Magneto-hydrodynamics of multi-phase flows in heterogeneous systems with large property gradients

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.