连铸过程中湍流传输和两相区凝固的数值模拟

综述了在连铸数值模拟过程中，为评估流体流动对铸坯热量传递和凝固过程影响所开发的有效导热模型和耦合模型。根据文献和用商业CFD软件计算的结果分析了在连铸湍流传输和两相区凝固的数值模拟过程中影响模型预测精确性的关键因素，包括有效导热模型中有效导热系数的确定、数值模拟模型的选取、湍流模型的应用、连铸坯凝固过程中湍流向层流的过渡、两相区流动中多孔介质的渗透率取值、固相分率与温度和成分的关系等，并给出选取合适模型参数的原则。     

连铸板坯凝固传热过程的计算机模拟

建立了板坯连铸的凝固传热数学模型，充分考虑了弧形铸坯的几何特点，采用有限单元法求解控制方程。通过变参数φ来考虑铸坯内钢水和两相糊状区的导热系数，计算了参数φ、结晶热通量、拉速和二冷强度对铸坯表面温度和坯壳厚度的影响。结果表明，模型的准确性得到提高，拉速对固液界面有明显影响，二冷强度对铸坯表面温度影响非常大。     

基于连续模型的板坯连铸凝固过程的数值模拟

结合实际测量数据，建立了基于连续模型的板坯连铸过程流场、温度场和凝固的三维耦合数学模型。计算结果表明：该模型可用于描述连铸板坯结晶器和整个二冷喷水区的凝固进程；凝固坯壳的生长限制了流体流动的空间，加快了水口出口钢流的动量衰减；流体流动加快了铸坯内部传热机制由对流向热传导传热的转变进程，控制了两相区的发展。     

反向凝固结晶器中流动与传热的数值模拟

文中根据连续统一模型建立了描述反向凝固结晶器中的流动与传热的数学模型。研究结果表明了反向凝固工艺母带增长的三阶段规律。即快速增长。平衡相持和快速回熔^[1,3,5]。通过母带厚度的实验值和模拟值的比较。验证了模型的正确性。     

连铸凝固传热时液相有效导热系数的定量化

在已验证的电磁-热-溶质传输耦合模型的基础上,以某钢厂同时装配有M-EMS和F-EMS的方、圆坯先进铸机为研究对象,对二维切片凝固传热模型中液相有效导热系数的放大倍数m值进行了定量化研究。结果表明,溶质再分配作用下,方、圆坯凝固终点处的钢液液相线温度较浸入式水口入口处的分别约下降了23.27和5.54℃;与二维切片模型相比,采用耦合模型计算时,铸坯凝固终点位置分别后移了1.8和0.9m;为保证同时准确获取铸坯表面温度分布状态及其内部凝固终点位置,在本方、圆坯工况下,二维切片模型中纯液相和糊状区内液相有效导热系数放大倍数的推荐值范围分别为2.2~2.4和1.1~1.2。     

方坯连铸凝固传热的复合数值模拟

根据连铸机特点和铸流场特性，在拉坯方向上将整个铸流长度划分为上部计算域和下部计算域。对于铸坯温度场的数值模拟，上部计算域充分耦合钢液对流对传热的影响，采用了三维稳态流动传热耦合模型；下部计算域则将铸流场对传热的影响考虑为有效导热系数，并忽略拉坯方向上的传热效果，采用了二维非稳态有效导热系数模型。计算过程和结果表明，采用此复合模拟方法保证了数值模拟的准确性并降低了仿真程序的计算成本。     

反向凝固结晶器中流动与传热的计算机仿真研究

建立了描述反向凝固结晶器中流动与传热的数学模型，并在此模型基础上进行了计算机模拟和仿真。结果表明了反向凝固工艺母带增长的三阶段规律，即快速增长、平衡相持和快速回熔。通过比较母带厚度的实验值和模拟值，验证了模型的正确性。     

An analytical solution of directional solidification with mushy zone

An analytical heat transfer model is presented that describes the temperature distribution and the positions of solidus and liquidus isotherms in the unidirectional solidification of binary alloys. The proposed technique employs the mathematical expedient of replacing the interfacial thermal resistance by equivalent layers of material. The application of the model is demonstrated by comparison with experimental data and with a finite difference method.     

Finite element method simulation of mushy zone behavior during direct-chill casting of an Al-4.5 pct Cu alloy

In this article, the stresses, strains, sump depth, mushy zone length, and temperature fields are calculated through the simulation of the direct-chill (DC) casting process for a round billet by using a finite-element method (FEM). Focus is put on the mushy zone and solid region close to it. In the center of the billet, circumferential stresses and strains (which play a main role in hot cracking) are tensile close to the solidus temperature, whereas they are compressive near the surface of the billet. The stresses, strains, depth of sump, and length of mushy zone increase with increasing casting speed. They are maximum in the start-up phase and are reduced by applying a ramping procedure in the start-up phase. Stresses, strains, depth of sump, and length of mushy zone are highest in the center of the billet for all casting conditions considered.     

Modeling of solute redistribution in the mushy zone during solidification of aluminum-copper alloys

A mathematical model has been established to predict the formation of macrosegregation for a unidirectional solidification of aluminum-copper alloys cooled from the bottom. The model, based on the continuum formulation, allows the calculation of transient distributions of temperature, velocity, and species in the solidifying alloy caused by thermosolutal convection and shrinkage-induced fluid flow. Positive segregation in the casting near the bottom (inverse segregation) is found, which is accompanied by a moving negative-segregated mushy zone. The effects of shrinkage-induced fluid flow and solute diffusion on the formation of macrosegregation are examined. It is found that the redistribution of solute in the solidifying alloy is caused by the flow of solute-rich liquid in the mushy zone due to solidification shrinkage. A higher heat-extraction rate at the bottom increases the solidification rate, decreasing the size of the mushy zone, reducing the flow of solute-rich liquid in the mushy zone and, as a result, lessening the severity of inverse segregation. Comparisons between the theoretical predictions from the present study and previous modeling results and available experimental data are made, and good agreements are obtained.     

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.     

Mathematical simulation on coupled flow, heat, and solute transport in slab continuous casting process

A three-dimensional comprehensively coupled model has been developed to describe the transport phenomena, including fluid flow, heat transfer, solidification, and solute redistribution in the continuous casting process. The continuous casting process is considered as a solidification process in a multicomponent solid-liquid phase system. The porous media theory is used to model the blockage of fluid flow by columnar dendrites in the mushy zone. The relation between flow pattern and the shape of the solid shell is demonstrated. Double diffusive convection caused by thermal and concentration gradients is considered. The change in the liquidus temperature with liquid concentration is also considered. The formation mechanism of macrosegregation is investigated. Calculated solid shell thickness and temperature distribution in liquid core are compared with the measured quantities for validating the model.     

The movement of the concave casting surface during mushy-type solidification and its effect on the heat-transfer coefficient

The air gap formation process at the casting/mold interface of a hollow cylinder casting was investigated for alloys solidifying in a mushy type by measuring the displacements of the casting and the mold surfaces during solidification. The formation process of the air gap between the convex casting surface and the outer mold and the heat-transfer coefficient through the gap have been well documented by previous publications. However, the air gap between the concave casting surface and the inner mold, or the core, was found to form differently during mushy solidification, in which the air gap formed during solidification, reached a maximum gap distance, and then decreased due to the contraction of the solidified casting on the expanding inner mold. The gap formation was caused by an inward collapse of the coherent dendrite networks at the concave interface because of low pressure inside of the casting due to solidification shrinkage. The coherent dendrite networks at the convex interface did not collapse inward. The heat-transfer coefficients estimated by measuring the air gap thickness showed a similar tendency to the calculated values obtained by the inverse heat-conduction analysis.     

The influence of convection during solidification on fragmentation of the mushy zone of a model alloy

Experiments have been conducted to observe fragmentation events in a model alloy (succinonitrile and acetone) solidifying in the presence of forced convection in the superheated melt. Measurements of fragmentation rates have been made, and an attempt was made to relate the results to the controllable parameters of the system. A microscope-video system recorded the mushy zone-melt interface, and the fragmentation process and fragmentation rates could be determined from a frame-by-frame analysis of the video images. Experiments were conducted for varying cooling rates, overall temperature differences, melt flow rates, and for two different concentrations of acetone (1.3 and 6.1 wt pct). Significant dendritic fragmentation occurred for all runs. In addition, the influence of buoyancy forces is clearly evident from particle motion near the mushy zone-melt interface. Fragmentation rates appear to correlate well with the magnitude of particle velocities near the interface, with increasing fragmentation being associated with higher particle velocity magnitude (either in the same or the opposite direction to the mean flow) for the 1.3 wt pct acetone mixture. However, the correlation is quite different for the higher concentration. The relationship between these results and the possible mechanisms for fragmentation are discussed. Although it appears that either constitutional remelting or capillary pinching are likely of importance, hydrodynamic shear forces or some other mechanism as yet undiscovered cannot be completely discounted, although circumstantial evidence suggests that mechanical shearing is inconsistent with observations made both here and already in published literature. The results provide a step in the development of solidification models that incorporate fragmentation processes in the mushy zone as an important mechanism of grain refinement and a potential source of macrosegregation in ingots and large castings.