Abstract
The complex interplay between thermal, hydrodynamic, and electromagnetic, forces governs the evolution of multi-phase systems in high technology applications, such as advanced manufacturing and fusion power plant operation. In this work, a new formulation of the time dependent magnetic induction equation is fully coupled to a set of conservation laws for multi-phase fluid flow, energy transport and chemical species transport that describes melting and solidification state transitions. A finite-volume discretisation of the resulting system of equations is performed, where a novel projection method is formulated to ensure that the magnetic field remains divergence free. The proposed framework is validated by accurately replicating a Hartmann flow profile. Further validation is performed through correctly predicting the experimentally observed trajectory of Argon bubbles rising in a liquid metal under varying applied magnetic fields. Finally, the applicability of the framework to technologically relevant processes is illustrated through the simulation of an electrical arc welding process between dissimilar metals. The proposed framework addresses an urgent need for numerical methods to understand the evolution of multi-phase systems with large electromagnetic property contrast.
Highlights
The complex interplay between thermal, hydrodynamic, and electromagnetic, forces governs the evolution of multi-phase systems in high technology applications, such as advanced manufacturing and fusion power plant operation
Describing this metal additive manufacturing scenario, or any scenario with spatial gradients in electromagnetic properties requires a formulation of the conservation law for magnetic field strength that captures these gradients properly; it is worth highlighting that large property gradients usually pose serious computational challenges
For the case of multi-phase flows with externally applied magnetic fields, experimentally measured Ar bubble trajectories, in a Ga–In–Sn liquid metal, are used to further validate the framework
Summary
The complex interplay between thermal, hydrodynamic, and electromagnetic, forces governs the evolution of multi-phase systems in high technology applications, such as advanced manufacturing and fusion power plant operation. Once the electrical arc is extinguished, the portion of the metallic substrate that melted will begin to solidify and any changes caused by the melting events will be inherited by the s ubstrate[14,16] Describing this metal additive manufacturing scenario, or any scenario with spatial gradients in electromagnetic properties requires a formulation of the conservation law for magnetic field strength that captures these gradients properly; it is worth highlighting that large property gradients usually pose serious computational challenges. Such a magnetic induction equation could be used to supplement the conservation of mass, momentum and energy transfer equations that describe the evolution of a system containing a mixture of chemical components. For cases where the magnetic field is known to oscillate, such as alternating current joining processes[11,13,15,29], and oscillations of the liquid metal coolant in fusion reactors, a time dependent and complete form of the induction equation should be used[8,19]
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