Aspect Ratio Dependence of Thermocapillary Flow Instability of Moderate-Prandtl Number Fluid in Annular Pools Heated from Inner Cylinder

This paper presented a set of direct numerical simulations on the thermocapillary flow instability of moderate-Prandtl number fluids in annular pools heated from inner cylinder. The emphasis is on the aspect ratio dependence of the critical Marangoni number of flow destabilization and the formation mechanism of the different flow patterns. It was found that the two-dimensional axisymmetric steady flow will bifurcate into three types of oscillatory flows, including the oscillatory concentric rings, the alternating straight spoke and the rotating wave patterns. The bifurcation process depends mainly on the aspect ratio of the annular pool when the radius ratio is fixed. With the increase of the aspect ratio, the first instability flow pattern is oscillatory concentric rings and the corresponding critical Marangoni number and the oscillatory frequency decrease first, and then increase slightly. When the flow pattern transits to the alternating straight spoke pattern at the aspect ratio of 0.415, there are an abrupt increase of the critical Marangoni number and a sudden decrease of the oscillatory frequency. Furthermore, when the rotating wave pattern appears, the critical Marangoni number decreases gradually, but the corresponding oscillatory frequency has only a slight decrease.