对流作用下枝晶生长行为的相场法

Phase-field method of dendritic growth under convection

基于Wheeler等提出的纯扩散相场模型,建立耦合溶质场、温度场和流场的相场模型,采用有限差分法对控制方程进行数值求解,研究Ni-Cu合金凝固过程中单晶粒枝晶和多晶粒枝晶在强制对流作用下的生长行为。结果表明:熔体的流动显著改变凝固前沿的传热和传质,从而改变枝晶的生长行为。在流速为6.43m/s的垂直强制对流作用下,上游枝晶受过冷熔体冲刷,枝晶尖端溶质浓度和温度低,实际过冷度大,枝晶生长迅速,稳态生长速度比纯扩散时增加28%;热量和溶质在下游富集,下游枝晶尖端溶质浓度和温度高,实际过冷度小,枝晶生长缓慢,稳态生长速度比纯扩散时减小26%。

Based on the Wheeler model,the phase-field model was built by coupling with the concentration field,temperature field and flow field.An explicit finite difference numerical method was used to solve the phase-field model equations and simulate both of the single and multi-grain dendritic growth of Ni-Cu alloys in a forced flow.The results show that the fluid flow alters the local heat and solute transfer at the solidification front,thus the dendritic growth behavior is significantly influenced.Under forced flow with a flow velocity of 6.43 m/s,the temperature and the concentration of the upstream dendritic crystal are low because of the undercooled melt flushing,the greater actual supercooling of the upstream dendritic crystal makes the dendritic crystal become fast,the tip velocity at steady state increases by about 28% compared with the case without flow.The heat and solute are enriched in the downstream,the temperature and the concentration of the downstream dendritic crystal are high,the less actual supercooling of downstream dendritic crystal makes the dendritic crystal growth become slow,the tip velocity at steady state decreases by about 26% compared with the case without flow.