Effect of Prandtl number on heat transport enhancement in Rayleigh-Benard convection under geometrical confinement
Effect of Prandtl number on heat transport enhancement in Rayleigh-Benard convection under geometrical confinement
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DOI：
10.1103/physrevfluids.3.013501
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发表时间：
2018-01-09
影响因子：
2.7
通讯作者：
Xia, Ke-Qing
中科院分区：
文献类型：
--
作者：
Chong, Kai Leong;Wagner, Sebastian;Xia, Ke-Qing
本文采用直接数值模拟的方法研究了不同普朗特数流体中的瑞利-贝纳德对流中，几何约束对热输运和流动结构的影响。我们的模拟跨越了二十年的普朗特数Pr，0.1 = 0.5，约束诱导增强Nu没有实现较小的值Pr，如0.1和0.2。Pr的热传输增强的依赖性可以被理解为在其与热羽流的覆盖面积的热边界层（BL），其中较大的覆盖率观察到较大的Pr由于较小的热扩散率。我们进一步证明了Gamma（opt）与热层线和动量层线的交叉密切相关，并发现当热层线和动量层线的厚度比超过一定值（约为1）时，Nu急剧下降。此外，通过检查的时间平均流场和二维模式分解，它被发现，对于较小的Pr的大尺度环流是强大的对流单体的几何约束。我们进一步发现，Gamma（opt）与Pr呈现幂律关系，即Gamma（opt）= 0.11 Pr-0.060 +/- 0.004。与Chong等人[Phys. Rev. Lett. 115，264503（2015）]，我们的发现提供了几何限制的更完整的画面。
We study, using direct numerical simulations, the effect of geometrical confinement on heat transport and flow structure in Rayleigh-Benard convection in fluids with different Prandtl numbers. Our simulations span over two decades of Prandtl number Pr, 0.1 = 0.5, confinement-induced enhancement in Nu is not realized for smaller values of Pr, such as 0.1 and 0.2. The Pr dependence of the heat transport enhancement can be understood in its relation to the coverage area of the thermal plumes over the thermal boundary layer (BL) where larger coverage is observed for larger Pr due to a smaller thermal diffusivity. We further show that Gamma(opt) is closely related to the crossing of thermal and momentum BLs and find thatNu declines sharply when the thickness ratio of the thermal and momentum BLs exceeds a certain value of about one. In addition, through examining the temporally averaged flow fields and two-dimensional mode decomposition, it is found that for smaller Pr the large-scale circulation is robust against the geometrical confinement of the convection cell. We further found that Gamma(opt) exhibits a power-law relation with Pr as Gamma(opt) = 0.11 Pr-0.060 +/- 0.004. Together with the result Gamma(opt) = 29.37 Ra-0.31 found by Chong et al. [Phys. Rev. Lett. 115, 264503 (2015)], our findings provide a more complete picture of the geometrical confinement.