Thermocapillary Flow And Instability Analysis In A Ringent Cylindrical Pool

In melt crystal growth process, the thermocapillary flow induced by the temperature gradient becomes a prominent factor influencing on the homogeneity of crystal. It is worthy to investigate the stability, physical mechanism and characteristics of thermocapillary convection so as to improve the product line and quality of materials. In order to understand the fundamental characteristics of thermocapillary convection in a ringent cylindrical pool with an azimuthal temperature non-uniform, an adiabatic solid bottom and free surface under microgravity condition, this paper conducts a series of unsteady three-dimensional numerical simulations with the finite difference method. The distributions of temperature and velocity in ringent cylindrical pool are then obtained and effects of a series of non-dimensional parameters on the thermocapillary convection are analyzed. Also, the instability analysis of thermocapillary flow and physical mechanism of three-dimensional oscillatory flow with different characteristics are reported. The aspect ratio for ringent cylindrical pool is As=0.02-0.2, the Prandtl number Pr=0.011-1, the capillary Reynolds number Re=5.5×104-8×106.The simulation results indicate that thermocapillary convection is steady three-dimensional flow at the small temperature non-uniform. Two axisymmetric second convection cells exist in vertical direction of dominating flow. When temperature non-uniform number exceeds some critical value, the flow will undergo a transition to three-dimensional oscillatory flow. The critical conditions for the onset of oscillatory flow are determined. Details of the characteristics of steady flow and oscillatory flow are also discussed.When Prandtl number is low, oscillations of flow fields and temperature fields first happen at vicinity of cold wall and propagate to the hot wall conversely because of the less temperature gradient near hot wall. In temperature wave propagation process, the temperature of fluids increase correspondingly and temperature gradient of fluid existing in pool center is higher than the one in other parts which are symmetrical about A-B section. Therefore, oscillations diffuse to two sides at the same time. When Prandtl number is moderate, oscillations of temperature fields still propagate to the hot wall conversely and diffuse to two sides at the same time. But, the augmentation of kinetic diffusion makes temperature wave propagation be weakened. The velocity wave caused by temperature wave mix with surface thermocapillary flow and rhombic oscillations of temperature which propagate to the hot wall conversely generate. With the Reynolds number increasing, the dimensionless temperature oscillation amplitudes and the oscillation frequencies both increase. And with depth's increasing, the temperature fluctuation will expand to entire pool, and the dimensionless temperature oscillation amplitudes increase, too.