基于八叉树网格技术的相场法金属凝固过程组织模拟的研究
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摘要
凝固过程组织模拟能够在晶粒以及更细小的尺寸上模拟铸件凝固的微观演变过程，实现铸件凝固组织以及力学性能的预测，逐渐成为成形过程模拟的一个研究热点。相场法作为一种数值模拟方法，采用扩散界面模型，将界面处理成为一定厚度的连续界面，而避免了追踪复杂界面，因而在凝固过程组织模拟中被应用的越来越广泛，包括从纯金属到多元合金，二维到三维，共晶到包晶等。但是该方法对计算量的要求一直是限制其进一步发展的一个重要瓶颈，本文研究的主要目标即为提高相场法进行凝固组织模拟的计算效率以及计算能力。
本文首先从网格相互关系，数据结构，组建规则，遍历操作以及自适应网格等五个方面重点研究了八叉树自适应网格技术，同时构建了用于本文研究的相场法数学模型体系，具体包括纯金属相场模型，二元合金相场模型，各向异性处理技术以及本研究首次提出的多晶粒处理技术等；在讨论了基于八叉树网格一阶以及多阶导数离散技术的基础上，采用有限差分方法创造性的完成了基于八叉树网格的相场、浓度场以及温度场控制方程的离散和求解等工作，首次提出了在八叉树网格中巧妙的运用搜索层数值相同单元进行数值计算的方法，解决了温度导热系数与溶质传导系统量级不统一导致计算时间加长的问题；借助距离场生成技术完成了任意三维形状八叉树网格生成的研究工作，并给出了八叉树网格后处理显示中的网格节点坐标以及节点数值的处理方法，还对八叉树网格遍历以及自适应算法的并行计算技术进行了研究。
其次，采用八叉树自适应网格技术对纯金属单个等轴晶晶粒生长过程进行了数值模拟研究，与均匀网格数值模拟结果对比不仅证明了八叉树网格技术进行凝固组织模拟的可行性，同时也说明该技术在提高计算效率和计算能力的巨大优势，同时还分析了该技术的并行效率以及八叉树网格参数对凝固组织模拟结果的影响。对于等轴晶以及柱状晶的热物性参数对晶粒相貌生长影响进行了研究，并采用理论分析很好的解释了研究结果的变化规律；利用八叉树自适应网格技术的优势，对多个晶粒的等轴晶以及柱状晶生长过程进行数值模拟，模拟结果表明了该技术能很好的应用于此方面的研究。
再次，采用八叉树网格技术对二元合金等温凝固、非等温凝固两个方面进行了数值模拟工作，研究结果表明该技术能够很好的用于二元合金的凝固过程模拟数值实验，还通过二元合金凝固的微观偏析这一指数的变化规律从侧面证明了本技术应用于二元合金凝固组织模拟的准确性；在此基础上采用该技术对多个二元合金柱状晶生长过程进行了数值模拟，模拟结果表明了该技术同样适合于在此方面的研究。
最后，本文通过有机物溶液结晶实验以及实际浇注铝合金铸件金相实验，从纯金属以及二元合金两个方面对该技术进行凝固组织模拟结果进行了验证，结果表明本模拟结果在柱状晶生长中的熔断现象以及二元合金凝固树枝晶的生长与实验结果能够较好的吻合。
The numerical simulation of the solidification microstructure is subject to a growingbody of research because of the ability of showing the processing of the solidificationmicrostructure transformation in grains as well as finer size, predicting the microstructureof the casting and evaluating the mechanical properties of the casting. Based on the diffuseinterface model which makes the interface as a continuous interface with certain thicknessand avoids to track the complicated interface, the phase-field method as a numericalsimulation tool is applied widely in the numerical simulation of the solidificationmicrostructure, including from the pure metal to the multicomponent alloy, from the twodimension to three dimension, from the eutectic to peritectic and so on. The computationused for this method is the bottleneck for its further development. And the focus of thispaper is how to improve the computation efficiency and reduce the computation resourcewhen the phase field method is used for the numerical simulation of the solidificationmicrostructure.
Firstly, the adaptive mesh technology based on octree is research with the five aspectsof the relationship, the data structure, formation rules, the traversal operation and theadaptive mesh. The mathematical model of the phase field method is established includingthe pure metal model, the binary alloy model, the anisotropic and the multi-graintechnology. The control equation of the phase field, the concentration and the temperatureare discretization by the technology of the first and multi-order derivative gained in theoctree mesh. The method which the computation is done on the same level value cells isfirst proposed in this research. And it can solve the problem which the diffusion coefficientof the temperature and the concentration is not the same order. Based on the distancetechnology, this research gives the adaptive mesh generation mesh based on the octree.The method to obtain the position and the value of the mesh point in the post processorand the parallel computing techniques are also discussed in this research.
Secondly, the numerical simulation results of the single equiaxed grain growth of thepure metal are given. Contrast with the results using the uniform mesh, it can conclude thephase field with the adaptive mesh based on the octree which established in this paper hasthe ability not only to do the simulation of the solidification microstructure, but a greatimprovement for the computation and reduction the resource. The efficiency of the parallel and the affection of mesh parameters to the solidification microstructure are also discussedin this paper. Then this research gives the research on the relationship of thethermophysical parameters with the dendritic morphology of the equiaxed and columnargrains.
Thirdly, this paper gives the research on the numerical simulation of the isothermaland non-isothermal solidification of the binary alloy. It can be gained from the results thatthe phase-field model with adaptive mesh based on the octree can be applied well to thesimulation of the solidification microstructure of the binary alloy. And the variation of themicrosegregation of the binary alloy from the simulation results and the simulation resultsof the multi-columnar grains growth also gives the conclusion.
At last, two experiments including the organic solution crystallization and themetallographic experiment of the aluminium alloy casting are used to verify thesimulation results of the solidification microstructure of the pure metal and the binaryalloy. It is showed the simulation results and the experimental results are comparable inthe fuse of the columnar grain of the pure metal and the dendritic growth of the binaryalloy.
本文首先从网格相互关系，数据结构，组建规则，遍历操作以及自适应网格等五个方面重点研究了八叉树自适应网格技术，同时构建了用于本文研究的相场法数学模型体系，具体包括纯金属相场模型，二元合金相场模型，各向异性处理技术以及本研究首次提出的多晶粒处理技术等；在讨论了基于八叉树网格一阶以及多阶导数离散技术的基础上，采用有限差分方法创造性的完成了基于八叉树网格的相场、浓度场以及温度场控制方程的离散和求解等工作，首次提出了在八叉树网格中巧妙的运用搜索层数值相同单元进行数值计算的方法，解决了温度导热系数与溶质传导系统量级不统一导致计算时间加长的问题；借助距离场生成技术完成了任意三维形状八叉树网格生成的研究工作，并给出了八叉树网格后处理显示中的网格节点坐标以及节点数值的处理方法，还对八叉树网格遍历以及自适应算法的并行计算技术进行了研究。
其次，采用八叉树自适应网格技术对纯金属单个等轴晶晶粒生长过程进行了数值模拟研究，与均匀网格数值模拟结果对比不仅证明了八叉树网格技术进行凝固组织模拟的可行性，同时也说明该技术在提高计算效率和计算能力的巨大优势，同时还分析了该技术的并行效率以及八叉树网格参数对凝固组织模拟结果的影响。对于等轴晶以及柱状晶的热物性参数对晶粒相貌生长影响进行了研究，并采用理论分析很好的解释了研究结果的变化规律；利用八叉树自适应网格技术的优势，对多个晶粒的等轴晶以及柱状晶生长过程进行数值模拟，模拟结果表明了该技术能很好的应用于此方面的研究。
再次，采用八叉树网格技术对二元合金等温凝固、非等温凝固两个方面进行了数值模拟工作，研究结果表明该技术能够很好的用于二元合金的凝固过程模拟数值实验，还通过二元合金凝固的微观偏析这一指数的变化规律从侧面证明了本技术应用于二元合金凝固组织模拟的准确性；在此基础上采用该技术对多个二元合金柱状晶生长过程进行了数值模拟，模拟结果表明了该技术同样适合于在此方面的研究。
最后，本文通过有机物溶液结晶实验以及实际浇注铝合金铸件金相实验，从纯金属以及二元合金两个方面对该技术进行凝固组织模拟结果进行了验证，结果表明本模拟结果在柱状晶生长中的熔断现象以及二元合金凝固树枝晶的生长与实验结果能够较好的吻合。
The numerical simulation of the solidification microstructure is subject to a growingbody of research because of the ability of showing the processing of the solidificationmicrostructure transformation in grains as well as finer size, predicting the microstructureof the casting and evaluating the mechanical properties of the casting. Based on the diffuseinterface model which makes the interface as a continuous interface with certain thicknessand avoids to track the complicated interface, the phase-field method as a numericalsimulation tool is applied widely in the numerical simulation of the solidificationmicrostructure, including from the pure metal to the multicomponent alloy, from the twodimension to three dimension, from the eutectic to peritectic and so on. The computationused for this method is the bottleneck for its further development. And the focus of thispaper is how to improve the computation efficiency and reduce the computation resourcewhen the phase field method is used for the numerical simulation of the solidificationmicrostructure.
Firstly, the adaptive mesh technology based on octree is research with the five aspectsof the relationship, the data structure, formation rules, the traversal operation and theadaptive mesh. The mathematical model of the phase field method is established includingthe pure metal model, the binary alloy model, the anisotropic and the multi-graintechnology. The control equation of the phase field, the concentration and the temperatureare discretization by the technology of the first and multi-order derivative gained in theoctree mesh. The method which the computation is done on the same level value cells isfirst proposed in this research. And it can solve the problem which the diffusion coefficientof the temperature and the concentration is not the same order. Based on the distancetechnology, this research gives the adaptive mesh generation mesh based on the octree.The method to obtain the position and the value of the mesh point in the post processorand the parallel computing techniques are also discussed in this research.
Secondly, the numerical simulation results of the single equiaxed grain growth of thepure metal are given. Contrast with the results using the uniform mesh, it can conclude thephase field with the adaptive mesh based on the octree which established in this paper hasthe ability not only to do the simulation of the solidification microstructure, but a greatimprovement for the computation and reduction the resource. The efficiency of the parallel and the affection of mesh parameters to the solidification microstructure are also discussedin this paper. Then this research gives the research on the relationship of thethermophysical parameters with the dendritic morphology of the equiaxed and columnargrains.
Thirdly, this paper gives the research on the numerical simulation of the isothermaland non-isothermal solidification of the binary alloy. It can be gained from the results thatthe phase-field model with adaptive mesh based on the octree can be applied well to thesimulation of the solidification microstructure of the binary alloy. And the variation of themicrosegregation of the binary alloy from the simulation results and the simulation resultsof the multi-columnar grains growth also gives the conclusion.
At last, two experiments including the organic solution crystallization and themetallographic experiment of the aluminium alloy casting are used to verify thesimulation results of the solidification microstructure of the pure metal and the binaryalloy. It is showed the simulation results and the experimental results are comparable inthe fuse of the columnar grain of the pure metal and the dendritic growth of the binaryalloy.
引文
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