Oscillating characteristic of free surface from stability to instability of thermocapillary convection for high Prandtl number fluids

Abstract An investigation on oscillating characteristic of free surface in a liquid bridge for high Pr number fluids under gravity has been conducted numerically. Against the former studies, free surface is treated as a deformable surface in the direct numerical simulation (DNS) of liquid bridge by using a mass conserving level set method for the first time. The results show that, the moving track of vortex centers appears the shape of axisymmetric hook in the stable stage of thermocapillary convection, and the fluctuation of surface velocity is closely relative to the motion of cell flow toward the center and cold disk. In the process of transforming from the stable stage to oscillatory stage, the moving track of vortex centers of cell flow shows the asymmetry and step characteristic. The coupling effects of the temperature, velocity and free surface oscillations constitute complete mechanism of thermocapillary convection oscillations. The temperature firstly oscillates at the hot corner, and transfer direction of temperature oscillation is from the hot corner to inner. The velocity of surface flow is larger than that of internal flow, and the surface flow is supplied by the bulk return flow with the disturbance information of the velocity. The velocity oscillation lags behind the temperature oscillation at the hot corner. The closer to the intermediate height, the larger amplitudes of temperature and velocity are. The oscillation law of velocity and free surface at the intermediate height are the same, and there are two obvious oscillation bifurcations.