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Acta Mechanica Sinica

, Volume 35, Issue 4, pp 713–728 | Cite as

Boundary layer structure in turbulent Rayleigh–Bénard convection in a slim box

  • Hong-Yue Zou
  • Wen-Feng Zhou
  • Xi Chen
  • Yun Bao
  • Jun ChenEmail author
  • Zhen-Su She
Research Paper
  • 81 Downloads

Abstract

Logarithmic boundary layers have been observed in different regions in turbulent Rayleigh–Bénard convection (RBC). However, how thermal plumes correlate with the logarithmic law of temperature and how the velocity profile changes with pressure gradient are not fully understood. Here, we perform three-dimensional (3D) simulations of turbulent Rayleigh–Bénard convection in a slim box without the front and back walls, with aspect ratio \(\mathrm {width}{:}\mathrm {depth}{:}\mathrm {height}=L{:}D{:}H=1{:}1/6{:}1\) (corresponding to the x, y, and z coordinates, respectively), in the Rayleigh number \({Ra} = [1\times 10^8, 1\times 10^{10}]\) for Prandtl number \({Pr}=0.7\). To investigate the structures of the viscous and thermal boundary layers, we examine the velocity profiles in the streamwise and vertical directions (i.e. U and W) along with the mean temperature profile throughout the plume-impacting, plume-ejecting, and wind-shearing regions. The velocity profile is successfully quantified by a two-layer function of a stress length,, \(\ell _u^+ = \ell _0^+(z^+)^{3/2} \left[ 1+\left( {z^+}/{z_\mathrm{sub}^+}\right) ^4\right] ^{1/4}\), as proposed by She et al. (J Fluid Mech, 2017), though it is neither  Prandtl–Blasius–Pohlhausen (PBP) type nor logarithmic. In contrast, the temperature profile in the plume-ejecting region is logarithmic for all simulated cases, attributed to the emission of thermal plumes. The coefficient of the temperature log law, A, can be described by the composition of the thermal stress length \(\ell ^*_{\theta 0}\) and the thicknesses of thermal boundary layer \(z^*_\mathrm{sub}\) and \(z^*_\mathrm{buf}\), i.e. \(A \simeq z^*_\mathrm{sub}/\left( \ell ^*_{\theta 0}{z^*_\mathrm{buf}}^{3/2}\right) \). The adverse pressure gradient responsible for turning the wind direction contributes to intensively emitting plumes and the logarithmic temperature profile at the plume-ejecting region. The Nusselt number scaling and the local heat flux in the slim box are consistent with previous results for confined cells. Therefore, the slim-box RBC is a preferred system for investigating in-box kinetic and thermal structures of turbulent convection with the large-scale circulation in a fixed plane.

Keywords

Rayleigh–Bénard convection Wall-bounded turbulence Heat transport Direct numerical simulation 

Notes

Acknowledgements

The Project was supported by the National Natural Science Foundation of China (Grants 11452002, 11521091, and 11372362) and MOST (China) 973 Project (Grant 2009CB724100).

Supplementary material

10409_2019_874_MOESM1_ESM.rar (115 kb)
Supplementary material 1 (rar 114 KB)

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Hong-Yue Zou
    • 1
  • Wen-Feng Zhou
    • 1
  • Xi Chen
    • 1
  • Yun Bao
    • 2
  • Jun Chen
    • 1
    Email author
  • Zhen-Su She
    • 1
  1. 1.State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of EngineeringPeking UniversityBeijingChina
  2. 2.Department of Mechanics, College of EngineeringSun Yat-sen UniversityGuangzhouChina

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