Rotating magnetic field effect on convection and its stability in a horizontal cylinder subjected to a longitudinal temperature gradient
Rotating magnetic field effect on convection and its stability in a horizontal cylinder subjected to a longitudinal temperature gradient
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纵向温度梯度作用下水平圆柱体内旋转磁场对对流的影响及其稳定性
DOI：
10.1017/s0022112010003678
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发表时间：
2010
影响因子：
3.7
通讯作者：
D. Henry
中科院分区：
文献类型：
--
作者：
D. Lyubimov;A. V. Burnysheva;H. Hadid;T. Lyubimova;D. Henry
为了提高晶体质量，在凝固过程中使用旋转磁场（RMF）进行晶体生长。本文研究了受纵向温度梯度影响的水平无限圆柱通道对熔融金属对流流动及其稳定性的影响。对于非零普朗特数Pr的横截面上有四个涡旋的定常对流，用RMF（由磁泰勒数Tam参数化）进行了修正。当普朗特数为零时，截面内的流动对应圆形流线，纵向流动结构沿磁场旋转方向移动，其强度减小，变化量渐近为1/Tam。对于非零普朗特数，根据一侧的Tam和另一侧的普朗特数和Grashof数的不同值，可以得到不同的结构，从纵向速度和温度场旋转输运的圆形流线，到更常见的对四个截面涡的RMF几乎不敏感的逆流结构。对于非零Pr，流动强度随Tam增加而降低的趋势也被延迟，但最终达到了相同的渐近极限。Tam = 0时对流的稳定性分析表明，在Pr = Prt，0≈3 × 10−4附近阈值急剧增加，对应于通常的逆流剪切模式和新的侧壁剪切模式之间的转变。这种转换仍然存在于RMF中，但是随着Tam的增加，它会发生在较小的Pr值中。当Pr < Prt，0时，旋转磁场具有较强的稳定效应，特别是当Pr = 0时，阈值随Tam呈指数增长。相比之下，对于Pr > Prt,0（即在侧壁不稳定占主导地位的域中），RMF的稳定作用较弱。
A rotating magnetic field (RMF) is used in crystal growth applications during the solidification process in order to improve the crystal quality. Its influence on the convective flows in molten metals and on their stability is studied here in the case of a horizontal infinite cylindrical channel subjected to a longitudinal temperature gradient. The steady convective flows, which correspond to the usual longitudinal counterflow structure, with four vortices in the cross-section for non-zero Prandtl number, Pr, are modified by the RMF (parametrized by the magnetic Taylor number Tam). For zero Prandtl number, the flow in the cross-section corresponds to circular streamlines and the longitudinal flow structure is moved in the direction of the magnetic field rotation, with a decrease in its intensity and an asymptotic variation as 1/Tam. For non-zero Prandtl numbers, depending on the respective values of Tam on one side and Prandtl and Grashof numbers on the other side, different structures ranging from the circular streamlines with transport by rotation of the longitudinal velocity and the temperature field, to the more usual counterflow structure almost insensitive to the RMF with four cross-section vortices, can be obtained. The decrease in the flow intensity with increasing Tam is also delayed for non-zero Pr, but the same asymptotic limit is eventually reached. The stability analysis of these convective flows for Tam = 0 shows a steep increase of the thresholds around Pr = Prt,0 ≈ 3 × 10−4, corresponding to the transition between the usual counterflow shear mode and a new sidewall shear mode. This transition is still present with an RMF, but it occurs for smaller Pr values as Tam is increased. Strong stabilizing effects of the rotating magnetic field are found for Pr < Prt,0, particularly for Pr = 0 where an exponential increase of the threshold with Tam is found. For Pr > Prt,0 (i.e. in the domain where the sidewall instability is dominant), in contrast, the stabilization by the RMF is weak.