Optimal heat transport solutions for Rayleigh-Benard convection
Optimal heat transport solutions for Rayleigh-Benard convection
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DOI：
10.1017/jfm.2015.615
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发表时间：
2015-12-01
影响因子：
3.7
通讯作者：
Waleffe, Fabian
中科院分区：
文献类型：
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作者：
Sondak, David;Smith, Leslie M.;Waleffe, Fabian
对于各种普朗特数Pr和Rayleigh数Ra，得到了优化热传输的二维Rayleigh-Benard对流与无滑移水平壁的定常流动，Ra类似于10（9）。幂律缩放的Nu类似于Ra-伽马观察伽马接近0.31，其中努塞尔数Nu是一个无量纲的垂直热传输的措施。标度指数对Pr的任何依赖性被发现是非常弱的。另一方面，在相同的Ra下，具有不同水平波数的Nu的两个局部最大值的存在导致两种不同的流动结构的出现，作为优化热传输的候选者。对于Pr. 7，在较小的最大波数处实现最佳传输。在这些流体中，最佳结构是温暖上升流体的羽流，其在通道顶部附近产生左/右水平臂，导致与中央上升气流相邻的下降气流。当Pr > 7时，最佳结构为单一上升气流，无明显水平结构，最大波数较大。
Steady flows that optimize heat transport are obtained for two-dimensional Rayleigh-Benard convection with no-slip horizontal walls for a variety of Prandtl numbers Pr and Rayleigh number up to Ra similar to 10(9). Power-law scalings of Nu similar to Ra-gamma are observed with gamma approximate to 0.31, where the Nusselt number Nu is a non-dimensional measure of the vertical heat transport. Any dependence of the scaling exponent on Pr is found to be extremely weak. On the other hand, the presence of two local maxima of Nu with different horizontal wavenumbers at the same Ra leads to the emergence of two different flow structures as candidates for optimizing the heat transport. For Pr. 7, optimal transport is achieved at the smaller maximal wavenumber. In these fluids, the optimal structure is a plume of warm rising fluid, which spawns left/right horizontal arms near the top of the channel, leading to downdraughts adjacent to the central updraught. For Pr > 7 at high enough Ra, the optimal structure is a single updraught lacking significant horizontal structure, and characterized by the larger maximal wavenumber.