Two-dimensional Numerical Simulation Of Thermal Convection In An Annular Two-layer System

In the crystal growth process, the thermocapillary flow induced by the interface tension gradient becomes a prominent factor influencing the quality of crystal materials. The liquid encapsulation Czochralski (LEC) technology can effectively suppress thermocapillary convection in the melt. But there is a lack of the understanding on the basic characteristics of thermocapillary convection in the annular two-layer liquid system. It is of great theoretical significance and practical value to investigate the stability, physical mechanism and characteristics of thermocapillary convection in the two-layer system under the horizontal temperature gradient so as to improve the production processes and quality of materials.The physical and mathematical models of thermal convection in the annular two-layer systems under the horizontal temperature gradient were established. A set of two-dimensional numerical simulations was carried out using the finite-volume method. The distributions of temperature and velocity in the two liquid layers were then obtained and effects of parameters, such as Marangoni (Ma) number, buoyant and geometric parameter et al, on the thermal convection were analyzed. Also, the critical Ma number at different conditions was determined and the physical mechanism of the unstable thermal convection was revealed.It is found that: (1) for small Ma number, the flow is steady. With the increase of Ma number and the aspect ratio, the flow strength becomes much stronger and the deformation of the isotherms increases sharply. In considering the effect of buoyancy, the thermal convection in the melt is enhanced. (2) While Ma number exceeds the critical value, an unsteady multicultural structure is developed, and the additional cells appear near the cold lateral wall. During the oscillatory process, the flow cells move to the hot wall and then fade away in the vicinity of the hot wall. When the Ma number is small, the multicultural structure and the oscillations of velocity and temperature mainly appear near the cold wall. With the increase of the Ma number, the oscillations of velocity and temperature increase and propagate to the hot wall, and the multicultural structure expands to a wider region. (3) The critical Ma number decreases with the increase of the aspect ratio and the decrease of the radius ratio. In the annular pool with a free surface, the buoyancy can delay convective instability of the two-layer system and make the critical Ma number increase. The effect of buoyancy is much obviously in the shallow pool. The critical Ma number decreases and the instability of the system enhances when the top surface is bounded by the rigid wall, and in this condition the buoyancy makes the system apt to lose stability and the critical Ma number decrease.