Effects Of Surface Deformation On The Stability Of Thermal Convection In The Czochralski Configuration

Czochralski crystal growth method is the most common crystal growth method in industry.Due to the wetting effect,the liquid near the wall will climb and generate the surface deformation.However,in the past years,the surface deformation were often ignored,and the free surface was considered to be flat.In recent years,with the development of research,more and more scholars began to pay attention to the influence the surface deformation on the flow patterns and the instabilities of thermal convection in the liquid pool.This paper presents a series of three dimensional numerical simulations on the thermal convection in a Czochralski configuration with the surface deformation.The effect of surface deformation on the flow patterns and evolutions have been discussed.Frist,the numerically simulation of the complex flow induced by thermocapillary and buoyancy forces in the Czochralski configuration with surface deformation was carried out.The results showed that for the flat surface or for the surface deformation caused by wetting effect,three small rolling cells which are flow in opposite rotation directions with each others were observed in the liquid pool when the Re _T is small.Once the surface deformation which caused by the growth angle of the crystal was take into account,the basic flow is formed by two cells,and the strength of the cell under the crystal increases with the increase of the Re _T.With the further increase of Re _T,the basic flow transit to unstable state.The critical thermocapillary Reynolds number for the flow transition decreases as the volume ratio increases.The surface deformation enhances the instability of thermal capillary-buoyancy convection and a series of flow transition patterns were observed:when the surface deformation caused by wetting effect was taken into account,as the Re _T increases,the flow loses the stability and transits to a spoke-like flow pattern or a fork-like flow pattern.Once the surface deformation caused by the growth angle of the crystal was take into account,the flow transits to local oscillating flow patterns.With the increase of the Re _T,a wave source and a wave sink appear on the free surface randomly,the waves propagate in radial and circumferential direction,and then the reverse transition phenomenon was obtained.Then,the effect of surface deformation on the thermal-solute capillary-buoyancy convection of the binary mixtures in the Czochralski configuration was studied.In the Czochralski configuration with flat surface,when the driving force is small,the influence of crystal rotation generates the clockwise rotating cells under the crystal,and the rotation of the crucible enhances the flow strength of the counter-clockwise rotating cell in the liquid pool.The flow stability map at different rotation rate were drew,and it was found that with the increase of crystal rotation rate,and the critical thermocapillary Reynolds number increase first and then decrease.When the crucible rotation rate increases,the critical thermocapillary Reynolds number increases.After the flow losing stability,many complex flow patterns were found on the free surface,such as:spoke patterns,flower bud patterns,and the spiral hydrosoultal waves.For the coupled thermal-solute capillary-buoyant convection in Czochralski configuration with surface deformation,the critical thermocapillary Reynolds number increases as the volume ratio increases.When the surface deformation caused by the wetting effect was take into account,as the thermocapillary Reynolds number increases,the flow loses stability and transits to a spoke-like patterns with a wave number of 16.