纯物质过冷熔体中自由枝晶生长相场模型的自适应有限元法模拟  

Adaptive finite element method-based simulation of phase-field model of free dendrite growth in pure substance supercooled melt

作　　者：朱昶胜[1,2] 雷鹏[1] 冯力[2] 肖荣振[2] 

机构地区：[1]兰州理工大学计算机与通信学院,甘肃兰州730050 [2]兰州理工大学甘肃省有色金属新材料重点实验室,甘肃兰州730050

出　　处：《兰州理工大学学报》2014年第4期18-23,共6页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(51161011;11364024);甘肃省科技支撑计划(1204GKCA065)

摘　　要：基于自适应有限元方法,通过求解表征纯物质相场模型的非线性抛物型方程,研究镍过冷熔体中不同起伏情况下单个完整等轴枝晶的演化过程.模拟结果表明:采用自适应有限元方法求解相场模型时结果更接近真实物理模型,在计算终止时整个计算域节点数仅为2.79×105个,远小于采用相同网格间距普通方法的1.6×106个,较大不同计算域对枝晶尖端速度的平衡值影响不大;随着起伏强度的增大,枝晶尖端获得更高的温度梯度,等温线波动更大,一次枝晶臂表面失稳,二次枝晶臂向过冷溶液中凸起的趋势越强,二次枝晶臂越发达.Based on adaptive finite element method, the pure substance phase-field model characterized by the non-linear parabolic partial differential equations were solved. A single complete isometric crystal evolution process in nickel supercooled melt was investigated under different fluctuation intensity. The simulation result showed that the phase field model employing adaptive finite element method was closer to the actual physical model. The number of system grid nodes were just 2. 79 ×10^5, which was far less than 1.6 ×10^6 when the common method was used. When the computation domain was larger enough, the domain size had little influence on the dendrite tip speed. With the increase of fluctuation intensity, the dendrite tips would obtain a higher temperature gradient that made the surface of primary crystalline arms lose and isothermal curves would fluctuate dramatically surface stability and the secondary arms become developed, protruding into the suppercooled melt.

关 键 词：相场模型 枝晶生长 自适应有限元法 尖端速度 

分 类 号：TG244[金属学及工艺—铸造] O242[理学—计算数学]