Research On Flow Characteristics Of Silicon Melt With Bidirectional Temperature Gradients In Annular Pool

The complex thermocapillary-buoyancy convection with bidirectional temperature gradients exists widely in various natural phenomena and engineering fields.It is known that the temperature distribution on free surface and temperature field of fluid are directly affected by the parallel or vertical temperature gradient imposing on the liquid layer.Therefore,the flow depends on the bidirectional temperature gradients.Up to now,researches are mainly focused on the thermocapillary-buoyancy convection with unidirectional temperature gradient.However,flow characteristics and its stability with bidirectional temperature gradients are still unclear.In this thesis,the complex flow of silicon melt with bidirectional temperature gradients in annular pool are investigated by numerical simulation.The main aims are to understand the flow characteristics and flow pattern evolution.The influences of Marangoni number,heat flux,ambient temperature,geometric dimension and rotational Reynolds number are discussed and the physical mechanism of flow instability is revealed.Moreover,the transition of the thermocapillary convection from the one dominated by the radial temperature gradient to another dominated by the vertical temperature gradient is investigated.The results of the study are helpful to enrich and develop the dissipative structure theory of complex flow in the fluid layer,and provide theoretical guidance for the single crystal growth of silicon.The main works and results are listed as follows:Firstly,a series of three-dimensional numerical simulations are carried out to analyze the flow characteristics of the rotation-thermocapillary convection in an annular pool with a depth of 3mm(Ar=0.06,η=0.3).The results show that a large amount of radiation heat is lost to ambient environment from the free surface.Therefore,when the other parameters are fixed,the heat flux applied to the bottom of the annular pool must be large enough,otherwise solid silicon will appear in the annular pool.Then the first type of critical heat flux,which is to ensure the whole silicon in the annular pool is in the molten state,is calculated.Generally speaking,when the other parameters are fixed,the larger the Marangoni number is,the smaller the first type of critical heat flux is.When the annular pool is static,the melt flow is in the three-dimensional steady or unsteady state,and the flow pattern on the free surface depends on the radial and vertical temperature gradients.For a three-dimensional steady flow,if the bottom heat flux exceeds a certain critical value,the flow will become unsteady.Then the second kind of critical heat flux,which is to judge the onset of oscillatory flows,is determined.When the annular pool begins to rotate,the flow pattern on the free surface becomes more abundant due to the centrifugal force and the Coriolis force.When the rotational Reynolds number is large enough,the flow will transit into an axisymmetric steady flow.It indicates that the strong rotation centrifugal force and Coriolis force could stabilize the complex thermocapillary convection.If the heat flux exceeds the second kind of critical value,the flow will directly transit from axisymmetric steady state into three-dimensional oscillatory state.The flow instability mechanism can be explained by the asynchronous change of temperature and velocity.When the other parameters are constant,the larger the Marangoni number is,the lower the second kind of critical heat flux is.In addition,when the rotation Reynolds number and Marangoni number are fixed,the higher the ambient temperature is,the smaller the first kind of critical heat flux is.Moreover,high ambient temperature and rotation rate are beneficial to obtain the axisymmetric steady flow.For a thermocapillary flow with bidirectional temperature gradients,Raising the ambient temperature or heat flux imposing at the bottom can increase the vertical temperature gradient as well.Therefore,flow can transit from the one dominated by the radial temperature gradient to the one dominated by the vertical temperature gradient dominated.However,when the annular pool is stationary,the flow at the large Marangoni number is in chaotic state before completing this flow transition due to the large thermocapillary force.But when the rotation rate is high,the surface temperature fluctuations can be suppressed effectively.Therefore,it is conducive to maintain the flow in regular oscillatory state with strong rotation centrifugal force and Coriolis force during the flow transition.Secondly,a systematic study is carried out on the rotation-thermocapillarybuoyancy convection in the annular pool with depth of 6mm(Ar=0.12,η=0.3).Under microgravity condition,the standing waves and travelling waves with different wave number appear on the free surface with the increase of Marangoni number and decrease of the heat flux.When the annular pool begins to rotate,the flow pattern on the free surface is influenced by the centrifugal force and the Coriolis force.If the rotational Reynolds number is large,the flow will transit into an axisymmetric steady flow.In addition,the ambient temperature has a significant effect on the rotationthermocapillary convection.When other parameters are constant,the higher the ambient temperature is,the lower the two kinds of critical heat fluxes are.When the thermocapillary convection is dominated by the radial temperature gradient,the free surface temperature increases monotonically along the radial direction.Therefore,the melt flow starts from the outer wall to the inner wall on the free surface along the radial direction.When the thermocapillary convection is dominated by the vertical temperature gradient,the highest temperature on the free surface locates in the middle of the annular pool.Therefore,the melt flow starts from the middle region to the outer and inner walls along radial direction on the free surface.By increasing the heat flux or the ambient temperature,the flow can transit from the one dominated by the radial temperature gradient to the one dominated by the vertical temperature gradient.When the rotating Reynolds number is large,the flow keeps in three-dimensional oscillatory state during this flow transition.Under gravity condition,due to the large dynamic Bond number,the buoyancy convection is enhanced significantly.Because of the intervention of the buoyancy convection,the flow is strengthened obviously.When the annular pool is static,the flow is easily to be chaos.And when the rotation Reynolds number is high,the flow transits into a regular three-dimensional oscillatory one.Compared with the flow under microgravity,the flow structure is nearly unchanged,even the flow intensity is increased.Therefore,the effect of thermocapillary convection on the melt flow is still obvious.Thirdly,a systematic study was carried out on the rotation-thermocapillarybuoyancy convection in the deep annular pool of 30mm(Ar=0.6,η=0.3).Under microgravity condition,when the annular pool is stationary,irregular flow pattern appears on the free surface and the flow is easily to be chaos.When the rotation Reynolds number is high,regular flow pattern can be observed on the free surface,and the flow transits into a regular three-dimensional oscillatory flow.Under the condition of constant gravity,the effect of buoyancy convection is greatly enhanced,and the flow structure in the melt is dominated by buoyancy convection.Because of the great increase of the flow intensity,the flow is more easily to transit into a chaotic one.Even with the large rotation Reynolds number,the flow is very complex with poor periodicity.Therefore,when the depth of the annular pool is greater,a high rotation rate is necessary to maintain the flow in the oscillatory state.