Oscillatory two- and three-dimensional thermocapillary convection
Oscillatory two- and three-dimensional thermocapillary convection
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DOI：
10.1017/s0022112098001232
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发表时间：
1998-06
影响因子：
3.7
通讯作者：
Jieyong Xu;A. Zebib
中科院分区：
文献类型：
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作者：
Jieyong Xu;A. Zebib
通过数值模拟研究了二维和三维热毛细管驱动对流的特性和稳定性。在Re[Les]1.3×104和Ax[Les]7.0的雷诺数(Re)-空腔长宽比(Ax)平面上，对Prandtl数(Pr)分别为10.0、6.78、4.4和1.0的流体绘制了二维Hopf分叉中性曲线。研究发现，只有当Ax超过一个临界值Axcr时，才有可能出现依赖于时间的运动，该临界值随着Pr的减小而增加。对于Pr[Ges]4.4，有两条共存的中性曲线。在不同的Re和Ax对应的定态和振荡态下，给出了流线和等温线。在临界点附近进行了振荡流动的能量分析，以确定导致不稳定的机制。给出了Ax=3.0和Pr=10的第一个不稳定区域的两个临界点附近的流动结果。在三维情况下，重点讨论了位于y=0和y=Ay的侧壁和跨向运动对转折的影响。总体而言，侧壁对振动有一定的减振作用，从而增大了第一临界雷诺数。然而，跨向波的存在会降低这一临界雷诺数。在大长宽比Ax=Ay=15时，在第一不稳定区临界雷诺数较低时，Pr=13.9的结果与无限层线性稳定性分析的结果符合得很好。
The character and stability of two- and three-dimensional thermocapillary driven convection are investigated by numerical simulations. In two dimensions, Hopf bifurcation neutral curves are delineated for fluids with Prandtl numbers (Pr) 10.0, 6.78, 4.4 and 1.0 in the Reynolds number (Re)–cavity aspect ratio (Ax) plane corresponding to Re[les ]1.3×104 and Ax[les ]7.0. It is found that time-dependent motion is only possible if Ax exceeds a critical value, Axcr, which increases with decreasing Pr. There are two coexisting neutral curves for Pr[ges ]4.4. Streamline and isotherm patterns are presented at different Re and Ax corresponding to stationary and oscillatory states. Energy analyses of oscillatory flows are performed in the neighbourhood of critical points to determine the mechanisms leading to instability. Results are provided for flows near both critical points of the first unstable region with Ax=3.0 and Pr=10. In three dimensions, attention is focused on the influence of sidewalls, located at y=0 and y=Ay, and spanwise motion on the transition. In general, sidewalls have a damping effect on oscillations and hence increase the magnitude of the first critical Re. However, the existence of spanwise waves can reduce this critical Re. At large aspect ratios Ax=Ay=15, our results with Pr=13.9 at the lower critical Reynolds number of the first unstable region are in good agreement with those from infinite layer linear stability analysis.