Abstract In the production of single-crystal turbine blades for use in aircraft engines with unidirectional solidification techniques, it is confirmed that the casting geometry had great influence on the formation of macrosegregation or spurious/stray crystals. In this study, a two-phase solidification model is used to investigate the geometrical effect on the unidirectional solidification of Al–7.0 wt.% Si alloy. The study is based on the experiment of Ghods et al. (2016a) , in which the diameter of the sample is changed between φ9.5 and φ3.2 mm along the solidification direction to highlight the geometrical effect. The first part of the investigation is to verify the numerical model by ‘reproducing’ the experimentally obtained macrosegregation and phase distribution in an as-cast sample. The second part is to explore the macrosegregation mechanism. It is found that the main geometrical effect is the modification of the bulk and the interdendritic melt flow during solidification. Different flow patterns are found in different locations, e.g. below or above the cross-section contraction; however, details of the macrosegregation formation can be explained by a scalar product of two vectors, i.e. the flow velocity and the concentration gradient of the melt. Based on the positive/negative value of the scalar product, i.e. the flow direction in comparison with the direction of the concentration gradient, it is possible to determine where a negative/positive segregation will occur. The above scalar product is also found valid for analysing the possible formation of spurious/stray crystals, and it is numerically demonstrated that the cross-section expansion in casting geometry leads to high risk of spurious/stray crystals.

中文翻译：

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铝硅合金单向凝固过程中宏观偏析形成的几何效应

摘要 在采用单向凝固技术生产用于飞机发动机的单晶涡轮叶片时，已证实铸件几何形状对宏观偏析或杂散晶体的形成有很大影响。在这项研究中，两相凝固模型用于研究几何对 Al–7.0 wt.% Si 合金单向凝固的影响。该研究基于 Ghods 等人的实验。(2016a) ，其中样品的直径沿凝固方向在 φ9.5 和 φ3.2 mm 之间变化，以突出几何效果。调查的第一部分是通过“再现”在铸态样品中实验获得的宏观偏析和相分布来验证数值模型。第二部分是探索宏观偏析机制。发现主要的几何效应是凝固过程中体积和枝晶间熔体流动的改变。在不同的位置发现不同的流动模式，例如在横截面收缩的下方或上方；然而，宏观偏析形成的细节可以通过两个向量的标量积来解释，即熔体的流速和浓度梯度。基于标量积的正/负值，即流动方向与浓度梯度方向的比较，可以确定哪里会发生负/正偏析。发现上述标量积也可用于分析可能形成的虚假/杂散晶体，