Three-dimensional numerical simulation of Marangoni flow instabilities in floating zones laterally heated by an equatorial ring

Abstract

Instability of Marangoni convection in floating zones (full zone configuration) of a low Prandtl number fluid under microgravity conditions is investigated by parallel supercalculus and direct three-dimensional and time-dependent simulation of the problem. A parametric analysis (still absent in literature) of the influence of the aspect ratio of the liquid column on the features of the three-dimensional bifurcation of Marangoni flow is carried out. A novel distribution is introduced for the surface heat flux corresponding to the radiative flux generated by a ring heater positioned around the equatorial plane of the full zone at a distance h from the free interface. Axisymmetric computations are used to obtain the steady basic state, then the three-dimensional Navier–Stokes equations are solved to investigate the evolution of azimuthal disturbances. These disturbances always exhibit antisymmetric behavior with respect to the equatorial plane. The mirror symmetry with respect to this plane is broken. Strong interaction occurs in fact between the toroidal convection rolls located in the upper part and lower part of the liquid column. This leads for some values of the aspect ratio to a heretofore unseen “apparent” doubling or quadrupling of the azimuthal wave number of the azimuthal velocity distribution in the midplane. The present analysis points out that the instability of the half zone flow is not relevant for the full zone configuration.