Direct simulation of single bubble motion under vertical magnetic field: Paths and wakes

Abstract

Motion of single Ar bubbles rising in GaInSn under vertical magnetic fields is studied numerically using a volume-of-fluid method and adaptive mesh refinement technique for two-phase interface treatment; a consistent and conservative scheme calculates induced current density and Lorentz force. Numerical results are compared with published experimental data [C. Zhang, S. Eckert, and G. Gerbeth, “Experimental study of single bubble motion in a liquid metal column exposed to a DC magnetic field,” Int. J. Multiphase Flow 31, 824–842 (2005)], where bubble diameters range from 2.5 to 6.4 mm, producing Reynolds numbers that vary between 2000 and 4000. Maximum experimental magnetic field strength was set to 0.3 T because of experimental restrictions, although we increased it to 0.5 T for firm conclusions. Apart from terminal rising velocity comparisons, we focused on variations in bubble motion paths and wake structures under magnetic fields, which cannot be observed experimentally because liquid metal is opaque. Magnetic field effects on bubble trajectory are exerted through vortex structure modification, which reinforced the conjecture that path instability is mainly attributed to wake instability. In bubble motion without magnetic fields, vortex threads in the bubble wake wrap around each other while vortex filaments incline parallel to the field with increasing magnetic intensity. Additionally, high magnetic fields will induce secondary bubble path instabilities, which contribute to the high Reynolds number flow that instabilities develop around the bubble, producing an asymmetrical Lorentz force distribution. This instability vanishes under higher magnetic intensities because flow instability is suppressed. Rising bubble aspect ratios decrease considerably under magnetic fields and may also contribute to smaller vorticities at the bubble surface. A close relationship between fluctuations in rising velocity and shape variations is found.