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不同普朗特数下二维湍流瑞利-贝纳德对流中的传热统计

Statistics of Heat Transfer in Two-Dimensional Turbulent Rayleigh-Bénard Convection at Various Prandtl Number.

作者信息

Yang Hui, Wei Yikun, Zhu Zuchao, Dou Huashu, Qian Yuehong

机构信息

Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China.

State-Province Joint Engineering Lab of Fluid Transmission System Technology, Hangzhou 310018, China.

出版信息

Entropy (Basel). 2018 Aug 7;20(8):582. doi: 10.3390/e20080582.

DOI:10.3390/e20080582
PMID:33265671
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7513110/
Abstract

Statistics of heat transfer in two-dimensional (2D) turbulent Rayleigh-Bénard (RB) convection for Pr=6,20,100 and 106 are investigated using the lattice Boltzmann method (LBM). Our results reveal that the large scale circulation is gradually broken up into small scale structures plumes with the increase of Pr, the large scale circulation disappears with increasing Pr, and a great deal of smaller thermal plumes vertically rise and fall from the bottom to top walls. It is further indicated that vertical motion of various plumes gradually plays main role with increasing Pr. In addition, our analysis also shows that the thermal dissipation is distributed mainly in the position of high temperature gradient, the thermal dissipation rate εθ already increasingly plays a dominant position in the thermal transport, εu can have no effect with increase of Pr. The kinematic viscosity dissipation rate and the thermal dissipation rate gradually decrease with increasing Pr. The energy spectrum significantly decreases with the increase of Pr. A scope of linear scaling arises in the second order velocity structure functions, the temperature structure function and mixed structure function(temperature-velocity). The value of linear scaling and the 2nd-order velocity decrease with increasing Pr, which is qualitatively consistent with the theoretical predictions.

摘要

利用格子玻尔兹曼方法（LBM）研究了Pr = 6、20、100和106时二维（2D）湍流瑞利 - 贝纳德（RB）对流中的传热统计。我们的结果表明，随着Pr的增加，大尺度环流逐渐分解为小尺度结构羽流，大尺度环流随着Pr的增加而消失，并且大量较小的热羽流从底壁到顶壁垂直上升和下降。进一步表明，随着Pr的增加，各种羽流的垂直运动逐渐起主要作用。此外，我们的分析还表明，热耗散主要分布在高温梯度位置，热耗散率εθ在热传输中已越来越占据主导地位，εu随着Pr的增加可能没有影响。运动粘度耗散率和热耗散率随着Pr的增加而逐渐降低。能谱随着Pr的增加而显著降低。在二阶速度结构函数、温度结构函数和混合结构函数（温度 - 速度）中出现了线性标度范围。线性标度值和二阶速度随着Pr的增加而降低，这在定性上与理论预测一致。

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