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首页> 外文期刊>ISIJ international >Numerical Analysis on Cold Crucible Using 3D H-φ Method and Finite Volume Method with Non-staggered BFC Grid System
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Numerical Analysis on Cold Crucible Using 3D H-φ Method and Finite Volume Method with Non-staggered BFC Grid System

机译：无交错BFC网格系统的3DH-φ法和有限体积法对冷坩埚的数值分析

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摘要

Generally, numerical analysis of MHD systems including cold crucible requires much amounts of calculating resources. These systems often include 3D electromagnetic field, fluid flow in irregular boundaries, solidification, even coupling between electromagnetic field and fluid flow. Two kinds of basically different simulation techniques are necessary for effective calculation of these MHD systems. These are FEM (Finite Element Method) for calculation of electromagnetic field and FVM (Finite Volume Method) with BFC (Body Fitted Coordinate) for fluid flow. But many researchers have been tried to solve these problems by other methods because the use of the combined method consumes large quantity of memory and computing time. Most of numerical models on cold crucible do not include the analysis of fiuid flow. For calculation of electromagnetic field, 2D axisymmetric wire model, it's improved model or Boundary Element Method have been widely used instead of fully 3D FEM. In this study, 3D H-φ formulation for electromagnetic field by FEM and a technique using non-staggered grid system for fluid flow by FVM with BFC were employed to save the memory space and calculation time in numerical analysis of cold crucible. A package of numerical models including electromagnetic, fluid dynamic, heat transfer and solidification model was constructed and applied to the numerical simulation of cold crucible. Validity of the electromagnetic model was confirmed by comparison between the results from calculation and those from direct measurement. Verification of the developed code on fluid dynamic calculation was carried out by its comparison with the commercial code PHOENICS. Influence of some important operating parameters on the meniscus shape and solidification front were investigated using the developed package. Temperature distribution in the molten tin was uniform because of the circulating flow induced by non-uniform distribution of electromagnetic force and the heat transfer through mold wall at the melt-mold contacted region was noticeably reduced as a result of magnetic pressure.
机译：通常，对包括冷坩埚在内的MHD系统进行数值分析需要大量计算资源。这些系统通常包括3D电磁场，不规则边界中的流体流动，凝固，甚至电磁场和流体流动之间的耦合。要有效地计算这些MHD系统，必须使用两种基本不同的仿真技术。它们是用于计算电磁场的FEM（有限元法）和带有BFC（体坐标）的FVM（有限体积法）用于流体流动。但是，许多研究人员已尝试通过其他方法来解决这些问题，因为使用组合方法会消耗大量的内存和计算时间。冷坩埚上的大多数数值模型不包括流体流动分析。在计算电磁场时，已广泛使用2D轴对称线模型，改进模型或边界元方法代替完全3D有限元法。在这项研究中，采用有限元法对电磁场进行3DH-φ公式化，以及采用不交错网格系统通过带有BFC的FVM进行流体流动的技术来节省冷坩埚数值分析的存储空间和计算时间。建立了包括电磁，流体动力学，传热和凝固模型在内的一整套数值模型，并将其应用于冷坩埚的数值模拟。通过比较计算结果和直接测量结果，确认了电磁模型的有效性。通过将其与商业代码PHOENICS进行比较，验证了所开发的流体动力学计算代码。使用开发的软件包，研究了一些重要的操作参数对弯液面形状和凝固前沿的影响。熔融锡中的温度分布是均匀的，这是因为电磁力的不均匀分布引起的循环流，并且由于磁压而显着降低了在熔融模具接触区域通过模壁的传热。

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