relatively low roll speeds ranging between 4 and 12 m⧹min. Different positions and penetrations of the nozzles in the liquid pool have also been analysed. It has been shown that the tubular nozzle leads to the formation of a solid shell that is thicker at the centre of the caster. The slot nozzle gives a more uniform thickness of the solid shell along the roll width. In both configurations, a thicker solid shell is formed close to the roll edges, due to the presence of the side dams.It has also been demonstrated that the slot nozzle gives lower levels of turbulence at the free surface, which can have positive effects on the product quality.     

双辊薄带连续铸轧熔池内金属流动及传热特性的研究

本文建立了双辊式薄带连续铸轧熔池内二维传热流动数学模型，使用有限元计算方法实现了控制方程及边界条件的数值求解，计算结果揭示了熔池内的流场、凝固温度场的特点和规律。     

Modeling on Dendrite Growth of Medium Carbon Steel during Continuous Casting

Dendrite growth is an important phenomenon during steel solidification. In the current paper, a numerical method was used to analyse and calculate the dendrite tip radius, dendrite growth velocity, liquid concentration, temperature gradient, cooling rate, secondary dendrite arm spacing, and the dendrite tip temperature in front of the solid/liquid (S/L) interface for the solidification process of medium carbon steels during continuous casting. The current model was well validated by published models and measurement data. The results show that in the continuous casting process, the dendrite growth rate is dominated by the casting speed. Dendrite growth rate, liquid concentration at the S/L interface, temperature gradient and cooling rate decrease with proceeding solidification and solid shell thickness growth, while other parameters such as dendrite tip radius, secondary dendrite arm spacing, and dendrite tip temperature in front of the S/L interface become larger with solidification progress and solid shell thickness growth. Parametric investigations were carried out. The effects of the stability coefficient, temperature gradient and casting speed on the micro‐structural parameters were discussed. Under the same conditions, higher casting speed promotes coarser secondary dendrite arm spacing and enlarges the dendrite tip radius, while decreasing temperature gradient, reducing the dendrite growth rate and making the solute distribute more uniform.     

Vibration Method to Detect Liquid–Solid Fraction and Final Solidifying End for Continuous Casting Slab

Accurate measurement of liquid–solid fraction of casting slab in the secondary cooling zone and precise prediction of final solidifying end of casting slab have momentous significances for internal defects improvement of continuous casting slabs, such as the segregation and shrinkage porosity etc. However, the on‐line detection of slab solidification processing and final solidifying end haven't accomplished, which have been acknowledged as metallurgy problem all over the world. The paper presents a novel method, which called vibration method, to detect the liquid fraction and locate the final solidifying end of continuous casting slab. A physical simulation device using the materials of organic glass and water has been set up according to the similarity theory. Basing on theoretical deduction, physical experiment and numerical simulation, the research results provide guidance and reference for the on‐line detection of liquid–solid fraction and final solidifying end of the slab.     

Numerical Simulation of Filling Process During Twin-Roll Strip Casting

The modeling and controlling of flow and solidification of melt metal in the filling process is important for obtaining the optimal pool level and the formation of the solidified metal layer on the surface of twin-rolls during the twin-roll strip casting. The proper delivery system and processing parameters plays a key role to control flow characteristics in the initial filling stage of the twin-roll strip casting process. In this paper, a commercial CFD software was employed to simulate the transient fluid flow, heat transfer, and solidifications behaviors during the pouring stage of twin-roll strip casting process using different delivery systems. A 3D model was set up to solve the coupled set of governing differential equations for mass, momentum, and energy balance. The transient free-surface problem was treated with the volume of fluid approach, a k–? turbulence model was employed to handle the turbulence effect and an enthalpy method was used to predict phase change during solidification. The predicted results showed that a wedge-shaped delivery system might have a beneficial impact on the distribution of molten steel and solidification. The predicted surface profile agreed well with the measured values in water model.     

双辊薄带连铸技术状况的调查分析

调查了双辊薄带铸轧生产线的运行状况。整理出其工业化应用所需要的基础数据,如用于相关设计和决策的连浇时间、作业率等。给出了生产能力的算例。利用经典的传热凝固理论和经验对双辊连铸的关键参数进行界定,导出了辊缝d(铸带厚度)和辊径D、液位h和最大浇铸速度Vcm的关系。分析了铁辊和铜辊的差异。总结分析了双辊铸带宏观偏析有别于连铸坯的现象和机制。     

Simple model for thermal calculation in twin-roll strip casting process

The numerical model for the solidification process of metal in the twin-roll type strip caster is presented in this paper. In the model the temperature change as well as the eliminating process of latent heat is calculated along the stream lines obtained by a comparatively simple velocity field. The calculations are carried out on the strip casting of type 304 stainless steel under various casting parameters. The results so obtained show a good fit to the experimental ones, and suggest that the control of the height of molten pool is of importance to the establishment of the optimal operation.     

双辊铸轧薄带钢铸轧力计算公式及控制模型

在经典轧制理论和现代连铸理论相结合的基础上,推导出了铸轧力计算公式,并建立了一个非线性状态空间模型,描述双辊结晶器内的金属凝固和塑性变形.此模型可以作为双辊铸轧薄带钢过程铸轧力的实时在线控制模型.     

薄板坯连铸连轧的液芯压下技术

介绍了国内外薄板坯连铸连轧流程中液芯压下技术的发展与应用情况,分析了液芯压下过程中铸坯的凝固机理以及变形的应变特点,并根据铸坯的凝固机理和坯壳凝固前沿的应变条件,提出了确定单辊压下量、压下量分配和总压下量的基本方法。     

On the use of analytic approximations for describing the macroscopic heat flow during solidification

In this paper both conceptual and numerical analyses of the integral profile method as applied to solidification problems are conducted. Two important examples are considered,viz. a case where the nonsteady state exact solution of the thermal field is known and a thermal analysis of continuous casting. It is shown that the method as it was generalized by Hills may lead in the latter case to serious contradictions with basic thermodynamic principles. It is also shown that the method developed by Tien using a different set of boundary conditions is unsuitable for treating general solidification problems. It is thus concluded that approximate solutions of the thermal field during solidification must be evaluated under rather severe boundary conditions.     

铝电磁铸轧液固区中流体行为

介绍了铝电磁连续铸轧液固相区中电磁场的基本特性,描述了流体的运动轨迹与液固相界面的耕合形式,探讨了它们对液固相边界层的作用效果,分析了正弦波扰动对液固相界面稳定性的影响。     

双辊连铸工艺参数对薄带坯质量的影响

介绍了双辊薄带坯连铸的表面质量和内在质量与连铸工艺的关系。对于辊径为φ500mm．辊面宽250mm的双辊连铸机（浇注奥氏体不锈钢带坯）而言,控制连铸速度18—22m／min,双辊间熔池液位高度约110mm,铸辊压力25—40kN,熔池采用层流式布流,水口深度约10mm,以及液面采用惰性气体保护时,可以最大限度获得裂纹少、板型好、表面光洁、内部夹杂少的较佳表面质量和内在质量的铸带坯。     

水平连铸结晶器内真实换热边界计算及传递模型

连铸结晶器内冷却水的流动、传热和金属液的传热、凝固全耦合计算时,模型计算效率低、收敛性差,而不考虑真实冷却水流场只进行金属液传热-凝固耦合时,模型计算精度较低,可将冷却水流动-传热和金属液传热-凝固过程分别建模,并基于二次开发的温度场量原位传递程序,将模型串联耦合。结果表明,通过耦合流场计算得到的真实冷却边界替代传统均匀界面换热系数的边界条件施加方式,在保证模型计算效率和计算精度的前提下,可准确模拟铸坯晶粒的尺寸、取向和数量,经试验验证,模拟结果与试验结果高度吻合。     

Two-phase modeling of mushy zone parameters associated with hot tearing

A two-phase continuum model for an isotropic mushy zone is presented. The model is based upon the general volume-averaged conservation equations, and quantities associated with hot tearing are included, i.e., after-feeding of the liquid melt due to solidification shrinkage is taken into account as well as thermally induced deformation of the solid phase. The model is implemented numerically for a one-dimensional model problem with some similarities to the aluminium direct chill (DC) casting process. The variation of some key parameters that are known to influence the hot-tearing tendency is then studied. The results indicate that both liquid pressure drop due to feeding difficulties and tensile stress caused by thermal contraction of the solid phase are necessary for the formation of hot tears. Based upon results from the one-dimensional model, it is furthermore concluded that none of the hot-tearing criteria suggested in the literature are able to predict the variation in hot-tearing susceptibility resulting from a variation in all of the following parameters: solidification interval, cooling contraction of the solid phase, casting speed, and liquid fraction at coherency.     

铝带坯双辊铸轧过程瞬态传热数学模型

采用拉格朗日随体坐标建立了铝双辊铸轧过程瞬态传热数学模型。模型考虑了金属凝固动力学条件和采用试验测定的辊／铝带坯界面接触换热系数边界条件，用有限差分方法对控制方程进行了数值求解，并由现场测试数据验证了传热数学模型的正确性。     

Modeling of the Twin-Roll Casting Process: Transition from Casting to Rolling

During twin-roll casting, an alloy melt is passing the gap between two counter-rotating rolls, where cooling and solidification leads to the continuous formation of a solid strand. In order to describe this process, a two-phase Eulerian–Eulerian volume-averaging model is presented that accounts for (1) transport and growth of spherical grains within a flowing melt, (2) the formation of a coherent solid network above a specific solid fraction and (3) the viscoplastic flow of the solid network with the interstitial melt during casting and compression. For the considered case of an inoculated Al–4wt%Cu alloy, the process conditions are chosen such that two relatively thick viscoplastic semi-solid shells meet between the rolls, and thus, the material is pressed together and squeezed against the casting direction. The squeezed out material consists of segregated melt and some solid that quickly disappears after melting. It is observed during this study that macrosegregation distributions are inherently connected to the mush deformation that is enforced during the hot rolling process.     

IAD法在双辊铸轧薄带温度场数值模拟中的应用

双辊铸轧薄带过程中的凝固传热现象十分复杂。用交替方向隐式插分法通过VB语言计算了薄带坯的动态温度场,进而模拟了薄带坯的凝固传热过程,对实际生产有重要的参考价值。     

Heat-flux measurements of industrial on-site continuous copper casting and their use as boundary conditions for numerical simulations

An embedded sensor, designed for rapid and accurate response times and using wireless data transmission, has been developed for the on-site measurement of temperatures in industrial continuous casting moulds. The sensor has been used to measure the temperature at several points in the mould during production in a Southwire copper casting process. The measured data has been used to calculate the temperature gradient in the mould to estimate the heat flux through it; this is then used as a boundary condition for numerical simulations of solidification. For these, we employ a method that tracks the solidification front explicitly; this has an advantage over fixed-grid methods in simulations for materials having a short solidification interval, since the release of latent heat at the solidification front can be resolved without resorting to a very fine mesh. The special considerations required for setting the initial condition for the numerical scheme and the time taken for the superheated melt to form a solid shell are also discussed.     

Mathematical Analysis of the Solidification Behavior of Plain Steel Based on Solute- and Heat-Transfer Equations in the Liquid–Solid Zone

An analytical approximate solution to non-linear solute- and heat-transfer equations in the unsteady-state mushy zone of Fe-C plain steel has been obtained, assuming a linear relationship between the solid fraction and the temperature of the mushy zone. The heat transfer equations for both the solid and liquid zone along with the boundary conditions have been linked with the equations to solve the whole equations. The model predictions (e.g., the solidification constants and the effective partition ratio) agree with the generally accepted values and with a separately performed numerical analysis. The solidus temperature predicted by the model is in the intermediate range of the reported formulas. The model and Neuman’s solution are consistent in the low carbon range. A conventional numerical heat analysis (i.e., an equivalent specific heat method using the solidus temperature predicted by the model) is consistent with the model predictions for Fe-C plain steels. The model presented herein simplifies the computations to solve the solute- and heat-transfer simultaneous equations while searching for a solidus temperature as a part of the solution. Thus, this model can reduce the complexity of analyses considering the heat- and solute-transfer phenomena in the mushy zone.