Bénard-Marangoni convection in a differentially heated cylindrical cavity
Bénard-Marangoni convection in a differentially heated cylindrical cavity
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DOI：
10.1063/1.1876892
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发表时间：
2005-04
影响因子：
4.6
通讯作者：
S. Hoyas;A. M. Mancho;H. Herrero;N. Garnier;A. Chiffaudel
中科院分区：
文献类型：
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作者：
S. Hoyas;A. M. Mancho;H. Herrero;N. Garnier;A. Chiffaudel
本文研究了差热圆柱腔中的Benard-Marangoni对流问题。这项研究有两个主要目的：第一，从数值的角度证明几个实验中报道的随着纵横比的变化而发生的转变；第二，从理论和实验上研究垂直和水平温差在横向加热对流中的作用。首先，我们分析了高宽比在通过底部非零温度梯度施加动态流动的层中的作用。根据不同的参数，基本解是线性的或返回的流。根据垂直温差和其他与热有关的参数，问题分成静止结构或振荡结构。在共维两个分叉点上发现了相互竞争的解：具有不同波数的静止径向辊和具有热液波的径向辊。对于小的长宽比，发现Biot数对分叉没有影响，而对于大的长宽比，Biot数对分叉有影响。在第二部分中，我们介绍了在较大的长宽比和较强的表面张力效应下所获得的实验结果。讨论了水平梯度在实验和数值模拟中确定分叉类型的作用，以及垂直温度梯度的作用，并与以前的理论工作进行了比较。在模式、分叉序列和阈值方面，理论和实验之间得到了很好的一致，其中特征函数是通过调整线性稳定性分析中的两个参数来获得的，而实验中的模式是由于增加其中一个参数而导致的非线性二次分叉序列。
The work described in this paper concerns the study of a Benard–Marangoni convection problem in a differentially heated cylindrical cavity. The study had two main aims; first to justify from a numerical point of view the transitions that have been reported in several experiments as the aspect ratio is varied and, second, to study both theoretically and experimentally the role of vertical and horizontal temperature differences in lateral heating convection. Initially, we analyzed the role of the aspect ratio in layers where a dynamic flow is imposed through a nonzero temperature gradient at the bottom. The basic solutions are linear or return flows depending on different parameters. Depending on the vertical temperature difference and other heat-related parameters, the problem bifurcates either to stationary or oscillatory structures. Competing solutions at codimension two bifurcation points were found: stationary radial rolls with different wavenumbers and radial rolls together with hydrothermal waves. For small aspect ratios it was found that the Biot number does not influence the bifurcations, whereas for large aspect ratios it does. In the second part we present experimental results obtained at larger aspect ratios and for stronger surface tension effects. The role of horizontal gradients to determine the type of bifurcation both in experiments and in numerics approaching experimental conditions are discussed along with the role of vertical temperature gradients in comparison with previous theoretical works. Good agreement was obtained in terms of patterns, bifurcation sequences, and thresholds between theory, where eigenfunctions are obtained by tuning two parameters in a linear stability analysis, and experiments, where patterns are due to a nonlinear secondary bifurcation sequence caused by increasing one of the parameters.