Three-dimensional simulations of instabilities in a Marangoni-driven, low Prandtl number liquid bridge with magnetic stabilization to verify linear stability theory
Three-dimensional simulations of instabilities in a Marangoni-driven, low Prandtl number liquid bridge with magnetic stabilization to verify linear stability theory
复制标题
DOI：
10.1140/epjst/e2013-01776-4
复制
发表时间：
2013-03
期刊：
影响因子：
--
通讯作者：
K. Davis;Yue Huang;B. Houchens
中科院分区：
文献类型：
--
作者：
K. Davis;Yue Huang;B. Houchens
晶体生长中遇到的液体桥的全区模型进行了分析，通过线性稳定性分析和三维谱元模拟，忽略重力，普朗特数0.02。基态是轴对称的稳态。线性稳定性预测的流动转变和值ofReFZ，热毛细雷诺数，在不稳定性发生的字符。以前的线性稳定性研究结果表明，应用程序的稳定，轴向磁场稳定的基态。以前的三维模拟没有磁场预测的第一个过渡，同意与线性稳定性理论。然而，这些模拟也表明，在略高的ReFZ下继续时间积分会导致似乎是周期性的流动。通过与线性稳定性理论的比较发现，这种明显的周期性实际上是两个具有不同轴对称性的稳定模式之间的竞争。在三维模拟中施加轴向磁场，并验证磁场确实具有稳定流动和消除模态竞争的预期效果。方位流与线性稳定性理论预测的特征向量吻合得很好。
The Full-Zone model of a liquid bridge encountered in crystal growth is analyzed via linear stability analysis and three-dimensional spectral element simulations, neglecting gravitational forces, for Prandtl number 0.02. The base state is axisymmetric and steady state. Linear stability predicts the character of flow transitions and the value ofReFZ, the thermocapillary Reynolds number, at which instabilities occur. Previous linear stability findings show that application of a steady, axial magnetic field stabilizes the base state. Previous three-dimensional simulations with no magnetic field predict a first transition that agrees well with linear stability theory. However, these simulations also demonstrated that continued time integration at just slightly higherReFZleads to what appears to be periodic flow. Closer inspection and comparison with linear stability theory revealed that this apparent periodicity was actually competition between two steady modes with different axial symmetries. Here an axial magnetic field is applied in three-dimensional simulations and it is verified that the magnetic field does have the intended effect of stabilizing the flow and removing modal competition. The azimuthal flow shows excellent agreement with eigenvectors predicted by linear stability theory.