双层流体热毛细—浮力对流不稳定性及外部磁场主动控制
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摘要
热毛细对流是由于流体交界面温度分布不均匀引起的表面张力梯度驱动的流体流动，也称为Marangoni对流。这一对流广泛存在于晶体生长、铸造、镀膜等过程，其不稳定性可能导致许多不期望的结果，如晶体生长的不均匀性。本文以大尺寸晶体生长过程中双层流体内的流动不稳定性为研究对象，研究了双层流体热毛细-浮力对流不稳定性的产生条件、演化机理及其磁场主动控制规律；同时，研究了外部磁场对晶体生长过程中热质传输特性的影响规律。研究内容及获得的研究结果如下：
首先，通过数值模拟研究了环形液池内双层流体热毛细-浮力对流不稳定性的产生条件、演化机理及其磁场主动控制规律。研究发现，热毛细对流不稳定性的扰动产生于内壁面区域，并沿着温度梯度方向传播；液池深径比对热毛细-浮力对流具有重要影响，当深径比为0.5时，双层流体热毛细-浮力对流不稳定性产生的临界Ma数为2.33×103。随着深径比减小周向温度波数先增大后减小，但周向速度的平均振幅逐渐增大；随着重力加速度的增大，由表面张力效应引起的扰动能能量减小，同时周向温度波数也逐渐减小。环形液池的旋转能够有效抑制热毛细对流不稳定性，其流动从非稳态振荡流转变为稳态对流。不同类型磁场均能抑制热毛细对流不稳定性，其中轴向磁场对热毛细-浮力对流的抑制效果最好，勾型磁场的抑制效果次之，水平磁场的抑制效果最差。
其次，数值研究了外部磁场对大直径单晶硅生长中热质传输特性及杂质分凝效应的影响。研究发现，在轴向磁场和勾型磁场作用下，随着磁场强度增大，熔体内部氧浓度逐渐增大，熔体的对流结构逐渐趋于规则，且勾型磁场的抑制效果要好于轴向磁场。当应用旋转磁场时，晶体、熔体、坩埚三者同向旋转对晶体生长最有利。外部磁场能够有效改善晶体内部杂质的分布，水平磁场作用下杂质分布的梯度主要集中在晶体内部与磁场垂直的方向，而勾型磁场作用下杂质分布的梯度主要集中在晶体边缘，因此施加勾型磁场更有利于晶体生长。
此外，发展了Level set方法模拟双层流体交界面的变形，研究了双层流体热毛细-浮力对流自由界面变形的特征及磁场对热毛细-浮力对流的影响规律。研究显示，在Marangoni效应的作用下，自由界面在热端凸起冷端凹陷；自由界面的变形率随Ma数和宽深比的增大而增大，随磁场强度和重力加速度的增大而逐渐减小。双层流体交界面与壁面的接触条件对交界面变形和流型结构具有重要影响。
最后，采用剪切干涉法对矩形腔体内双层流体热毛细-浮力对流的温度场进行了验证实验，并采用代数重建算法对剪切干涉法获得的干涉图像进行了温度场的三维重建，重建结果与数值模拟结果吻合很好。
Thermocapillary convection is driven by surface tension gradient due to a non-uniform temperaturedistribution at the fluid interface, which is also called Marangoni convection. This flow phenomenonwidely exists in many engineering applications including crystal growth, metal casting, and filmcoating process. The instability of thermocapillary convection can cause adverse effects, i.e.,imperfections in crystal growth. In this thesis, the appearance and evaluation ofthermocapillary–buoyant convection instability in an annular two-layer fluids system and the effect ofmagnetic field on the convection instability were investigated. Meanwhile, the influence of externalmagnetic field on the heat and mass transfer in Cz method crystal growth process was investigated,also. The detailed content and results as follows:
Firstly, the appearance and evaluation of thermocapillary–buoyant convection instability in anannular two-layer fluids system and the effect of magnetic field on it were investigated by numericalsimulation. The oscillation of thermocapillary convection instability initiates around the inner wallregion, and propagates along the direction of temperature gradient. The aspect ratio has obvious effecton thermocapillary convection, in which the azimutahl wave number increases at first and thendecreases as the aspect ratio decreases, but the average oscillatoty amplitude of azimuthal velocity isstrengthened gradually. When aspect ratio is0.5, the critical Ma number of themocapillary-buoyantconvection instability is2.33x103. With the gravitational acceleration increasing, the energy ofdisturbance from surface tension is reduced, and the azimuthal wave number decreases. The rotationof annular pool can suppress the thermocapillary convection instability effectively, and the oscillatoryconvection becomes steady convection. All the magnetic fields can suppress the thermocapillaryconvection, in which the electromagnetic damping of thermocapillary convection instability underaxial magnetic field is the most advantageous, that of cusp magnetic field is the second, and thehorizontal magnetic field results in the weakest damping.
Secondly, the influence of external magnetic field on the heat and mass transfer and segregation ofimpurity in Cz method crystal growth process was investigated by numerical simulation. Under theinfluence of axial and cusp magnetic fields, with magnetic field intensity increasing the temperaturegradient on the interface of melt and crystal decreases, the oxygen concentration increases gradually,and the convective pattern becomes more regular and, the damping effect of cusp magnetic field isstronger than that of axial magnetic field. When rotating magnetic field is applied to, the rotations ofcrystal, crucible and fluid are in the same direction, a better crystal quality can be obtained. Theexternal magnetic field can improve the impurity distribution in crystal. The gradient of impuritydistribution mainly locates at the direction of θ=π/2and θ=3π/2of crystal under horizontalmagnetic field, but that of under cusp magnetic field locates at the margin of crystal. The applicationof cusp magnetic field is better for the control of impurity segregation.
Developed Level set method was applied to the simulation of interface characterstics of two-layerfluids, and the flow characteristics of thermocapillary-buoyant convection with a deformable interfacewas investigated. It is found that, under the impact of Marangoni effect on the interface bulges outnear the hot wall and bulges in near the cold wall. The deformability of free surface is increased with Ma number and aspect ratio increasing, but it is decreased as the magnetic field intensity andgravitational acceleration increase. The contact condition of interface with the end walls is importantfor the prediction of thermocapillary convection characteristics.
Lastly, the temperature field of thermacapillary-buoyant convection in a rectangular cavity wasinvestigated experimentally by Laser shear interference method, and the three-dimensionaltemperature field was reconstructed by algebraic reconstruction technique method. The constructedtemperature field is in good agreement with numerical simulation result.
首先，通过数值模拟研究了环形液池内双层流体热毛细-浮力对流不稳定性的产生条件、演化机理及其磁场主动控制规律。研究发现，热毛细对流不稳定性的扰动产生于内壁面区域，并沿着温度梯度方向传播；液池深径比对热毛细-浮力对流具有重要影响，当深径比为0.5时，双层流体热毛细-浮力对流不稳定性产生的临界Ma数为2.33×103。随着深径比减小周向温度波数先增大后减小，但周向速度的平均振幅逐渐增大；随着重力加速度的增大，由表面张力效应引起的扰动能能量减小，同时周向温度波数也逐渐减小。环形液池的旋转能够有效抑制热毛细对流不稳定性，其流动从非稳态振荡流转变为稳态对流。不同类型磁场均能抑制热毛细对流不稳定性，其中轴向磁场对热毛细-浮力对流的抑制效果最好，勾型磁场的抑制效果次之，水平磁场的抑制效果最差。
其次，数值研究了外部磁场对大直径单晶硅生长中热质传输特性及杂质分凝效应的影响。研究发现，在轴向磁场和勾型磁场作用下，随着磁场强度增大，熔体内部氧浓度逐渐增大，熔体的对流结构逐渐趋于规则，且勾型磁场的抑制效果要好于轴向磁场。当应用旋转磁场时，晶体、熔体、坩埚三者同向旋转对晶体生长最有利。外部磁场能够有效改善晶体内部杂质的分布，水平磁场作用下杂质分布的梯度主要集中在晶体内部与磁场垂直的方向，而勾型磁场作用下杂质分布的梯度主要集中在晶体边缘，因此施加勾型磁场更有利于晶体生长。
此外，发展了Level set方法模拟双层流体交界面的变形，研究了双层流体热毛细-浮力对流自由界面变形的特征及磁场对热毛细-浮力对流的影响规律。研究显示，在Marangoni效应的作用下，自由界面在热端凸起冷端凹陷；自由界面的变形率随Ma数和宽深比的增大而增大，随磁场强度和重力加速度的增大而逐渐减小。双层流体交界面与壁面的接触条件对交界面变形和流型结构具有重要影响。
最后，采用剪切干涉法对矩形腔体内双层流体热毛细-浮力对流的温度场进行了验证实验，并采用代数重建算法对剪切干涉法获得的干涉图像进行了温度场的三维重建，重建结果与数值模拟结果吻合很好。
Thermocapillary convection is driven by surface tension gradient due to a non-uniform temperaturedistribution at the fluid interface, which is also called Marangoni convection. This flow phenomenonwidely exists in many engineering applications including crystal growth, metal casting, and filmcoating process. The instability of thermocapillary convection can cause adverse effects, i.e.,imperfections in crystal growth. In this thesis, the appearance and evaluation ofthermocapillary–buoyant convection instability in an annular two-layer fluids system and the effect ofmagnetic field on the convection instability were investigated. Meanwhile, the influence of externalmagnetic field on the heat and mass transfer in Cz method crystal growth process was investigated,also. The detailed content and results as follows:
Firstly, the appearance and evaluation of thermocapillary–buoyant convection instability in anannular two-layer fluids system and the effect of magnetic field on it were investigated by numericalsimulation. The oscillation of thermocapillary convection instability initiates around the inner wallregion, and propagates along the direction of temperature gradient. The aspect ratio has obvious effecton thermocapillary convection, in which the azimutahl wave number increases at first and thendecreases as the aspect ratio decreases, but the average oscillatoty amplitude of azimuthal velocity isstrengthened gradually. When aspect ratio is0.5, the critical Ma number of themocapillary-buoyantconvection instability is2.33x103. With the gravitational acceleration increasing, the energy ofdisturbance from surface tension is reduced, and the azimuthal wave number decreases. The rotationof annular pool can suppress the thermocapillary convection instability effectively, and the oscillatoryconvection becomes steady convection. All the magnetic fields can suppress the thermocapillaryconvection, in which the electromagnetic damping of thermocapillary convection instability underaxial magnetic field is the most advantageous, that of cusp magnetic field is the second, and thehorizontal magnetic field results in the weakest damping.
Secondly, the influence of external magnetic field on the heat and mass transfer and segregation ofimpurity in Cz method crystal growth process was investigated by numerical simulation. Under theinfluence of axial and cusp magnetic fields, with magnetic field intensity increasing the temperaturegradient on the interface of melt and crystal decreases, the oxygen concentration increases gradually,and the convective pattern becomes more regular and, the damping effect of cusp magnetic field isstronger than that of axial magnetic field. When rotating magnetic field is applied to, the rotations ofcrystal, crucible and fluid are in the same direction, a better crystal quality can be obtained. Theexternal magnetic field can improve the impurity distribution in crystal. The gradient of impuritydistribution mainly locates at the direction of θ=π/2and θ=3π/2of crystal under horizontalmagnetic field, but that of under cusp magnetic field locates at the margin of crystal. The applicationof cusp magnetic field is better for the control of impurity segregation.
Developed Level set method was applied to the simulation of interface characterstics of two-layerfluids, and the flow characteristics of thermocapillary-buoyant convection with a deformable interfacewas investigated. It is found that, under the impact of Marangoni effect on the interface bulges outnear the hot wall and bulges in near the cold wall. The deformability of free surface is increased with Ma number and aspect ratio increasing, but it is decreased as the magnetic field intensity andgravitational acceleration increase. The contact condition of interface with the end walls is importantfor the prediction of thermocapillary convection characteristics.
Lastly, the temperature field of thermacapillary-buoyant convection in a rectangular cavity wasinvestigated experimentally by Laser shear interference method, and the three-dimensionaltemperature field was reconstructed by algebraic reconstruction technique method. The constructedtemperature field is in good agreement with numerical simulation result.
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