Numerical simulation of three-dimensional thermocapillary flows in liquid bridges

Instability of thermocapillary convection has been studied by using a numer ical code based on a control volume method. The momentum, continuity, and e nergy equations are solved in a cylindrical configuration with the thermoca pillary boundary conditions at the free surface. The convective fluxes are calculated via an upwinding method and the numerical values are updated via a single step time marching method. We report the results obtained for two different Prandtl numbers (I and 32). The disturbance growth has been dete rmined during the transition from the axisymmetric to the oscillatory three -dimensional flow; the oscillatory modes, critical Reynolds numbers, and fr equencies are compared with those obtained by stability analyses. Two diffe rent regimes occur in supercritical conditions: the oscillations initially emerge as a pulsating regime and, successively, become an azimuthally rotat ing structure. The latter is also subjected to further transitions characte rized by an increase of the number of fundamental frequencies.