轴向磁场作用下Czochralski浅液池内热对流特性研究
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摘要
为了有效抑制熔体热对流并提高晶体的生长质量,采用三维数值模拟方法研究了轴向磁场对双向温差作用下Czochralski浅液池内Marangoni-热毛细对流的影响。在一个给定的底部热流密度条件下,探讨了轴向磁场对稳态流动和非稳态流动的影响,确定了不同磁场强度下流动由三维稳态流动向三维非稳态流动转变的临界Macri。结果表明:随着磁场强度的增大,临界Macri不断增大。轴向磁场对液池内稳态和非稳态Marangoni-热毛细对流均具有较好的抑制效果。对于稳态流动,磁场的引入会使自由表面温度波动幅值受到削弱,波数减少;对于非稳态流动,监测点P处的温度振荡随着磁场强度的增加不断逐渐减弱直至消失,流动由三维非稳态过渡为三维稳态,相应地,温度波动结构也会发生转变。
In order to suppress the convection of melt and improve the quality of crystals,a series of three-dimension numerical simulations were conducted to investigate the effect of the axial magnetic field on the Marangoni-thermocapillary convection in a thin Czochralski configuration subjected to bidirectional temperature gradients. The critical number Macriwas determined at different magnetic strength when the heat flux keep a constant value. The effect of axial magnetic field on the steady flow and unsteady flow was also discussed. The results indicate that the critical Macriincreases monotonously with the increase of the magnetic field strength and the axial magnetic field can suppress the steady and unsteady Marangonithermocapillary convection significantly. For the steady flow,temperature fluctuations of the free surface are weakened and the wave numbers are decreased by the magnetic field. For the unsteady flow,the three-dimensional oscillatory convention gradually transits to the three-dimensional steady flow,and the wave numbers and spoke patterns also undergo a transformation.
In order to suppress the convection of melt and improve the quality of crystals,a series of three-dimension numerical simulations were conducted to investigate the effect of the axial magnetic field on the Marangoni-thermocapillary convection in a thin Czochralski configuration subjected to bidirectional temperature gradients. The critical number Macriwas determined at different magnetic strength when the heat flux keep a constant value. The effect of axial magnetic field on the steady flow and unsteady flow was also discussed. The results indicate that the critical Macriincreases monotonously with the increase of the magnetic field strength and the axial magnetic field can suppress the steady and unsteady Marangonithermocapillary convection significantly. For the steady flow,temperature fluctuations of the free surface are weakened and the wave numbers are decreased by the magnetic field. For the unsteady flow,the three-dimensional oscillatory convention gradually transits to the three-dimensional steady flow,and the wave numbers and spoke patterns also undergo a transformation.
引文
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[12]Ozoe H,Okada K.The Effect of the Direction of the External Magnetic Field on the Three-Dimensional Natural Convection in a Cubic Enclosure[J].International Journal of Heat and Mass Transfer,1989,32:1939-1954.
[13]Takagi Y,Okano Y,Minakuchi H,et al.Combined Effect of Crucible Rotation and Magnetic Fieldon Hydrothermal Wave[J].Journal of Crystal Growth,2014,385(1):72-76.
[14]彭岚,毛娜,王飞,等.双向温度梯度作用下Cz池内热对流的数值模拟[J].工程热物理学报,2015,36(6):1325-1328.
[15]王飞,彭岚,张全壮,等.水平温差对环形浅液池内Marangoni-热毛细对流的影响[J].物理学报,2015,64(14):17-24.
[2]Kamotani Y,Lee J,Ostrach S.An Experimental Study of Oscillatory Thermocapillary Convection in Cylindrical Containers[J].Physics of Fluids A:Fluid Dynamics,1992,4(3):955-962.
[3]Schwabe D.Buoyant-Thermocapillary and Pure Thermocapillary Convective Instabilities in Czochralski Systems[J].Journal of Crystal Growth,2002,237:1849-1853.
[4]Li Y R,Quan X J,Peng L,et al.Three-dimensional Thermocapillary-Buoyancy Flow in a Shallow Molten Silicon Pool with Cz Configuration[J].International Journal of Heat&Mass Transfer,2005,48(10):1952-1960.
[5]Li Y R,Peng L,Wu S Y,et al.Bifurcation of Thermocapillary Convection in a Shallow Annular Pool of Silicon Melt[J].Acta Mechanica Sinica,2007,23(1):43-48.
[6]Bazzi H,Nguyen C T,Galanis N.Numerical Study of the Unstable Thermocapillary Flow in a Silicone Float Zone underμ-g Condition[J].International Journal of Thermal Sciences,2001,40(8):702-716.
[7]Li D,Qi K,Hu W R.Characters of Surface Deformation and Surface Wave in Thermal Capillary Convection[J].Science in China,2006,49(5):601-610.
[8]Shi W Y,Li G Y,Liu X,et al.Thermocapillary Convection and Buoyant-Thermocapillary Convection in the Annular Pools of Silicon Melt and Silicone Oil[J].Journal of Superconductivity&Novel Magnetism,2010,23(6):1169-1172.
[9]Teitel M,Schwabe D,Gelfgat A Y.Experimental and Computational Study of Flow Instabilities in a Model of Czochralski Growth[J].Journal of Crystal Growth,2008,310(7):1343-1348.
[10]Peng L,Li Y R,Liu Y J,et al.Bifurcation and Hysteresis of Flow Pattern Transition in a Shallow Molten Silicon Pool with Cz Configuration[J].Numerical Heat Transfer,Part A:Applications,2007,51(3):211-223.
[11]Virbulis J,Wetzel T,Muiznieks A,et al.Numerical Investigation of Silicon Melt Flow in Large Diameter CZ-Crystal Growth under the Influence of Steady and Dynamic Magnetic Fields[J].Journal of Crystal Growth,2001,230(1):92-99.
[12]Ozoe H,Okada K.The Effect of the Direction of the External Magnetic Field on the Three-Dimensional Natural Convection in a Cubic Enclosure[J].International Journal of Heat and Mass Transfer,1989,32:1939-1954.
[13]Takagi Y,Okano Y,Minakuchi H,et al.Combined Effect of Crucible Rotation and Magnetic Fieldon Hydrothermal Wave[J].Journal of Crystal Growth,2014,385(1):72-76.
[14]彭岚,毛娜,王飞,等.双向温度梯度作用下Cz池内热对流的数值模拟[J].工程热物理学报,2015,36(6):1325-1328.
[15]王飞,彭岚,张全壮,等.水平温差对环形浅液池内Marangoni-热毛细对流的影响[J].物理学报,2015,64(14):17-24.