Time-dependent thermocapillary convection in a rectangular cavity: numerical results for a moderate Prandtl number fluid
Time-dependent thermocapillary convection in a rectangular cavity: numerical results for a moderate Prandtl number fluid
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DOI：
10.1017/s0022112093003106
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发表时间：
1993-12
影响因子：
3.7
通讯作者：
L. Peltier;S. Biringen
中科院分区：
文献类型：
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作者：
L. Peltier;S. Biringen
针对普朗特数为6.78的流体，数值模拟探讨了矩形浅腔内振荡热毛细对流的热对流机理。为此开发的计算机程序在拉伸的交错网格上以时间精确的方法整合了二维含时的N-S方程和能量方程。假定是平坦的自由面。结果表明，这种不稳定性依赖于流场内大尺度热结构与温度敏感自由面之间的时间耦合。这项研究的一个主要结果是绘制了一个稳定性图，该图显示了在2.3到3.8的范围内，区分定常和随时间变化的流动状态的临界Marangoni数作为展弦比的函数。在此范围内，预测了最小临界展宽比接近2.3，最小临界Marangoni数接近20000，在此范围内存在稳定的对流。
The present numerical simulation explores a thermal–convective mechanism for oscillatory thermocapillary convection in a shallow rectangular cavity for a Prandtl number 6.78 fluid. The computer program developed for this simulation integrates the two-dimensional, time-dependent Navier–Stokes equations and the energy equation by a time-accurate method on a stretched, staggered mesh. Flat free surfaces are assumed. The instability is shown to depend upon temporal coupling between large-scale thermal structures within the flow field and the temperature sensitive free surface. A primary result of this study is the development of a stability diagram presenting the critical Marangoni number separating the steady from the time-dependent flow states as a function of aspect ratio for the range of values between 2.3 and 3.8. Within this range, a minimum critical aspect ratio near 2.3 and a minimum critical Marangoni number near 20 000 are predicted, below which steady convection is found.