Verification of a scaling relation for dendritic solidification with interdendritic convection; simulation and experiment. Part I: Simulation

合金在陆地条件下的凝固不可避免地受到浮力流动的影响，这是由于偏析导致的熔体中的高密度梯度。大多数现有的铸态组织预测模型忽略了这一影响，它严重影响了物质的传输，并被认为会在单晶凝固过程中造成有害的缺陷，如雀斑。基于最近在二维近似下的相场研究，提出了一个标度关系式，该关系式预测了定向凝固中一次枝晶的最小和平均间距与合金、工艺条件和重力矢量的关系。使用今天的计算设施，这些预测将使用3D模拟来验证。由于不可能通过实验来定量评估枝晶间流动，因此计划在第二个项目期进行允许间接验证模拟的关键实验。合金凝固的相场模拟将与流体流动的格子-玻尔兹曼模拟相耦合。模拟将在大规模并行体系结构上使用自适应多网格策略进行。该项目有望给出陆地条件下决定枝晶凝固结构的复杂机制的完整图景。标度理论将指明一条改进微观组织模型的途径，用于铸造工艺的优化。

Alloy solidification under terrestrial conditions is inevitably influenced by buoyancy flow due to high density gradients in the melt caused by segregation. Most available models to predict casting microstructures neglect this effect which significantly affects transport of species and is known to cause detrimental defects like freckles in single crystal solidification. Based on recent phase-field studies in 2D approximation a scaling relation was proposed which predicts the minimum and average spacing of primary dendrites in directional solidification in dependence of the alloy, the process conditions and the vector of gravity. Using today’s computational facilities these predictions shall be verified using 3D simulations. Since it is impossible to quantitatively evaluate the interdendritic flow by experiments, critical experiments which allow an indirect verification of the simulations are planed for a second project period. Phase-field simulation of alloy solidification will be coupled to Lattice-Boltzmann simulation of fluid flow. The simulation will be performed using adaptive multi grid strategies on massive parallel architectures. The project is expected to give a complete picture of the complex mechanisms determining dendritic solidification structures under terrestrial conditions. The scaling theory will pinpoint a route to improved microstructure models to be used in optimization of casting processes.