连铸圆坯非均匀传热<strong>/</strong>凝固行为的无网格计算方法

doi:10.11900/0412.1961.2019.00433

金属学报

2020, Vol. 56

Issue (8): 1165-1174 DOI: 10.11900/0412.1961.2019.00433

本期目录 | 过刊浏览

连铸圆坯非均匀传热/凝固行为的无网格计算方法

蔡来强¹^,², 王旭东¹^,²(

), 姚曼¹^,², 刘宇³

1 大连理工大学材料科学与工程学院大连 116024
2 大连理工大学辽宁省凝固控制与数字化制备技术重点实验室大连 116024
3 东北电力大学机械工程学院吉林 132012

Meshless Method for Non-Uniform Heat Transfer/Solidification Behavior of Continuous Casting Round Billet

CAI Laiqiang¹^,², WANG Xudong¹^,²(

), YAO Man¹^,², LIU Yu³

1 School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, China
2 Key Laboratory of Solidification Control and Digital Preparation Technology (Liaoning Province), Dalian University of Technology, Dalian 116024, China
3 School of Mechanical Engineering, Northeast Electric Power University, Jilin 132012, China

引用本文:

蔡来强, 王旭东, 姚曼, 刘宇. 连铸圆坯非均匀传热/凝固行为的无网格计算方法[J]. 金属学报, 2020, 56(8): 1165-1174.
Laiqiang CAI, Xudong WANG, Man YAO, Yu LIU. Meshless Method for Non-Uniform Heat Transfer/Solidification Behavior of Continuous Casting Round Billet[J]. Acta Metall Sin, 2020, 56(8): 1165-1174.

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摘要:

基于移动最小二乘近似和变分原理，推导并建立了基于无网格Galerkin (EFG)法的连铸圆坯二维横截面传热/凝固计算模型。以实测结晶器热流为边界条件，模拟分析了圆坯的非均匀凝固行为，重点讨论了节点布置和支持域尺寸等影响无网格模型适用性和计算精度的关键问题。结果表明，建立的EFG模型在节点布置上十分灵活，提出的直角坐标系下的“同心圆”式节点布置方案，可以很好地处理圆坯曲线边界及坯壳凝固界面推进的问题。在支持域尺寸为平均节点间距的1.7倍时，均匀和随机2种节点布置方式下，模型都达到了较高的计算精度。研究结果证实了EFG模型应用于铸坯非均匀传热、凝固计算的可行性和正确性，在凝固界面追踪中体现出显著优势，为后续铸坯传热-力学行为耦合和裂纹预测的研究提供了基础。

关键词 ：无网格Galerkin法, 移动最小二乘近似, 非均匀凝固, 连铸圆坯

Abstract：

Compared with the mesh-based numerical calculation method, the meshless methods avoid the problems caused by geometric topology, nodal numbering and information transmission of discrete meshes or nodes, which shows significant advantages in solving the problems of complex computing domain boundaries, phase transformation, interface tracking, and crack propagation. Based on the moving least squares approximation and variational principles, a two-dimensional element-free Galerkin (EFG) model for heat transfer/solidification behavior of continuous casting round billets is derived and established in this work. Taking the measured heat flux as the boundary conditions, the non-uniform solidification behavior of the round billet is calculated and analyzed. The essential issues that affect the suitability and calculation accuracy of the meshless model are discussed, such as the nodal arrangement and the size of the supporting domain. The "concentric circle" nodal arrangement scheme in rectangular coordinate system is proposed, and the results show this scheme can conveniently deal with the problem of curve boundary and the solidified shell movement of round billet, showing great flexibility in node arrangement. When the supporting domain size is adopted to be 1.7 times of the average nodal spacing, the calculation accuracy is high under the regular and random nodal arrangement schemes. The results verify the feasibility and accuracy of EFG meshless model in the calculation of non-uniform heat transfer and solidification of billet. It shows a significant advantage in the phase transformation interface tracking, and provides a theoretical foundation for subsequent research on thermo-mechanical coupling and crack prediction analysis.

Key words： element-free Galerkin moving least squares approximation non-uniform solidification continuous casting round billet

收稿日期: 2019-12-16

ZTFLH:

TF777.4

基金资助:国家自然科学基金资助项目(51974056);国家自然科学基金资助项目(51474047);国家自然科学基金资助项目(51704073)

作者简介: 蔡来强，男，1990年生，博士生

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https://www.ams.org.cn/CN/10.11900/0412.1961.2019.00433 或 https://www.ams.org.cn/CN/Y2020/V56/I8/1165

图1 无网格Galerkin (EFG)法中的节点、积分点、支持域和背景网格示意图

图2 热电偶安装示意图和热流传感器结构示意图

表1 钢种的热物理性能[31]

图3 实测热流在弯月面下不同高度沿周向的分布

图4 EFG模型中的节点均匀布置和随机布置方式

图5 EFG均匀和随机节点布置方式与有限元法(FEM)计算的坯壳表面温度对比

图6 不同支持域尺寸坯壳表面温度沿浇铸方向的对比

图7 不同尺度参数对应支持域下的误差

图8 结晶器出口处铸坯断面温度分布

图9 弯月面下不同高度液固界面位置识别

图10 热流、坯壳表面温度和坯壳厚度沿浇铸方向的对比

图11 弯月面下75 mm、285 mm和结晶器出口的周向热流和坯壳厚度以及平均热流与出口处坯壳厚度的对比

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