摘要
在材料凝固的過程之中，經由不同的流場、溫度場與濃度場的交互作用下，將產生不同的顯微結構與材料性質。相較於在材料凝固之後採用機械加工或再結晶與其他方式以改變材料性質，數值模擬將有助於瞭解材料於凝固的過程中，流場、溫度場與濃度場對於材料顯微結構的影響，以節省研發成本並求得更高品質的材料。
本研究採用的數值方法為有限元素法，測試材料為錫鉛二元合金。先以Gambit建立網狀晶幾何模型與網格，搭配天空線存取模式配合LU分解法進行求解。並模擬網狀晶加入流場效應之後，考慮周圍的溫度與濃度的分佈以計算網狀晶偏移的角度。
本研究在不同的控制參數（溫度梯度、成長速率、金屬液體的初始濃度及剪力流的大小）下，分析流場對於（網狀晶之）溫度場與濃度場的影響，用以反推網狀晶偏移的角度，並探討控制參數對網狀晶偏移角度之影響。由於電腦儲存空間的限制，本研究亦改善原天空線的存取模式，節省電腦的儲存空間，並以二維溫度場與流場驗證了其可行性。

ABSTRACT

Numerical simulation of the solidification processes could be utilized to analyze the effect of the velocity, temperature and concentration fields to understand more about the microstructures and to enhance the quality of material during fabrication.
In this paper, combining the forward diffusion Schiel equation to constrain the geometrical shape of a cell, Gambit was used to build the three-dimensional mesh model of a cellular growth. The numerical method was finite element method, in which the skyline storage mode and the LU decomposition method were used to solve the matrix equation. A simple shear flow was given on the top of calculating domain and the temperature and concentration distributions around the tip of cell were observed. By the influence of the flow, a deflective angle could be calculated.
With the control of different parameters, including the temperature gradient, growth rate, concentration of initial metallic liquid and shear rate, the temperature and concentration distributions were analyzed and their corresponding deflective angles are calculated. Utilizing different parameters would magnify or reduce the effect of fluid field around the tip of cell and therefore the concentration distribution was changed and deflective angle became different. The skyline storage mode was also improved to save space of computational memory and its feasibility was verified by the examples of temperature and concentration fields being compared with analytical solutions.

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