提出二维湍流热对流DNS模拟的并行直接求解方法(Parallel Direct Method of DNS,PDMDNS),在"天河二号"超级计算机上实现高Ra和极高Ra湍流热对流大规模DNS计算。高分辨率的湍流热对流计算结果表明不同Ra(10~8≤Ra≤10^(13))的...提出二维湍流热对流DNS模拟的并行直接求解方法(Parallel Direct Method of DNS,PDMDNS),在"天河二号"超级计算机上实现高Ra和极高Ra湍流热对流大规模DNS计算。高分辨率的湍流热对流计算结果表明不同Ra(10~8≤Ra≤10^(13))的瞬时温度场的流场特性完全不同。较低Ra流场中有明显的大尺度环流和角涡;较高Ra流场中羽流运动充满随机性;更高Ra流场出现小尺寸漩涡并不断从上下底板产生,这些涡相互影响作用,随大尺度环流一起作绕行运动。二维湍流热对流的Nu与Ra存在标度关系,标度律约为0.3。展开更多
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...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 within the thermal boundary layers. We also compare the ratio of contributions to total heat transfer in BL–bulk separation and side–mid separation.展开更多
文摘提出二维湍流热对流DNS模拟的并行直接求解方法(Parallel Direct Method of DNS,PDMDNS),在"天河二号"超级计算机上实现高Ra和极高Ra湍流热对流大规模DNS计算。高分辨率的湍流热对流计算结果表明不同Ra(10~8≤Ra≤10^(13))的瞬时温度场的流场特性完全不同。较低Ra流场中有明显的大尺度环流和角涡;较高Ra流场中羽流运动充满随机性;更高Ra流场出现小尺寸漩涡并不断从上下底板产生,这些涡相互影响作用,随大尺度环流一起作绕行运动。二维湍流热对流的Nu与Ra存在标度关系,标度律约为0.3。
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 Chinathe People’s Government of Guangdong Province(Phase Ⅱ,Grant No.nsfc2015 570)
文摘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 within the thermal boundary layers. We also compare the ratio of contributions to total heat transfer in BL–bulk separation and side–mid separation.
