Estimation of Lorentz Force From Dimensional Analysis: Similarity Solutions and Scaling Laws
Estimation of Lorentz Force From Dimensional Analysis: Similarity Solutions and Scaling Laws
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DOI：
10.1109/tmag.2016.2539927
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发表时间：
2016-03
影响因子：
2.1
通讯作者：
M. Carlstedt;Konstantin Weise nee Porzig;M. Ziolkowski;R. Schmidt;H. Brauer
中科院分区：
文献类型：
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作者：
M. Carlstedt;Konstantin Weise nee Porzig;M. Ziolkowski;R. Schmidt;H. Brauer
在本文中，我们考虑使用量纲分析来建模电磁悬浮和制动问题，这些问题由洛伦兹力定律描述。基于麦克斯韦方程组，为了说明潜在的场问题，我们制定了一个简单学术示例的完整数学模型，其中永磁体以恒定速度在无限平板上移动。对于给定的问题，详细描述了用于尺寸分析的逐步过程。获得了参数数量减少的无量纲模型，突出了主导依赖性，并且对于所采用的量纲系统是不变的。使用无量纲模型，进行了简明的参数研究，以说明无量纲表示在以有效方式显示复杂数据方面的优势。我们对洛伦兹力对无量纲参数的依赖性进行了详尽的研究，以完成分析，并给出了问题的广义表示的结果。最后，根据实例推导并说明了比例定律。
In this paper, we consider the use of dimensional analysis for modeling electromagnetic levitation and braking problems, which are described by the Lorentz force law. Based on Maxwell's equations, to illustrate the underlying field problem, we formulate a complete mathematical model of a simple academic example, where a permanent magnet is moving over an infinite plate at constant velocity. The step-by-step procedure employed for dimensional analysis is described in detail for the given problem. A dimensionless model with a reduced number of parameters is obtained, which highlights the dominant dependences, and it is invariant to the dimensional system employed. Using the dimensionless model, a concise parametric study is conducted to illustrate the advantages of the dimensionless representation for displaying complex data in an efficient manner. We provide an exhaustive study of the dependences of the Lorentz force on the dimensionless parameters to complete the analysis, and we give results for a generalized representation of the problem. Finally, scaling laws are derived and illustrated based on practical examples.