D. Castagnolo et L. Carotenuto, Numerical simulation of three-dimensional thermocapillary flows in liquid bridges, NUM HEAT A, 36(8), 1999, pp. 859-877
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.