Abstract
The melt flow stability has a direct effect on crystal quality during the horizontal ribbon growth (HRG) process. The mixed convection in the HRG system includes thermocapillary convection, buoyancy convection, and the convection induced by the lid-driven boundary. In this study, the influences of relevant parameters such as Marangoni number, Rayleigh number, Biot number, and horizontal motion of the ribbon on flow and temperature fields have been analyzed using computational fluid dynamics. A thermal-fluid numerical model was developed by solving the Navier–Stokes and energy equations to obtain the flow, pressure, and temperature fields. The horizontal motion of the ribbon was assumed the lid-driven boundary. The results showed that the magnitude of the Marangoni number played a decisive role in the flow and temperature distribution inside the melt. In the case of a small Marangoni number, the increase in horizontal motion velocity of the ribbon was the main factor to induce convection in the melt, and the internal temperature distribution was carried out in a heat conduction mode. With the increasing Marangoni number, the thermocapillary convection was enhanced, and the convection induced by the ribbon motion was overwhelmed by the thermocapillary effect. Moreover, the increase in Biot number could reduce the temperature nonlinearity of the free surface. Particularly, the free surface temperature begins to oscillate as the Marangoni number is increased above a threshold. A larger Marangoni number could easily result in a temperature oscillation with a larger amplitude. The results indicated that the thermocapillary effect was more sensitive to temperature and flow oscillations, and should receive more attention.
Highlights
The thermocapillary effect, known as the thermal Marangoni effect, is a natural fluid motion driven by the temperature dependent surface tension gradient
The melt flow stability has a direct effect on crystal quality during the horizontal ribbon growth (HRG) process
In addition to the thermocapillary-buoyancy convection caused by the temperature gradient, forced convection will occur induced by the horizontal motion of the solid ribbon of velocity V g during the HRG process
Summary
The thermocapillary effect, known as the thermal Marangoni effect, is a natural fluid motion driven by the temperature dependent surface tension gradient. It is of great significance to study the effects combining with thermocapillary, buoyancy, and sliding wall motion on melt convection to optimize the HRG growth process and further obtain high-quality crystals. Kang et al. used the liquid of Pr = 390 as the experimental fluid to experimentally investigate the surface deformation and flow pattern of thermocapillary-buoyancy convection in a rectangular liquid pool. A model of thermocapillary-buoyancy convection in a rectangular liquid pool with the horizontal and vertical temperature gradients is proposed. Our aim is to gain a fundamental understanding of the characteristics and instability of the mixed thermocapillary-buoyancy convection with the bidirectional temperature gradients as well as the effect of the sliding wall on this flow.
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