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本文采用直接数值模拟的并行直接求解方法,计算了Ra=1010,0.05 Pr 20的系列Prandtl(Pr)数二维湍流热对流.通过流动显示技术,讨论了Pr数对羽流形态和大尺度环流结构的影响.在Ra=1010时,随着Pr数减小,羽流的运动和分布表现出更强的湍流性质,较高Pr数的羽流则表现出较强的规律性,当Pr4.3时,流场中存在明显的大尺度环流和角涡结构.不同Pr数的温度边界层厚度差异不大,并随Pr数存在标度率变化关系.当Pr数较低时,系统的传热Nusselt(Nu)数随着Pr数增加而增加,当Pr数较高时,Nu数随Pr数的变化不敏感.靠近底板处速度脉动随Pr数有显著的变化,Pr数越低速度波动越剧烈.通过底板中心位置水平脉动速度和平均场水平速度最大值给出的雷诺数Re〈u〉和ReUmax,两种Re数随Pr数的变化满足同一标度律,为Re~ Pr-0.81.
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关键词:
- Rayleigh-Bnard热对流 /
- Prandtl数 /
- 湍流特性 /
- 温度边界层
The high-resolution numerical simulations of two-dimensional (2D) turbulent Rayleigh-Bnard convection are conducted by using the Parallel direct method of DNS (PDM-DNS) with Ra=1010 and Pr in a range from 0.05 to 20. Using the flow visualization technique, the effects of Pr on the structure of plumes and large scale circulation (LSC) are investigated. With Pr decreasing, plumes become more active and the flow turns more turbulent. When Pr4.3, pronounced LSC and corner vortex exist. The thickness of thermal boundary layer varies slightly with the value of Pr changing, which obeys a scaling law. Nusselt number (Nu) increases with Pr value increasing when Pr value is low and becomes independent when Pr value is high. Furthermore, two definitions of Reynolds number (Re) are given. The Re〈u〉 angle is calculated from the fluctuation of horizontal velocity near the center of bottom plate, and the ReUmax is calculated from maximal horizontal velocity in the mean field. Both of them follow the same scaling Re~Pr0.81.-
Keywords:
- Rayleigh-Bnard convection /
- Prandtl number /
- turbulence /
- thermal boundary layer
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[19] Bao Y, Chen J, Liu B F 2015 J. Fluid Mech. 784 R5
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[21] Xu W, Bao Y 2013 Acta Mech. Sin. 45 1(in Chinese) [徐炜, 包芸 2013 力学学报 45 1]
[22] Sun X H, Zhang W 2004 IEEE Trans. Parall. Distr. 15 97
[23] Bao Y, Luo J H, Ye M X 2017 J. Mech. (Received)
[24] Breuer M, Wessling S, Schmalzl J, Hansen U 2004 Phys. Rev.. 69 026302
[25] Verzicco R, Camussi R 1999 J. Fluid Mech. 383 55
[26] Stevens R J A M, van der Poel E P, Grossmann S, Lohse D 2013 J. Fluid Mech. 730 295
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[1] Ahlers G, Grossmann S, Lohse D 2009 Rev. Mod. Phys. 81 503
[2] Grossmann S, Lohse D 2000 J. Fluid Mech. 407 27
[3] Grossmann S, Lohse D 2001 Phys. Rev. Lett. 86 3316
[4] Shishkina O, Horn S, Wagner S, Ching E S C 2015 Phys. Rev. Lett. 114 114302
[5] Wang Y, He X Z, Tong P 2016 Phys. Rev. Fluids 1 08230
[6] Salort J, Liot O, Rusaouen E 2014 Phys. Fluids 26 015112
[7] Wei P, Chan T S, Ni R, Zhao X Z 2014 J. Fluid Mech. 740 28
[8] Xie Y C, Xia K Q 2017 J. Fluid Mech. 825 573
[9] Wagner S, Shishkina O 2015 J. Fluid Mech. 763 109
[10] Toppaladoddi S, Succi S, Wettlaufer J S 2017 Phys. Rev. Lett. 118 074503
[11] Zhu X J, Stevens R J A M, Verzicco R, Lohse D 2017 Phys. Rev. Lett. 119 154501
[12] He X Z, Funfschilling D, Nobach H, Bodenschatz E, Ahlers G 2012 Phys. Rev. Lett. 108 024502
[13] Zhou Q, Xia K Q 2010 Phys. Rev. Lett. 104 104301
[14] Stevens R J A M, Lohse D, Verzicoo R 2011 J. Fluid Mech. 688 31
[15] Huang M J, Bao Y 2016 Acta Phys. Sin. 20 204702(in Chinese) [黄茂静, 包芸 2016 物理学报 20 204702]
[16] Zhou H Y, Xu W, Bao Y 2014 J. Hydrodyn. 29 34(in Chinese) [邹鸿岳, 徐炜, 包芸 2014 水动力学研究与进展 A辑29 34]
[17] Bao Y, Ning H, Xu W 2014 Acta Phys. Sin. 63 154703(in Chinese) [包芸, 宁浩, 徐炜 2014 物理学报 63 154703]
[18] van der Poel E P, Stevens R J A M, Lohse D 2013 J. Fluid Mech. 736 177
[19] Bao Y, Chen J, Liu B F 2015 J. Fluid Mech. 784 R5
[20] Chen J, Bao Y, Yin Z X 2017 Int. J. Heat Mass Tran.. 115 556
[21] Xu W, Bao Y 2013 Acta Mech. Sin. 45 1(in Chinese) [徐炜, 包芸 2013 力学学报 45 1]
[22] Sun X H, Zhang W 2004 IEEE Trans. Parall. Distr. 15 97
[23] Bao Y, Luo J H, Ye M X 2017 J. Mech. (Received)
[24] Breuer M, Wessling S, Schmalzl J, Hansen U 2004 Phys. Rev.. 69 026302
[25] Verzicco R, Camussi R 1999 J. Fluid Mech. 383 55
[26] Stevens R J A M, van der Poel E P, Grossmann S, Lohse D 2013 J. Fluid Mech. 730 295
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