激光焊接熔池中的金属凝固过程和该过程中产生的微观结构对焊缝的机械性能有重要的影响，金属凝固过程中常见的微观组织是枝晶组织，枝晶生长是一个复杂的微观过程，涉及流场的流动、传热、界面曲率及动力学等多种因素的影响。本文通过数值模拟的方式研究凝固过程中枝晶生长的规律，采用气体动理学格式 (Gas-kinetic scheme，GKS) 模拟流场和温度场，采用相场法 (Phase-field，PF) 模拟枝晶生长，并建立两者的耦合模型模拟复杂流动下的枝晶生长行为。通过数值模拟的方法对微观组织的生长机制进行研究，对理解和掌握焊接材料宏观属性有重要的指导意义。本文所做的工作如下：

(1) 本文根据气体动理学格式和相场法的基本原理，考虑熔体的流动、晶体的生长以及流场内的传热效应，建立了适用于模拟纯金属非等温凝固过程中枝晶生长的GKS-PF耦合模型。其中，采用PF方法模拟枝晶生长，采用GKS计算流场和温度场，两者通过温度场源项进行耦合。

(2) 分别采用模拟封闭方腔自然对流问题和模拟等轴枝晶的生长情况对GKS和GSK-PF耦合模型进行验证，应用GKS-PF耦合模型模拟自然对流作用下枝晶的生长过程。模拟结果表明，自然对流的存在加速了热流传输，改变了温度场的对称分布，在晶臂附近出现了涡流，促进了上游晶臂的生长，抑制了下游晶臂的生长，枝晶界面呈非对称形貌。

(3) 采用GKS-PF耦合模型研究了相场的主要参数，如过冷度、各向异性强度系数和耦合系数等对枝晶生长的影响规律。模拟结果表明：相场模型的主要参数对模拟结果有重要影响，随着过冷度、各向异性系数和耦合系数的增加，枝晶形貌发生了较大变化，能够更快、更明显地呈现出等轴枝晶的特征。

(4) 对多个枝晶互相影响的生长过程进行了模拟研究，提出了一种基于元胞自动机方法 (Cellular automata，CA) 的多枝晶随机择优生长取向模型，分别模拟了纯扩散条件下多个枝晶单择优取向角和多择优取向角枝晶生长形态。结果表明，多择优取向角时各个枝晶的碰撞更加激烈，形貌变得更加复杂。随后对自然对流作用下多个枝晶的生长过程进行了模拟研究，并且对比了不同生长条件下的枝晶轮廓，清晰的观察到了不同位置处枝晶形貌的变化。

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