Modelling Surface Instabilities of Incompressible Nonconducting and Conducting Fluids

The response of electrically conducting liquids to an unsteady applied current (or magnetic field) is an area of interest in different applications such as magnetized-target-fusion-based reactors. One of the critical elements for achieving fusion conditions using liquid compression is keeping the liquid-metal interface stable during the experiment and preventing instability formation at the interface. Therefore, a deep understanding of the liquid-metal surface evolution subjected to unsteady electric current is needed. To this end, a high-order numerical solver is developed to simulate the motion of the free surface. The level-set method is implemented to capture the free surface, while the nonconducting liquid is modelled as an incompressible flow. The implemented code is validated using several test cases such as water tank sloshing, the dam break problem, and classical air/water Rayleigh-Taylor instability. Having established the capability to model the free surface of nonconducting fluids, we discuss proper approaches to extend the present solver for conducting liquid metals, in which the Lorentz force is present and affect the evolution of the interface. This effort was supported by the Natural Sciences and Engineering Research Council of Canada discovery grant.