We report a liquid metal droplet impacting onto a cold substrate under the influence of vertical magnetic field numerically. During the impacting dynamics, the spreading and the solidification of the droplet are seriously influenced by the magnetohydrodynamic effects. The numerical methodology is implemented by coupling the volume of fluid method and the implicit enthalpy approach, the former is used to track the liquid/solid–gas interface, while the latter is employed to simulate the solidification process. At first, the numerical method is validated against a series of benchmark problems. Then, by varying the impacting velocities, the thermal contact resistance and the magnetic strengths, the variations of the maximum spreading diameter against different dimensionless parameters are reported. An interpolation scheme between the impacting effect, the thermal effect, and the magnetohydrodynamic effect is proposed to predict the maximum spreading factor, and very good agreement is observed compared to our numerical results. After that, we identify different impacting behaviors in different parameter regimes. For non-isothermal cases, we find that the solidification makes the droplet transit from full rebound to adhesion on the cold substrate, and the participation of the magnetic field promotes the pinch off phenomena during the retraction of the liquid drop. Mechanisms for the transitions between different impacting regimes are discussed, and the comparisons with the available experimental results and analytical solutions are also delivered. At last, we identify that the thickness growth of the solidified splat can be predicted by solving the simple one-dimensional Stefan problem, implying that the thermal dynamics is dominating over the hydrodynamic or the magnetohydrodynamic effects during the melting process of the spreading droplet. Our work therefore provides a general framework to model and study more complex configurations, such as the droplet impacting problems in the metallurgical industry and Tokamak devices, in which environment the droplet dynamics significantly depend on the non-isothermal magnetohydrodynamic effects.
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