A Strongly Coupled Analytical Study of the Interaction of Foreign Particles with a Solid-Liquid Interface in the Presence of Morphological and Fluid Instabilities

哈吉9700380 本项目的目的是对生长中的晶体界面和不溶性球形外来颗粒之间的相互作用进行分析研究。一个定向凝固设置被认为是研究温度和浓度的分布之间的耦合，由于颗粒运动，对流，溶质偏析，界面变形和移动界面附近的颗粒存在的流体流动。该数学模型以能量、溶质、质量和动量守恒方程为基础，辅以一组适当的边界条件。 生成的无量纲系统显示了几个无量纲分组，所有这些分组都在后续分析中发挥作用。 这将预测占主导地位的晶体形态，界面形状，对流和密度平流效应的稳定性标准，并确定阈值参数值，分开推动和捕获的颗粒。弱非线性分叉分析将用于确定理论预测是否可以通过实验验证。该方法需要使用摄动技术，渐近分析，双球坐标系，分支方法，弱非线性分析，和一些数值方法。 当我们接近21世纪时，科学家和技术人员正处于越来越大的压力下，以满足社会对更轻和更高可靠性材料的需求。 例如，在航空航天工业中，减轻重量有助于增加飞行中的有效载荷能力、节省运营成本、提高速度和更长距离的飞行。然而，较轻的材料需要通过添加不同物质的微小颗粒来增强。这反过来又使制造过程复杂化。 最终的铸件应该使这些颗粒均匀分布，但实际上，这很难实现。由于凝固过程中熔体中颗粒的迁移而产生缺陷，并且对最终产品的质量有害。实验工作已经提供了一些如何克服这些困难的迹象。鉴于大量的加工和物理变量，这些部分解决方案不能清楚地将加工历史与铸件的构成联系起来。量化各种工艺参数对最终铸件的影响仍然是关键任务，这是我们分析工作的目的。

Hadji 9700380 The objective of this project is to conduct an analytical study of the interaction between a growing crystal interface and insoluble spherical foreign particles. A directional solidification set-up is considered to study the coupling between the distributions of temperature and concentrations, fluid flow due to particle movement, convection, solute segregation, interfacial deformations and particle presence near the moving interface. The mathematical model, based on the conservation equations of energy, solute, mass and momentum, is complemented by a set of appropriate boundary conditions. The resulting non-dimensional system displays several dimensionless groupings, all of which have a role in the subsequent analysis. This will predict the dominant crystal morphology, stability criteria for interface shape, convection and density advection effects and determine the threshold parameter values that separate pushing and capture of particles. A weakly nonlinear bifurcation analysis will be used to determine if the theoretical predictions can be verified experimentally. The methodology requires the use of perturbation techniques, asymptotic analysis, the bispherical coordinate system, bifurcation methods appropriate to weakly nonlinear analysis, and some numerical methods. As we approach the twenty-first century, scientists and technologists are under increasing pressures to satisfy society's need for materials of lower weight and higher reliability. For instance, in the aerospace industry, a reduced weight facilitates an increased payload capacity in flight, operating cost savings, higher speeds and longer range flights. However, lighter materials need to be strengthened by the addition of tiny particles of a different substance. This in turn complicates the manufacturing process. The final cast should have these particles uniformly distributed but, in practical terms, this is difficult to achieve. Imperfections arise due to the migration of the particles in the melt during the solidification process, and are detrimental to the quality of the end product. Some indications of how to overcome these difficulties have been provided by experimental work. In view of the large number of processing and physical variables, these partial solutions are unable to clearly relate the processing history to the constitution of the cast. There remains the crucial task of quantifying the influence of the various processing parameters on the final cast, and this is the aim of our analytical work.