自由枝晶生长相场模型的自适应有限元法模拟

Phase-field modeling of free dendritic growth with adaptive finite element method

采用自适应有限元方法求解了相场模型的控制方程,利用自适应有限元法在求解效率和精度上的优势,模拟了计算域较大,界面层厚度较薄的情况下镍过冷熔体中单个完整等轴晶的演化过程,使相场模型模拟结果更接近于真实物理模型,并探讨了二次枝晶臂的演化机理.模拟结果表明,二次枝晶臂的演化主要由热扩散控制,并受随机扰动影响,在四个象限内呈现出不对称生长.同时,受枝晶臂生长时排出的潜热积聚作用,同一侧的枝晶臂对新的二次枝晶臂的产生有促进作用.此外,二次枝晶臂出现合并、缩颈熔断、轴向熔化和径向熔化等四种粗化方式.

A simple derivation of phase-field model for pure materials based on entropy functional is provided and then solved by adaptive finite element method（AFEM） to simulate the free dendritic growth from undercooled nickel melt.To investigate the evolutions of the dendrite and reproduce the real physical process,the modeling is performed in a larger domain and thinner interface with the highly computationally efficient and accurate AFEM.The simulated results show that the secondary arms grow in an unsymmetrical mode and their development is controlled by the thermal diffusion and affected by noises which are arbitrarily introduced in the phase-field governing equation.As the latent heat released during the migration of solid-liquid interface is accumulated sufficiently,it prompted initiation of other secondary arms at the same side of the primary arm.As the computation proceeds,the secondary arms become coarsened apparently through four different modes.