Magnetohydrodynamics Simulation of the Nonlinear Behavior of Single Rising Bubbles in Liquid Metals in the Presence of a Horizontal Magnetic Field

Rising bubbles in liquid metals in the presence of magnetic fields is an important phenomenon in many engineering processes. The nonlinear behavior of the terminal rise velocities of the bubbles as a function of increasing field strength has been observed experimentally, but it remains poorly understood. We offer an explanation of the phenomenon through numerical calculations. A single rising bubble in stagnant liquid metal in the presence of an applied horizontal magnetic field is simulated. The observed nonlinear behavior is successfully reproduced; the terminal velocity increases with the increase in the magnetic field strength in the lower magnetic field regions but decreases in higher regions. It is shown that, in the lower region, the increase in the average bubble rise velocity results from the suppression of the fluctuations in the bubble trajectory in the vertical plane perpendicular to the magnetic field, as a consequence of the Lorentz force resulting from the component of induced electric current due to the magnetic field, which (approximately) acts in the opposite direction to that of the flow velocity. For higher magnetic field strengths, the Lorentz force induces a broadened wake in the vertical plane parallel to the applied magnetic field, resulting in a decrease in the rise velocity.