Rising motion of a single bubble through a liquid metal in the presence of a horizontal magnetic field

Abstract

After a previous investigation of the rising motion of a gas bubble in a liquid metal under the influence of a vertical magnetic field, this new study focuses on the case of a uniform horizontal magnetic field. The numerical code is still the same: it is based on a volume-of-fluid technique and on an unstructured Cartesian adaptive grid system. A consistent and conservative scheme is adopted to compute the induced current density and the Lorentz force. In order to allow a benchmark, most of the parameters selected for this new investigation are the same as in an experiment recently performed in Dresden, Germany. The Ar bubble diameter is either 4.3 mm or 6.4 mm, the liquid metal is GaInSn, resulting in Reynolds numbers (Re) larger than in experiments with water (2000 to 4000, instead of 1000 or less) and allowing significant differences even without any magnetic field. In this paper, the magnetic field strength and therefore the interaction parameter are extended to values higher than in the experiment to provide data on the asymptotic behavior when these parameters get very large. The influence of the horizontal magnetic field on properties as the terminal rising velocity, the observed modifications of the rising paths, the shape of the bubble, and the wake structure is displayed and discussed. It is shown that the unstable bubble trajectory is closely related to the wake instability, which is itself strongly influenced by the horizontal magnetic field. When comparing the results with those obtained in the presence of a vertical magnetic field, significant differences appear together with the lack of axial symmetry, such as a slower rising motion of the bubble and the suppression of the “secondary path instability.” Increasing the intensity of the magnetic field results in an approximate exponential law to describe how the terminal rising velocity is reduced. The numerical predictions are interpreted in terms of the predominant physical mechanisms.