High resolution numerical study of a liquid bridge Marangoni flow with applied axial magnetic field for low Prandtl number fluids

摘要

The Full Zone model of the thermocapillary (Marangoni) flow in a liquid bridge with an axial magnetic field, measured by the Hartmann number Ha, is studied using a Chebyshev spectral method for low Prandtl number fluids. By introducing a 2nd order vorticity transport formulation, high resolution Gauss-Lobatto grids can be used to investigate the strong stabilization effects from intermediate magnetic fields, which were impossible with previous formulations. The instability mechanism of the axisymmetric base flow is studied up to Ha=500 for Pr=0.001 and up to Ha=300 for Pr=0.02 using linear stability analyses. Over these parameter spaces, the base flow first transitions to three-dimensional stationary disturbances with different axial symmetries. Solutions from the 2nd order vorticity transport formulation show good agreement with previous studies on weak magnetic fields. This work provides better understanding of the magnetohydrodynamic flow in intermediate field strengths, as well as guidance for optically heated float-zone crystal growth processes.