中文摘要：

为了研究铸造高温合金中的斑点偏析，建立了描述多元合金凝固过程传输行为的数学模型。基于伪二元相图方法，模型给出了液相线温度与固相分数及液相多元溶质浓度的耦合关系式。利用该模型对Ni-5．8Al-15．2Ta（质量分数，％）合金铸锭的垂直定向凝固过程进行了模拟。结果表明：该模型能够反映多组元镍基高温合金凝固过程中斑点偏析的形成及发展过程。凝固界面前沿附近热-溶质双扩散对流引起的密度倒置，是诱发斑点偏析的主要原因。在糊状区中形成的偏析通道中，富集溶质从糊状区流向液相区，通道周围局部流动可以通过糊状区从液相区补充通道中的流动。凝固初期形成的通道不能稳定存在，多个通道合并促使局部凝固前沿优先生长，最终形成稳定的偏析通道。

英文摘要：

A mathematical model was built to describe the transportation phenomena and the freckle formation during the solidification process of multicomponent Ni-base superalloy. A set of expressions of coupling liquidus and solid fraction as well as multicomponent concentrations was determined based on the pseudobinary phase diagram. The numerical simulation of Ni-5.8%Al-15.2%Ta （mass fraction） alloy during the vertically unidirectional solidification was performed by this continuum model. The results show that the model is reasonable to describe the formation and evolution of freckle in superalloy ingot. Freckles were significantly induced by the density inversion due to the thermosolutal convection in front of the solid/liquid interface. The solute-rich liquid in the channel flows from mush into liquid. In order to maintain the mass equilibrium in the channels, the fresh liquid may penetrate via the mushy zone from pure liquid region. The plumes appearing at the preliminary solidification stage were unstable and tended to converge. The stable channel was formed at the prior grown solidification front after the plumes were submerged.