基于三维LBM-CA模型模拟Al-4.7％Cu合金的枝晶形貌和成分分布

摘要

A new three-dimensional numerical model combining the lattice Boltzmann(LB) and cellular automaton(CA) methods was developed to simulate heat transport,fluid flow,solute diffusion,and dendritic growth in the process of the Al-4.7％Cu solidification of the single-phase solid solution alloy.In the coupled model,the dendritic growth was simulated by the cellular automaton method,and the temperature field,the flow field and the concentration field in the process of dendritic growth were numerically solved using the lattice Boltzmann method based on the molecule-kinetic theory.The simulation results verify that the change of dendrite morphology and the solute concentration during the solidification process which were reproduced.The effects of natural convection and undercooling on the dendrite morphology and composition distribution were studied quantitatively.The results show that under the condition of pure diffusion,the dendritic growth is symmetrical,the relationship between the tip velocity,the tip radius and the undercooling degree of the steady growth of simulated free dendrite is in good agreement with the predictions of the LiptonGlicksman-Kurz(LGK) model.Under the condition of natural convection,themorphology of dendrite growth is asymmetric,that is to say,the dendritic growth in the upstream region of the natural flow is promoted,as well as the dendrite growth in the downstream region is inhibited.The effect of undercooling on dendrite growth is also great,the increase of undercooling leads to the increase of dendrite growth,and the secondary arms increase and coarsen,the solute concentration at the solid-liquid interface of the dendrite tip increases,which aggravates the solute segregation.%建立了三维格子玻尔兹曼方法(LBM)-元胞自动机(CA)耦合数值模型,并用该模型模拟研究了Al-4.7％Cu(质量分数)固溶体合金的凝固过程.该耦合模型采用元胞自动机方法模拟枝晶的生长,同时采用基于分子动力学理论的格子玻尔兹曼方法模拟合金凝固过程中的温度场、流场以及溶质场.模拟结果再现了合金凝固过程中的三维枝晶形貌变化以及溶质富集过程,并将三维流场因素考虑进去,定量研究了自然对流、过冷度对单枝晶形貌和成分分布的影响.研究表明,在纯扩散条件下,枝晶呈现对称的生长现象,模拟自由枝晶稳态生长的尖端速度、尖端半径和过冷度的关系与Lipton-Glicksman-Kurz (LGK)理论模型吻合得较好.在自然对流条件下,枝晶的生长形貌呈现不对称性,即枝晶生长在迎流方向上得到了促进,在顺流方向上受到了抑制.熔体过冷度对枝晶生长的影响较大,过冷度的增加导致枝晶生长加快,二次枝晶增多且呈现出粗化现象,枝晶尖端固液界面处的溶质浓度偏高,加重了溶质偏析.