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本文采用湍流热对流的并行直接数值模拟（PDM-DNS），计算了系列Ra数的二维方腔和三维扁方腔的Rayleigh-Bénard热对流.针对平均场计算结果，选取Ra=109，1010，5×1010，讨论了二维方腔和展向平均三维扁方腔热对流流动特性.发现二维方腔和三维扁方腔流动中都存在大尺度环流和角涡，而且随着Ra数的增加，大尺度环流的形状变圆，角涡尺寸变小.在二维方腔流动中，大尺度环流呈椭圆形，有四个角涡，而展向平均三维扁方腔流动中，大尺度环流呈梭形，只有两个角涡.由于角涡特性的不同，二维方腔流动中羽流向上运动的范围比展向平均三维扁方腔流动更广，造成二维流动局部区域温度分布高温层厚度变大.温度边界层厚度λθ与Ra数之间存在标度关系，二维方腔和三维扁方腔热对流温度边界层变化的标度指数基本一致，标度关系的系数稍有不同.
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关键词:
- Rayleigh-Bé /
- nard热对流 /
- 温度边界层 /
- 湍流 /
- 并行直接数值模拟
The parallel direct method of direct numerical simulation (PDM-DNS) for Rayleigh-Bénard (RB) convection is used in this paper. The differences and similarities in flow characteristic between two-dimensional (2D) and three-dimensional (3D) turbulent RB convection are studied using mean field for Ra=109, 1010, 5×1010, and Pr=4.3. Each of 2D and 3D cases has a large-scale circulation and corner rolls. The shape of large-scale circulation becomes round and the size of corner roll turns small as Ra increases. In 2D RB convection, there are four corner vortices at the corner of the square cavity and a stable large-scale circulation which is elliptical. For spanwise averaged 3D RB convection with two corner vortices, large-scale circulation reveals spindle shape. Due to the characteristic of the corner roll, the region plume dominating is wider in 2D RB convection than in the spanwise-averaged 3D case. Further, the Ra-dependence of thermal boundary layer properties is also studied. The thermal boundary layer thickness is scaled with Ra and the scaling exponents of λθ with Ra in the 2D and 3D cases are very similar.-
Keywords:
- Rayleigh-Bé /
- nard convection /
- thermal boundary layer /
- turbulence /
- PDM-DNS
[1] Ahlers G, Grossmann S, Lohse D 2009 Rev. Mod. Phys. 81 503
[2] Malkus W V R 1954 Proc. R. Soc. Lond. A 225 196
[3] Siggia E D 1994 Annu. Rev. Fluid Mech. 26 137
[4] Grossmann S, Lohse D 2000 J. Fluid Mech. 407 27
[5] van der Poel E P, Stevens R J A M, Lohse D 2013 J. Fluid Mech. 736 177
[6] Xu W, Bao Y 2013 Acta Mech. Sin. 45 1 (in Chinese)[徐炜, 包芸2013力学学报45 1]
[7] Zhang Y Z, Bao Y 2015 Acta Phys. Sin. 64 154702 (in Chinese)[张义招, 包芸2015 64 154702]
[8] Stevens R J A M, Verzicco R, Lohse D 2010 J. Fluid Mech. 643 495
[9] Kaczorowski M, Chong K L, Xia K Q 2014 J. Fluid Mech. 747 73
[10] Zhou Q, Stevens R J A M, Sugiyama K, Grossmann S, Lohse D, Xia K Q 2010 J. Fluid Mech. 664 297
[11] Shishkina O, Thess A 2009 J. Fluid Mech. 633 449
[12] Sun C, Cheung Y H, Xia K Q 2008 J. Fluid Mech. 605 79
[13] Wang J, Xia K Q 2003 Eur. Phys. J. B 32 127
[14] Zhou Q, Xia K Q 2013 J. Fluid Mech. 721 199
[15] Burnishev Y, Segre E, Steinberg V 2010 Phys. Fluids 22 035108
[16] Stevens R J A M, Lohse D, Verzicco R 2011 J. Fluid Mech. 688 31
[17] Scheel J D, Kim E, White K R 2012 J. Fluid Mech. 711 281
[18] Lui S L, Xia K Q 1998 Phys. Rev. E 57 5494
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[1] Ahlers G, Grossmann S, Lohse D 2009 Rev. Mod. Phys. 81 503
[2] Malkus W V R 1954 Proc. R. Soc. Lond. A 225 196
[3] Siggia E D 1994 Annu. Rev. Fluid Mech. 26 137
[4] Grossmann S, Lohse D 2000 J. Fluid Mech. 407 27
[5] van der Poel E P, Stevens R J A M, Lohse D 2013 J. Fluid Mech. 736 177
[6] Xu W, Bao Y 2013 Acta Mech. Sin. 45 1 (in Chinese)[徐炜, 包芸2013力学学报45 1]
[7] Zhang Y Z, Bao Y 2015 Acta Phys. Sin. 64 154702 (in Chinese)[张义招, 包芸2015 64 154702]
[8] Stevens R J A M, Verzicco R, Lohse D 2010 J. Fluid Mech. 643 495
[9] Kaczorowski M, Chong K L, Xia K Q 2014 J. Fluid Mech. 747 73
[10] Zhou Q, Stevens R J A M, Sugiyama K, Grossmann S, Lohse D, Xia K Q 2010 J. Fluid Mech. 664 297
[11] Shishkina O, Thess A 2009 J. Fluid Mech. 633 449
[12] Sun C, Cheung Y H, Xia K Q 2008 J. Fluid Mech. 605 79
[13] Wang J, Xia K Q 2003 Eur. Phys. J. B 32 127
[14] Zhou Q, Xia K Q 2013 J. Fluid Mech. 721 199
[15] Burnishev Y, Segre E, Steinberg V 2010 Phys. Fluids 22 035108
[16] Stevens R J A M, Lohse D, Verzicco R 2011 J. Fluid Mech. 688 31
[17] Scheel J D, Kim E, White K R 2012 J. Fluid Mech. 711 281
[18] Lui S L, Xia K Q 1998 Phys. Rev. E 57 5494
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