Magnetic convection

磁场已被用于各种制造工艺，如半导体材料的直拉法晶体生长和/或连续铸钢工艺，因此可以通过平息熔体的对流来预期更高质量的凝固产品。这是因为液态金属的普朗特数低至0.01。振荡对流是液态金属普遍存在的现象，导致凝固产物组织不均匀。为了避免这些现象，有时会在试错库中使用强磁场，而不详细了解热、质量和动量传递等传输现象的相关机制。在本研究计划中，对磁场的影响进行了精确的建模和精确的数值分析。首先考虑的是提拉法晶体生长过程中的熔体对流。所考虑的系统是在高度为H的圆柱形坩埚中熔化InSb的金属，…直径超过1.25H，晶体棒直径0.625H。晶棒被冷却，自由表面被辐射冷却。然后，在没有磁场的情况下，即使在轴对称的坩埚中也计算了单个单面对流辊。在水平横向磁场作用下，计算了磁场垂直面上升流动、平行平面下降流动的自由表面稳定对流。这使得自由表面上的椭圆形温度等高线有望提供椭圆形横截面单晶棒。通过文献调查，我们发现了Kajigaya等人的一份报告。制作了水平磁场作用下的椭圆形单晶棒。这意味着目前的理论分析得到了他们的实验报告的有力支持，并为其生长单晶棒提供了理论解释。作为第二个研究课题，研究了磁化力引起的对流。其中之一是关于氧气从垂直管道顶部和底部开口流出的对流和扩散过程，该垂直管道位于一个强度为12特斯拉的超导磁体的钻孔中。竖管直径50 mm，长600 mm，充满纯氧气体。在时间零时，打开管道的顶部和底部开口，从而实现氧气的自然通风。在没有磁场的情况下，氧气的平均分子质量略大于环境空气的平均分子质量，从而导致氧气快速流出。随着磁场强度的增加，垂直管道中间高度处的平均氧气浓度逐渐降低。在12特斯拉时，氧气浓度在2000秒后降至初始浓度的30%。用质量和动量平衡方程模拟了目前的现象，并进行了数值求解。得到的中间高度氧气的瞬时浓度与前人的实验结果吻合得很好，从而保证了模型方程的成立。详细的图形可视化阐明了上述特点。当管道中氧气的下半部从下部开口流出，管道的上半部充满空气时，磁化力作用将氧气拉回管道中心高度，高浓度氧气长时间保持在中等高度。随着扩散的进行，管道中高度处的氧气浓度逐渐降低。除此之外，还有大量的研究成果。它们分别是提拉法生长晶体中的尖形磁场、超导磁体中的旋转磁场、塞贝克对流和由于磁化力而产生的准非引力场。较少

The magnetic field has been employed for various manufacturing processes such as Czochralski crystal growth of semi-conducting material and/or continuous steel casting processes so that higher quality of solidified products can be expected by calming the convection of molten materials. This is because the Prandtl number of liquid metal is as low as 0.01. The oscillatory convection is common for liquid metal and causes nonuniform structure in the solidified product. To avoid these phenomena sometimes strong magnetic field has been employed in trial and error bases without detailed understanding on the related mechanism of transport phenomena such as heat, mass and momentum transfer. In the present research program, an exact modeling on the effect of magnetic field and acurate numerical analyzes were carried out.The first system considered is melt convection in a Czochralski crystal growth process. The system considered is molten metal of InSb in a cylindrical crucible with H in height, … More 1.25H in diameter with a crystal rod of 0.625H in diameter. The crystal rod is cooled and the free surface is radiatively cooled. Then, without a magnetic field, a single one-sided convection roll was computed even in an axi-symmetric crucible. With a horizontal lateral magnetic field, a stable convection over a free surface was computed with rising flow in a perpendicular plane of a magnetic field and downward flow in a parallel plane. This caused elliptic temperature contours over a free surface to expect to provide an elliptic cross-sectional single crystal rod. By making a literature survey, we found a report by Kajigaya et al. to have manufactured an elliptic cross sectional single crystal rod of GaAs in a horizontal magnetic field. This means present theoretical analyzes are strongly supported by their experimental report and to give theoretical explanation for their growing of a single crystal rod.As a second research subject, the convection due to magnetizing force was studied. One of them is about the convection and diffusion process of oxygen gas flowing out from top and bottom openings of a vertical pipe located1 in a bore of a super-conducting magnet as strong as 12 Tesla. The vertical pipe is 50 mm in diameter and 600 mm in length and is filled with pure oxygen gas. At time zero, top and bottom openings of the pipe are opened and natural ventilation of oxygen gas is resulted. The average molecular weight of oxygen gas is slightly larger than that of ambient air to result in quick flowing out of oxygen gas in the case of no magnetic field. As the magnetic strength was increased, the average concentration of oxygen at a mid height of the vertical pipe was found to decrease more and more gradually. At 12 Tesla, the concentration of oxygen decreased to 30 % of the initial one after 2000 seconds. Present phenomena was modeled by balance equations for mass and momentum and numerically solved. Then the resulted transient concentration of oxygen gas at a mid height agreed quite well with previous experiments to assure the model equations. Detailed graphic visualization clarified above characteristics. When bottom half of oxygen gas in the pipe flows out from a bottom opening with the top half of the pipe filled with air, then magnetizing force works to pull back the oxygen gas into the central height of the pipe and high concentration of oxygen gas was kept at the mid-height for a long time. The concentration of oxygen gas at a mid-height of the pipe decreased gradually with diffusion.There are extensive research results other than this. They are the cusp-shaped magnetic field in a Czochralski crystal growth, the rotational magnetic field, Seebeck convection and quasi non-gravitational field due to magnetizing force in a bore of a super-conducting-magnet. Less