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Ensemble Averaged Two-phase Eulerian Model for Columnar/Equiaxed Solidification of a Binary Alloy

机译:合奏平均两相欧拉模型用于二元合金的柱状/等式凝固

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A new two-phase eulerian model for the columnar and equiaxed dendritic solidification has been developed. The mean conservation equations are derived by means of a statistical phase averaging technique, and the mathematical formulation of the model can be used for both columnar and equiaxed solidification. We present a new set of equations to simulate the segregations during the columnar solidification of a binary alloy. The use of such an averaging procedure has several advantages compared with the volume averaging technique which has been widely used during the last decade. Firstly, the statistical approach does not need the definition of a representative elementary volume. Secondly, it is consistent with the random aspect of the equiaxed grain germination and motion as well as the possible turbulent behaviour of the fluid flow. The averaged equations are closed by means of the cell model approximation. This technique can be successfully used to model the various interactions between the liquid and the solid. It may also incorporate the effects of the inhomogeneities of the various scalar fields, e.g., the solute and temperature gradients. First tests of the model are presented in two asymptotic situations, namely the wholly equiaxed and the columnar solidification.
机译:已经开发出一种新的两相欧拉模型,用于柱状柱和平衡的树突凝固。平均保护方程通过统计相位平均技术导出,并且该模型的数学制剂可用于柱状和等轴凝固。我们提出了一组新的等式,以模拟二元合金的柱状凝固过程中的偏析。与在过去十年中广泛使用的体积平均技术相比,使用这种平均程序具有若干优点。首先,统计方法不需要代表性基本体积的定义。其次,它与等轴萌发和运动的随机方面一致,以及流体流动可能的湍流行为。通过单元模型近似关闭平均方程。该技术可以成功地用于模拟液体和固体之间的各种相互作用。它还可以包括各种标量场的不均匀性的影响,例如溶质和温度梯度。该模型的第一次测试在两个渐近情况下呈现,即全等式和柱状凝固。

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