3D numerical simulation of on ground Marangoni flow instabilities in liquid bridges of low Prandtl number fluid

Abstract

The influence of gravity on the Marangoni flow instability in half zone liquid bridges in the case of liquid metals is investigated by direct 3D and time‐dependent simulation of the problem. The computations are carried out for different heating conditions and environments (zero g conditions and on ground liquid zone heated from above or from below). The case of cylindrical shape (simplified model) and of melt/air interface deformed by the effect of gravity (real conditions) are considered. The comparison among these situations gives insight into the separate (gravity) effects of buoyancy forces and of the free surface deviation with respect to straight configuration. Body‐fitted curvilinear co‐ordinates are adopted to handle the non‐cylindrical problem. The liquid bridge exhibits different behaviours according to the allowed bridge shape. If the shape is forced to be cylindrical, the flow field is stabilized in the case of heating from above and destabilized if gravity is reversed. If the deformation is taken into account, gravity always stabilizes the Marangoni flow regardless of its direction (parallel or antiparallel to the axis) and the 3D flow structure is different according to the heating condition (from above or from below). In the latter case, the critical Marangoni number is larger and the critical wave number is smaller, compared with the opposite condition. In addition, for Pr=0.02 (Gallium), a surprising heretofore unseen behaviour arises. No steady bifurcation occurs and the flow becomes unstable directly to oscillatory disturbances. This phenomenon has never been reported before in the case of low Prandtl number liquids.

Citation

Lappa, M., Yasushiro, S. and Imaishi, N. (2003), "3D numerical simulation of on ground Marangoni flow instabilities in liquid bridges of low Prandtl number fluid", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 13 No. 3, pp. 309-340. https://doi.org/10.1108/09615530310464526