耦合长程流动及溶质传输的铝合金铸坯凝固组织直接宏观建模

The quantitative relationship between the casting process and grain structure during solidification is an important issue of the materials science and engineering. Exploring the impact of macroscopic fluid flow on the grain structure is a challenge. This study intends to establish a direct macroscopic model of the grain structure during the aluminum alloy casting, which reveals the interaction mechanism between the macroscopic transportation and grain structure. The coupling algorithm and software of the cellular automaton method for grain structure and the finite element method for macroscopic transportation will be developed to obtain the relationship among the long distance fluid flow, grain sedimentation, species transportation and grain structure of aluminum alloy casting. Based on the multi-phase volume average model, the equilibrium equations of energy, momentum and species will be established with the consideration of free equiaxed sedimentation. The liquid phase is subdivided into a uniform composition interdendritic liquid plus an extradendritic liquid. Mass exchanges are considered between the solid phase and the liquid phase. The models of nucleation and growth will be established based on thermodynamics and kinetics of solidification. A set of methods such as the arbitrary Lagrangian-Eulerian approach, the adaptive dynamic grid, the enthalpy temperature formulation and the stabilized SUPG/PSPG/LSIC term for the solving convection-diffusion equations with the phase change will be proposed. The multi-component, multi-phase and multi-scale coupling problem will be solved, and the grain structure of the direct chill slab casting of aluminum alloy will be predicted even with the condition of unfixed calculation domain and unsteady macroscopic transportation.

研究铸造条件与凝固组织之间的定量关系是材料科学与工程的重要内容。处理产品尺度上的长程流动是凝固组织模拟的一项挑战。本研究建立铝合金凝固组织直接宏观模拟数学模型，揭示宏观传输与凝固组织相互作用机理。开发有限元/宏观传输与元胞自动机/凝固组织的耦合算法及软件，探明长程流动、等轴晶运动及溶质分布对凝固组织的影响规律。宏观上建立多相体积平均模型，确定热流质守恒关系，描述等轴晶自由运动。介观上定义晶粒包络面，将凝固晶粒分为晶粒内液相与固相；通过不同扩散程度的偏析表达式，对计算单元中晶粒内液相与固相建立溶质流量平衡关系。基于凝固热力学、动力学，建立形核长大及共晶生长模型。提出任意拉格朗日欧拉法、自适应动网格、焓与温度混合格式及SUPG稳定与LSIC约束等求解技术，处理流固耦合相变对流扩散方程；解决多场多相多元多尺度耦合稳定性问题，实现非固定域非稳定长程流动条件下铝合金半连续铸造凝固组织的预测。

耦合长程流动及宏观偏析是模拟实际铸造过程中凝固组织的一项挑战。凝固组织与宏观偏析的形成涉及宏观、介观和微观多个尺度上的物理现象。研究凝固过程演变，有助于铸造工艺优化，具有重要的工程应用价值。 . 本研究针对多组元合金热顶充填凝固过程，建立了凝固组织直接模拟CAFE模型。模型在宏观尺度上采用有限元（FE）方法求解质量、动量、能量和溶质守恒方程，在介观尺度上采用元胞自动机（CA）方法计算凝固过程中的晶粒形核、生长和演变；在微观尺度上采用考虑过冷的微观偏析模型处理CA胞元的凝固转变。通过欧拉方法进行前处理和后处理，采用拉格朗日方法求解非固定域的多尺度耦合问题。开发了有限元/宏观传输与元胞自动机/凝固组织的模拟软件，探明长程流动、等轴晶运动及溶质分布对凝固组织的影响规律。解决了多场多相多元多尺度耦合稳定性问题，实现了非固定域非稳定长程流动条件下凝固组织及宏观偏析的预测。. 针对多组元铝合金半连续铸造过程的数值模拟结果表明，模型能够合理地预测晶粒细化和未细化铸坯中的晶粒组织和宏观偏析。未细化铸坯中出现了典型的等轴晶到柱状晶转变。晶粒细化铸坯中全部为等轴晶粒，且其宏观偏析程度比未细化铸坯中更轻。随着形核过冷度的降低，潜热释放加快，糊状区宽度收窄，熔体过冷区缩小，凝固组织从典型的CET组织变为完全的等轴晶组织，铸坯表面的负偏析和心部的正偏析缓解，而底部的负偏析则加重。模拟结果与实际基本一致。. 此外，建立了间接耦合凝固组织的宏观偏析多相模型。应用于电渣重熔及真空电弧熔炼等铸造工艺的直接与间接模拟结果表明，宏观偏析受凝固组织及等轴晶运动的影响。

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