密度差异驱动过冷熔体流动影响合金凝固微观组织的相场法研究

The multi-field coupling phase-field model which incorporates the melt flow that is induced by the density change for binary alloy is established based on a previously developed single system multicomponent alloys diffusion phase-field model and the two-phase diffuse-interface model for Hele-Shaw flows, and the factor of gravitation is also considered. A conjugate-gradient pressure Poisson solver is adopted to solve numerically the continuity and momentum equations for the flow, an reasonable and effective calculation method is presented for the phase-field and energy equations, and the parallel algorithm is used to improve computation efficiency of the model, a good case in point is to simulate the microstructural evolution with large-scale during solidification process by using A1-Cu binary alloy with a larger scale. The effect of buoyancy-driven flow, gravitational sedimentation on microstructure is studied, a profound analysis of the relation between crystal segregation, grain reproduction, dendritic morphology selection, growth orientation is given. By comparing to available sharp-interface results, the laws of the convergence with respect to the diffuse interface width are revealed, the effect of the melt flow that is induced by the density change for binary alloy on the dendrite tip selection parameter is examined, and the influence mechanism of processing parameters on multi-physical coupled fields during solidification processes is explored.The research is not only beneficial to understand mechanism deeply for formation of solidification structure, but also has the important value in engineering application for the produce of semiconductor crystal materials using crystal growth with floating zone method in the ground gravity field environment.

本项目基于单相系统多元合金纯扩散相场模型与广义Hele-Shaw流动二相扩散界面方法，并考虑地面重力场因素，建立一个合金凝固过程中因固-液相密度差异驱动熔体流动的多场耦合相场模型。采用基于雅可比预条件共轭梯度法的压力泊松求解器求解流动场连续方程和动量方程，设计合理有效的相场模型数值求解方法，探索应用并行算法提高模型计算效率，以Al-4.5%Cu二元合金为例较大尺度地模拟凝固微观组织的演化过程。研究浮力对流、重力沉淀等对微观组织的影响，深入分析该流动与晶内偏析、晶粒繁殖、枝晶形态选择、生长方向等方面的关系。通过与解析解获得的尖锐界面模型对比，揭示关于扩散界面宽度收敛的规律，研究固液相密度差异驱动熔体流动对枝晶选择参数的影响，并探索工艺参数对凝固过程各物理场分布的影响机制。该项目不仅有助于深入理解凝固组织形成机制，而且对地面重力场环境中浮区晶体生长法制备半导体晶体等方面具有重要的工程应用价值。

将计算枝晶生长的多元合金单相系统多晶粒纯扩散相场模型与计算动量、质量及能量传输的LBM（Lattice Boltzmann Method）相耦合，建立了适用于模拟自然对流作用下合金枝晶生长的多场耦合相场模型以及耦合流场的共晶组织生长的相场模型；将Sola算法、SIMPLE等算法与相场模型相耦合，分别建立了模拟在强迫对流状态下枝晶生长的相场-Sola模型、相场-SIMPLE模型；综合考虑溶质在晶界富集对区域自由能的影响，建立了多次相变中固-固相变的形核模型；通过构建温度控制的顺序函数，将液-固相变模型与固-固相变模型耦合建立了一种新的液-固-固多相场模型；应用界面能的校正形式，建立了二元合金小晶面（faceted）枝晶生长的相场模型。. 针对传统求解多场耦合相场模型的数值计算方法中存在的计算量大、计算效率低、求解精度不高、模拟尺度小等瓶颈问题，探索高效的多场耦合相场模型先进计算技术，研究了自适应有限元法、基于MPI的并行系统结构、GPU并行编程、MPI+OpenMP混合编程、CUDA+GPU软硬件体系结构及MPI+CUDA不同粒度混合并行编程等高性能数值计算方法。. 以二元Al-4.5%Cu合金、Ni-Cu合金、Si-Ni合金、Fe-C合金、高纯丁二腈(SCN)等为例进行具体物理过程的仿真，较大尺度地模拟了凝固微观组织演变规律，研究了熔体流动、传热、传质与凝固过程枝晶形貌演变、枝晶形状选择参数、微观偏析、铸造工艺参数等之间的关系；模拟研究了强迫层流对微观偏析的影响、强迫对流下流速和流向对片状共晶生长形貌的影响、流动对定向凝固的界面形态演化影响、强迫层流对多晶粒非等温生长过程的影响以及非等温条件下低雷诺数过冷熔体强迫层流对流动法向枝晶生长的影响等；基于液-固-固多相场模型，以Fe-C为例研究了多相变的连续演变过程；基于小晶面（faceted）枝晶生长的相场模型，模拟研究了Si-Ni二元合金小晶面生长过程。. 将各高性能算法的模拟结果与微观可解理论值等晶体生长经典理论及实验结果进行了对比研究，验证了其可靠性；将各种高性能计算方法进行对比，评价了各种算法的性能，同时完善和改进计算模型，并评价模型和算法的有效性。该项目达到更深入理解凝固组织形成机制，为模拟预测铸件凝固微观组织和铸造缺陷奠定理论基础，为优化铸件的工艺和实现最佳的质量控制提供科学依据。