Two-Dimensional Numerical Simulation for Flow Pattern Transition of Thermal-Solutal Capillary Convection in an Annular Pool

In order to understand the transition characteristics of the thermal-solutal capillary convection in an annular pool, a series of two-dimensional numerical simulations were conducted. The bottom of the pool is adiabatic rigid wall and the top is adiabatic and non-deformable free surface. The inner and outer cylindrical walls maintain at constant temperature and solute concentration, respectively. The thermo-capillary force is supposed to equal to the solute-capillary force, but their directions are contrary. Results show that the thermal-solutal capillary convection is steady at a small Reylonds number. When the capillary Reynolds number exceeds a critical value, the steady flow transits into unstable thermal-solutal capillary convection. The transition from the steady to oscillatory flow undergoes a Hopf bifurcation. Furthermore, the effects of the liquid layer aspect ratio, the radius ratio, the Prandtl number and the Lewis number on the onset of flow pattern transition are discussed. The physical mechanism of the unstable thermal-solutal capillary convection is also analyzed.