A time-dependent formulation of the mushy-zone free-boundary problem
A time-dependent formulation of the mushy-zone free-boundary problem
复制标题
糊状区域自由边界问题的时间相关公式
DOI：
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发表时间：
2005
影响因子：
3.7
通讯作者：
M. Worster
中科院分区：
文献类型：
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作者：
T. Schulze;M. Worster
本文给出了在任意参照系下有效的糊状带自由边界问题的时变控制方程和边界条件。由于界面速度$m{w}$与枝晶速度$m{v}$和流体速度$m{u}$不同，时间演化的糊状带模型比稳定情况下的模型更为复杂。我们考虑可忽略溶质扩散率的极限，其中在浆液界面上有四种类型的边界条件，这取决于流过界面的方向和相对于固相的界面运动方向。我们通过研究一类一维问题来说明这些边界条件，在这些问题中，二元材料在实验室参考系中从固定的冷点冷却，同时流体以速率$Q$泵送通过产生的糊状层，糊状层本身以速率$V$平移。这允许我们展示四种类型的糊状层接口中的三种。我们表明，第四种类型在此场景中不会发生。
We present time-dependent governing equations and boundary conditions for the mushy-zone free-boundary problem that are valid in an arbitrary frame of reference. The model for time-evolving mushy zones is more complicated than in the steady case because the interface velocity $m{w}$ can be distinct from both the velocity of the dendrites $m{v}$ and the fluid velocity $m{u}$. We consider the limit of negligible solutal diffusivity, where there are four types of boundary condition at the mush–liquid interface, depending on both the direction of flow across the interface and the direction of the interface motion relative to the solid phase. We illustrate these boundary conditions by examining a family of one-dimensional problems in which a binary material is chilled from a fixed cold point in the laboratory frame of reference while fluid is pumped through the resulting mushy layer at a rate $Q$ and the mushy layer itself is translated at a rate $V$. This allows us to exhibit three of the four types of mushy-layer interfaces. We show that the fourth type cannot occur in this scenario.