Two-dimensional Numerical Simulation For Flow Pattern Transition Of Thermal-solutal Capillary Convection With Binary Mixture In An Annular Pool

It is well known that the surface tension of solution always varies with temperatureand solute concentration. Once the temperature and solute concentration are un-uniformalong the free surface, the induced surface tension gradient can drive a convective flow.This flow is called as the thermal-solutal capillary convection. This complex capillaryconvection plays a very important role in crystal growth, semiconductor processing,liquid melt solidification and the condensation heat transfer of mixture vapor etc.In order to understand the transition characteristics of the thermal-solutal capillaryconvection, the physical and mathematical models of the thermal-solutal capillaryconvection in an annular pool are established, and two-dimensional numericalsimulation is conducted using the finite-volume method. The bottom of the pool isadiabatic rigid wall and the top is adiabatic and non-deformable free surface. The innerand outer cylindrical walls maintain at constant temperature and solute concentration,respectively. For the simplification, the Soret effect and the Dufour effect are allneglected. The thermo-capillary force is supposed to equal the solute-capillary force,but their directions are contrary. The critical Reynolds number for the flow patterntransition from steady to unsteady flow is obtained. In addition, the transitionmechanism is also analyzed.The results show that (1) at a small Marangoni number, the flow is steadythermal-solutal capillary convection. With the increase of the aspect ratio, radius ratioand the Prandtl number, the steady convection is enhanced.(2) When the Reylondsnumber exceeds a critical value, the steady flow transits into unstable thermal-solutalcapillary convection. It is found that the variation of the amplitude A of the radialvelocity oscillation satisfies the relationship of A∝(Re Recri)1/2, where Recriis thecritical Reynolds number. Therefore, the transition from the steady to oscillation flowundergoes a supercritical Hopf bifurcation.(3) With the increase of the aspect ratio,radius ratio and the Prandtl number, the critical Reylonds number of the flow transitiondecreases and the flow loses its stability easily.(4) Furthermore, when the Lewis (Le)number is greater than1, the critical Reynolds number decreases with the increase ofthe Le number. Since response speed of the thermal Marangoni effect is faster than thatof the solutal Marangoni effect in local spot of the annular pool, the thermo-capillaryforce is dominant. Therefore, it overcomes the viscous force and drives the movement of the clockwise flow cell from inside to outside in an annular pool. However, when theLe number is less than1, it is contrary.