Natural convection in a long vertical cylinder under gravity modulation
Natural convection in a long vertical cylinder under gravity modulation
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DOI：
10.1017/s0022112088002198
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发表时间：
1988-08
影响因子：
3.7
通讯作者：
M. Wadih;B. Roux
中科院分区：
文献类型：
--
作者：
M. Wadih;B. Roux
本研究系针对重力调变条件下，差热圆柱体之对流起始。它特别涉及无限长的垂直圆柱体的情况下，当负的温度梯度保持在向上的方向。分析了调制对标准定常情况下线性理论给出的稳定极限的影响。本文提出了一种基于Floquet理论的方法，在调制幅度ε较小的情况下，当频率ω为固定值时，该方法可以有效地抑制调制信号的畸变。一个通用的技术，称为矩阵方法，它可以很容易地适应各种几何形状和边界条件，已经开发。在某些情况下，已经推导出了分析方法。最后，在非常一般的边界条件和周期约束下，对有限ε，给出了大ω的渐近分析。本文建立了当ε [Lt ] ω为大ω值时，周期重力调制下对流开始的渐近关系式，讨论了该不等式的数学和物理基础。
This study is devoted to the onset of convection in differentially heated cylinders under gravity modulation. It specifically concerns the case of a vertical cylinder of infinite length, when a negative temperature gradient is maintained in the upward direction. The effect of modulation on the stability limits given by linear theory in the standard steady case is analysed. A method based on Floquet theory is proposed in the case of small values of the modulation amplitude ε, for a fixed value of the frequency ω. A general technique, called matrix method, which can easily be adapted to various kinds of geometries and boundary conditions, has been developed. Analytical approaches have been derived in some cases. Finally, an asymptotic analysis is presented for large ω, under very general boundary conditions and periodic constraints, for finite ε. An asymptotic relation is established for the onset of convection under periodic gravity modulation for large ω values, when ε [Lt ] ω; the mathematical and physical foundations of this inequality are discussed.