Abstract

A recent three-dimensional (3D) model that revisited earlier theoretical work for longitudinal electromagnetic stirring in the continuous casting of steel blooms is analyzed further to explore how the bloom width interacts with the pole pitch of the stirrer to affect the magnetic flux density. Whereas the first work indicated the presence of a boundary layer in the steel near the interface with the stirrer, with all three components of the magnetic flux density vector being coupled to each other, in the analysis presented here we find that the component along the direction of the travelling wave decouples from those in the other two directions and can even be determined analytically in the form of a series solution. Moreover, it is found that the remaining two components can be found via a two-dimensional computation, but that it is not possible in general to determine these components without taking into account the surrounding air. The validity of the asymptotically reduced model solution is confirmed by comparing it with the results of 3D numerical computations. Moreover, the asymptotic approach provides a way to compute the time-averaged Lorentz force components that requires two orders of magnitude less computational time than the fully 3D approach.

中文翻译：

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钢连铸纵向电磁搅拌模型的分析。

摘要

重新分析了最近的三维（3D）模型，该模型重新研究了钢坯连续铸造中纵向电磁搅拌的早期理论工作，从而进一步研究了钢坯宽度如何与搅拌器的极距相互作用以影响磁通密度。尽管第一项研究表明钢中与搅拌器的界面附近存在边界层，并且磁通密度矢量的所有三个分量都相互耦合，但在此处介绍的分析中，我们发现沿方向的分量行波的波解与其他两个方向的波解耦，甚至可以以级数解的形式解析地确定。而且，发现可以通过二维计算找到剩余的两个分量，但是通常不可能在不考虑周围空气的情况下确定这些成分。通过将其与3D数值计算结果进行比较，可以确认渐近简化模型解的有效性。此外，渐近方法提供了一种计算时间平均洛伦兹力分量的方法，该方法所需的计算时间比完全3D方法少两个数量级。