An analysis of convection in a mushy layer with a deformable permeable interface
An analysis of convection in a mushy layer with a deformable permeable interface
复制标题
具有可变形渗透界面的糊状层中的对流分析
DOI：
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发表时间：
2008
影响因子：
3.7
通讯作者：
P. Voorhees
中科院分区：
文献类型：
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作者：
S. Roper;S. H. Davis;P. Voorhees
本文研究了具有可变形和可渗透的糊状物-液体界面的薄近共晶糊状物的定向凝固中糊状物层的动力学。我们研究的发病对流使用线性稳定性分析，和弱非线性增长的液体包裹体的信号发病的烟囱。这种分析相比，过去的分析，其中的糊状液体界面被替换为一个刚性的不可渗透的盖子。我们发现这两个模型之间的定性协议，但刚性盖近似给出了实质上不同的定量行为。在线性理论中，刚盖近似导致高估的临界瑞利数和波数的不稳定性。振荡不稳定性开始的条件也在成分数C中改变了约5倍。在弱非线性理论中，对于自由边界分析，液体包裹体的起始位置在未扰动前沿附近，而对于刚盖近似，液体包裹体的起始位置在糊状层的中心。对于六边形图案，在其中上六边形和下六边形是稳定的参数空间的区域之间的边界作为液体和糊状物区域之间的耦合的结果而移动。
We study the dynamics of a mushy layer in directional solidification for the case of a thin near-eutectic mush with a deformable and permeable mush–liquid interface. We examine the onset of convection using linear stability analysis, and the weakly nonlinear growth of liquid inclusions that signal the onset of chimneys. This analysis is compared to past analyses in which the mush–liquid interface is replaced by a rigid impermeable lid. We find qualitative agreement between the two models, but the rigid-lid approximation gives substantially different quantitative behaviour. In linear theory, the rigid-lid approximation leads to an over-estimate of the critical Rayleigh number and wavenumber of the instability. The condition for the onset of oscillatory instability is also changed by a factor of about 5 in composition number C. In the weakly nonlinear theory, the location of the onset of liquid inclusions is near the undisturbed front for the free-boundary analysis, whereas it lies at the centre of the mushy layer when the rigid-lid approximation is used. For hexagonal patterns, the boundary between regions of parameter space in which up and down hexagons are stable, shifts as a result of coupling between the liquid and mush regions.