Numerical study of heat-transfer in two-and quasi-two-dimensional Rayleigh–Bénard convection  

作　　者：Zhen-Yuan Gao Jia-Hui Luo Yun Bao 高振源;罗嘉辉;包芸(Department of Mechanics,Sun Yat-Sen University)

机构地区：Department of Mechanics,Sun Yat-Sen University,Guangzhou 510275,China

出　　处：《Chinese Physics B》2018年第10期405-412,共8页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.11772362 and 11452002);the Special Scientific Research Fund for Super Computing in the Joint Fund of the National Natural Science Foundation of China;the People’s Government of Guangdong Province(Phase Ⅱ,Grant No.nsfc2015 570)

摘　　要：A detailed comparative numerical study between the two-dimensional（2 D） and quasi-two-dimensional（quasi-2 D）turbulent Rayleigh–B＇enard（RB） convection on flow state, heat transfer, and thermal dissipation rate（TDR） is made. The Rayleigh number（Ra） in our simulations ranges up to 5×10^10 and Prandtl number（Pr） is fixed to be 0.7. Our simulations are conducted on the Tianhe-2 supercomputer. We use an in-house code with high parallelization efficiency, based on the extended PDM–DNS scheme. The comparison shows that after a certain Ra, plumes with round shape, which is called the ＂temperature islands＂, develop and gradually dominate the flow field in the 2 D case. On the other hand, in quasi-2 D cases, plumes remain mushroom-like. This difference in morphology becomes more significant as Ra increases, as with the motion of plumes near the top and bottom plates. The exponents of the power-law relation between the Nusselt number（Nu） and Ra are 0.3 for both two cases, and the fitting pre-factors are 0.099 and 0.133 for 2 D and quasi-2 D respectively,indicating a clear difference in magnitude of the heat transfer rate between two cases. To understand this difference in the magnitude of Nu, we compare the vertical profile of the horizontally averaged TDR for both two cases. It is found that the profiles of both cases are nearly the same in the bulk, but they vary near boundaries. Comparing the bifurcation height zb with the thermal boundary layer thickness dq, it shows that zb 〈 δθ（3 D） 〈 δθ（2 D） and all three heights obey a universal power-law relation z ~Ra^-0.30. In order to quantify the difference further, we separate the domain by zb, i.e., define the area between two zb（near top and bottom plates respectively） as the ＂mid region＂ and the rest as the ＂side region＂, and integrate TDR in corresponding regions. By comparing the integral it is found that most of the difference in TDR between two cases, which is connected to the heat transfer rate, occurs wA detailed comparative numerical study between the two-dimensional（2 D） and quasi-two-dimensional（quasi-2 D）turbulent Rayleigh–B＇enard（RB） convection on flow state, heat transfer, and thermal dissipation rate（TDR） is made. The Rayleigh number（Ra） in our simulations ranges up to 5×10^10 and Prandtl number（Pr） is fixed to be 0.7. Our simulations are conducted on the Tianhe-2 supercomputer. We use an in-house code with high parallelization efficiency, based on the extended PDM–DNS scheme. The comparison shows that after a certain Ra, plumes with round shape, which is called the ＂temperature islands＂, develop and gradually dominate the flow field in the 2 D case. On the other hand, in quasi-2 D cases, plumes remain mushroom-like. This difference in morphology becomes more significant as Ra increases, as with the motion of plumes near the top and bottom plates. The exponents of the power-law relation between the Nusselt number（Nu） and Ra are 0.3 for both two cases, and the fitting pre-factors are 0.099 and 0.133 for 2 D and quasi-2 D respectively,indicating a clear difference in magnitude of the heat transfer rate between two cases. To understand this difference in the magnitude of Nu, we compare the vertical profile of the horizontally averaged TDR for both two cases. It is found that the profiles of both cases are nearly the same in the bulk, but they vary near boundaries. Comparing the bifurcation height zb with the thermal boundary layer thickness dq, it shows that zb 〈 δθ（3 D） 〈 δθ（2 D） and all three heights obey a universal power-law relation z ~Ra^-0.30. In order to quantify the difference further, we separate the domain by zb, i.e., define the area between two zb（near top and bottom plates respectively） as the ＂mid region＂ and the rest as the ＂side region＂, and integrate TDR in corresponding regions. By comparing the integral it is found that most of the difference in TDR between two cases, which is connected to the heat transfer rate, occurs w

关 键 词：Rayleigh-Benard convection Nusselt number TURBULENCE thermal dissipation 

分 类 号：O357.5[理学—流体力学]