流动作用下晶体生长的大尺度定量相场模拟与原位观察研究

Owing to the avoidance of explicit tracking of the solid-liquid interface and the convenience to treat the topology change of the interface, the phase-field approach has emerged as a widely being used numerical simulation method to study the dendritic crystal growth during solidification over the past two decades. Yet, as the extremely low computing efficiency of the phase-field simulation, the dimension scale for studies of dendrite growth usually is limited which results in the difficulty to quantitatively compare the simulation with experimental data directly, especially for the alloy dendrite growth with consideration of liquid flow effects due to the dependence of melt convection strength on the scale of simulation domain. Hence, in combination with the in situ and real-time experimental observation of dendrite growth by means of synchrotron X-ray radiography, it is highly necessary to simulate the dendrite growth from melt with consideration of liquid flow in large-scale so that the growth dynamics and interaction of dendritic grains can be fully illustrated. Therefore, in this project, based on the finite element method using adaptive mesh, the distributed parallel numerical calculation method with multi-set of meshes and dynamic loading balance algorithm will be firstly developed to solve the phase-field governing equations. Then, the phase-field simulations of metallic alloy dendrite growth in directional solidification and equiaxed dendritic crystal growth from melt by continuously cooling down under influence of thermo-solutal convection will be performed in large-scale(i.e. 5mm × 10mm) using the elaborated efficient numerical calculation method. Finally, in situ and real-time experimental observations will be carried out to study the dendrite growth and to benchmark the phase-field simulations. The growth and interactions of dendritic grains in solidification will be elucidated with these analyses of simulation and experimental data, and thus a progress of solidification fundamentals regarding to crystal growth will be achieved.

由于固液界面不需要显式地追踪，界面拓扑变化处理也比较便利，相场方法已成为近年来研究凝固晶体生长的一种常用方法。但是相场模拟的计算效率比较低，模拟尺度一般都比较小，将模拟的晶体生长与实验进行直接定量比较尚存在一些困难，尤其是耦合流动的合金凝固模拟。因此，结合目前发展起来的高分辨率同步辐射X射线原位实时观察实验，很有必要同时开展考虑流动作用的晶体生长大尺度模拟，深刻理解凝固枝晶生长动力学和晶粒间的相互作用。为此，本项目首先基于自适应网格有限元算法，开发支持多套网格和动态负载平衡的分布式并行相场计算方法。然后，采用这一高效的数值方法，在大尺度范围内（如5 mm × 10 mm），模拟研究存在热溶质对流时，金属合金定向凝固枝晶生长和连续冷却条件下的等轴晶生长规律。最后，基于同步辐射X射线原位实时观察数据，并结合模拟结果，分析晶体生长动力学和晶粒之间的相互作用规律，发展与枝晶生长相关的凝固基础理论。

由于固液界面不需要显式地追踪，界面拓扑变化处理也比较便利，相场方法已成为近年来研究凝固晶体生长的一种常用方法。但是相场模拟的计算效率比较低，模拟尺度一般都比较小，将模拟的晶体生长与实验进行直接定量比较尚存在一些困难，尤其是耦合流动的凝固模拟。因此，为提高相场模拟的效率和尺度，在项目的资助下，一方面从数值计算方法上出发，开发出了万核级别的自适应网格有限元并行计算相场模拟程序，并在天河二号上顺利实施；另一方面，在数学模型上，对相场方程进行了非线性预条件处理，弱化相场计算对界面处网格尺寸的依赖性。然后，利用所建立的模型和开发的程序进行了二维和三维的模拟，在二维上实现了厘米尺度数千个晶粒的模拟，三维模拟也达到了毫米级别。根据模拟研究了二维与三维枝晶生长的差异，以及液体流动的影响。采用这一高效的数值方法，进行了与同步辐射X射线原位观察实验尺度（如5.04mm × 12.26mm × 0.2mm）完全一致的二维与三维相场模拟，研究了大尺度并存在热溶质对流时，金属合金凝固枝晶生长动力学、微观偏析和自然对流特点，明确了晶体生长动力学和晶粒之间的相互作用规律，发展了与枝晶生长相关的凝固基础理论。