Numerical method to depict the time-varying Lorentz force field under harmonic magnetic field

Abstract

The time-varying Lorentz force field(tvLFf), induced by harmonic magnetic field, is widely used in materials pocessing, one of its typical applications is electromagnetic stirring in continuous casting. However, knowledge about the tvLFf is quite limited, only its time-averaged component is studied, and the profile of its time-varying component is unknown up to now. In this paper, the author develops a method to depict the tvLFf using 11 features, which are classified into 3 categories: Strength features, Morphology features and Tide features. All 11 features are created or extracted based on an analysis of the time-varying force ellipse, ruled by the amplitudes and initial phase angles of the induced eletromagnetic field. The elliptical characteristics of the time-varying Lorentz force are derived mathematically and via necessary numerical calculations, by which the effect of stirring or driving is clarified. The author finds that, the amplitudes of the induced eletromagnetic field are proportional to the magnitude of the exciting current, and that Strength features are proportional to the square of the magnitude of the exciting current, while the initial phase angles, Morphology features, and Tide features do not change with the magnitude of the exciting current, when frequency is fixed and the physical properties are constant. Finally, the author presents a model to illustrate the analyzing process, and a detailed visualization of the tvLFf is presented, with revealed features in conformity to the published results.