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Finite element analysis of electromagnetic and fluid flow phenomena in rotary electromagnetic stirring of steel

机译：钢旋转电磁搅拌中电磁和流体流动现象的有限元分析

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This paper describes a fixed-grid methodology for the numerical simulation of electromagnetically driven flow in three-dimensional inductively stirred systems. It is based on a hybrid differential-integral formulation of the electromagnetic field to limit the finite difference/element solution of the electromagnetic field problem to the fluid flow domain. The electromagnetic field in the system was described using current vector potential (T) and reduced magnetic scalar potential (ψ) formulation of the field. The fluid flow problem was represented by turbulent Navier-Stokes equation. The governing equations were discretized using Galerkin method of weighted residual, and the discretized electromagnetic and fluid flow equations were solved simultaneously using an efficient finite element segregated algorithm. This new method was used to simulate sub-mold rotary electromagnetic stirring in continuous casting of steel. The computed results have shown that the electromagnetic force field generates a strong rotational flow within the vertical section covered by the stirrer, and a relatively strong secondary flow beyond the stirrer. It has also been shown that the rotational and secondary flows were driven primarily by the vorticity of the force field at the billet corners. The induced flow in the molten pool was found to be turbulent and the effective mixing region in the molten pool was about three times the length of the stirrer. The principal conclusion emerging form this work is that the secondary flow promotes mixing beyond the region confined by the stirrer, and the extent of mixing depends on the frequency of the applied rotating magnetic field.
机译：本文介绍了一种固定网格方法，用于三维感应搅拌系统中电磁驱动流的数值模拟。它基于电磁场的混合微分积分公式，将电磁场问题的有限差分/元素解限制在流体流域内。系统中的电磁场是使用电流矢量电势（T）和磁场的减小的磁标量电势（ψ）表示的。流体流动问题用湍流的Navier-Stokes方程表示。使用加权残差的Galerkin方法离散化控制方程，并使用有效的有限元分离算法同时求解离散化的电磁和流体流动方程。该新方法用于模拟钢连续铸造中的亚模旋转电磁搅拌。计算结果表明，电磁力场在搅拌器覆盖的垂直截面内产生了强大的旋转流，并在搅拌器之外产生了相对较强的二次流。还显示出，旋转流和二次流主要是由坯料角处的力场的涡度驱动的。发现在熔池中引起的流动是湍流的，并且在熔池中的有效混合区域约为搅拌器的长度的三倍。从这项工作中得出的主要结论是，二次流促进混合超出搅拌器所限定的区域，并且混合的程度取决于所施加的旋转磁场的频率。

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