Coupling the VOF and the MHD models for the simulation of bubble rising in a metallic liquid

In the last few decades magnetohy-drodynamic (MHD) effects have attracted growing interest because of its potential impact on numerous industrial technologies such as metallurgy, crystal growth, electron or laser beam melting/evaporation of surfaces, etc… An example of such flow is the Bubble driven flows which have found wide applications in industrial technologies. In metallurgical processes gas bubbles are injected into a bulk liquid metal to drive the liquid into motion, to homogenise the physical and chemical properties of the melt or to refine the melt. For such gas–liquid metal two-phase flows, external magnetic fields provide a possibility to control the bubble motion in a contactless way. Our interest is devoted to the motion of gas bubbles in liquid metals under the influence of a magnetic field. The numerical scheme used in this paper is based on the volume of fluid (VOF) method interFoam of the OpenFoam code, which uses an interface tracking algorithm for the simulation of the two-phase flow coupled with an incompressible laminar magneto-hydrodynamics model mhdFoam of same code. The solver is at its earlier stage and in this paper; we consider the case of a single, isolated bubble rising in a tube of stagnant liquid metal exposed to a longitudinal magnetic field.