Numerical study of the unstable thermocapillary flow in a silicon float zone under μ–g condition
Numerical study of the unstable thermocapillary flow in a silicon float zone under μ–g condition
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DOI：
10.1016/s1290-0729(01)01259-5
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发表时间：
2001-09
影响因子：
4.5
通讯作者：
H. Bazzi;C. T. Nguyen;N. Galanis
中科院分区：
文献类型：
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作者：
H. Bazzi;C. T. Nguyen;N. Galanis
本文研究了在μ g条件下由一对同轴圆盘支撑的硅（Pr=0.016）浮子区内热毛细流动的流体动力学不稳定性问题。采用时间全隐式有限控制体积法和圆柱坐标系交错空间网格法直接求解三维瞬态模型的守恒方程组。结果表明，当马兰戈尼数较低或盘间温差较低时，流动保持稳定，并由一个完美的轴对称环面结构组成，漩涡中心位于靠近冷盘的自由表面下方。超过第一个临界马兰戈尼数，比如Macr1≈48，从轴对称到稳定的三维状态的转变已经被观察到。流动结构由一个剧烈扭曲的环面组成，其涡中心沿径向和轴向位移，并沿“鞍状”曲线分布。在第二个临界马兰戈尼数，比如Macr2≈80，发生从三维稳态到三维振荡态的转变。在一些方位不稳定性的作用下，整个速度场和温度场绕主轴旋转；因变量在时间和空间上周期性地变化。流动不稳定性与理论上的“不稳定旋涡环”相似，被认为是流体动力学的起源。详细描述了内部流动结构及其动力特性，并与以往的数值和实验数据进行了比较。
In this work, the problem of the hydrodynamic instabilities of the thermocapillary flow inside a Silicon (Pr=0.016) float zone supported by a pair of coaxial disks and operating under μ–g conditions has been investigated. The system of the conservation equations corresponding to a three-dimensional transient model was directly solved by employing a finite control volumes method fully-implicit in time and a staggered spatial mesh in the cylindrical coordinates system. Results have shown that for a low Marangoni number or a low temperature difference between the disks, the flow remains steady and consists of a perfectly axisymmetrical toroidal structure with the vortex center located beneath the free surface near the cold disk. Beyond the first critical Marangoni number, say Macr1≈48, the transition from the axisymmetrical to the steady three-dimensional state has been observed. The flow structure consists of a drastically distorted torus with its vortex centers displaced both radially and axially and is located along a ‘saddle-like’ curve. At the second critical Marangoni number, say Macr2≈80, the transition from this three-dimensional-steady-state to the three-dimensional-oscillatory state occurs. Under the effects of some azimuthally travelling instabilities, the entire velocity and temperature fields rotate around the main axis; and a dependent variable varies periodically both in time and space. The flow instabilities, which appear similar to those of the theoretical ‘unstable vortex ring’, are believed to be of the hydrodynamic origin. A detailed description of the internal flow structure and its dynamic behavior as well as a comparison with the previous numerical and experimental data have been given.