Effect of free surface heat loss and rotation on transition to oscillatory thermocapillary convection

Oscillatory thermocapillary convection in an open cylindrical annulus heated from the inside wall is investigated numerically. Results for aspect ratio of 1 and Prandtl number of 30 are obtained to compare the simulations with available space experiments. The influence of surface heat loss as quantified by a Biot number (Bi) or spacecraft or orbital rotation through the Coriolis force, as quantified by a vector Taylor number of magnitude Ta, on the critical Reynolds number (Rec) and pattern of convection is investigated. The flow is steady and axisymmetric at sufficiently low values of Re. In the absence of rotation, we observe a two-lobed, isotherm pattern travelling clockwise at the free surface near Rec. A two- or three-lobed pulsating or a three-lobed rotating pattern is observed with increasing Re beyond Rec. Isotherm patterns on the free surface are in good agreement with experimental results. With Ta less than 1, which is relevant to the experiments, the effect of rotation on Rec and flow field is small. Here Rec is found to decrease with increasing Ta. Heat loss from the free surface stabilizes the flow. Increasing Bi leads to an increase in Rec and a small decrease in the critical frequency. The critical parameters and their dependence on the container size are in good agreement with the experiments, assuming Bi⩽20.