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An analytical and numerical study of coupled transient natural convection and solidification in a rectangular enclosure

机译：矩形壳体中瞬态自然对流和凝固耦合的分析和数值研究

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摘要

The transient process of the solidification of a pure liquid phase-change material in the presence of natural convection in a rectangular enclosure is considered both analytically and numerically. One vertical boundary is held at a temperature below the melting-point of the material, the other above; the horizontal boundaries are both assumed adiabatic. A nondimensional analysis of the problem, principally in terms of the Rayleigh (Ra) and Stefan (St) numbers, indicates that some asymptotic simplification is possible for materials often considered in the literature (water, gallium, lauric acid). This observation suggests a way to simplify the full problem when Ra 1 and St 1, giving a conventional boundary value problem for the liquid phase and pointwise-in-space first-order ODEs for the evolution in time of the solidification front. The method is tested against full 2D finite-element-based transient numerical simulations of solidification. In addition, simpler approaches for determining the average thickness of the solid layer, based on boundary-layer and enclosure flow correlations, are also investigated.
机译：在解析和数值上都考虑了在矩形对流中自然对流存在下纯液相变材料凝固的瞬态过程。一个垂直边界保持在低于材料熔点的温度下，另一个保持在上面。水平边界均假定为绝热的。对问题的无量纲分析（主要是瑞利（Ra）和斯特凡（St）数）表明，对于文献中经常考虑的材料（水，镓，月桂酸），可以进行一些渐近简化。该观察结果提出了一种简化方法，可以在Ra 1和St 1时简化整个问题，从而为液相和空间点逐点一阶ODE提供常规的边界值问题，以解决凝固前沿的时间演化问题。 。针对完全基于2D有限元的凝固瞬态数值模拟测试了该方法。另外，还研究了基于边界层和围护流动相关性确定固体层平均厚度的更简单方法。

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