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How surface roughness reduces heat transport for small roughness heights in turbulent Rayleigh–Bénard convection

Published online by Cambridge University Press:  11 December 2017

Yi-Zhao Zhang ,
Chao Sun ,
Yun Bao  and
Quan Zhou Open the ORCID record for Quan Zhou [Opens in a new window]
Yi-Zhao Zhang
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
Chao Sun
Affiliation:
Center for Combustion Energy and Department of Thermal Engineering, Tsinghua University, 100084 Beijing, China
Yun Bao
Affiliation:
Department of Mechanics, Sun Yat-Sen University, Guangzhou 510275, China
Quan Zhou*
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
*
†Email address for correspondence: [email protected]
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Abstract

Rough surfaces have been widely used as an efficient way to enhance the heat-transfer efficiency in turbulent thermal convection. In this paper, however, we show that roughness does not always mean a heat-transfer enhancement, but in some cases it can also reduce the overall heat transport through the system. To reveal this, we carry out numerical investigations of turbulent Rayleigh–Bénard convection over rough conducting plates. Our study includes two-dimensional (2D) simulations over the Rayleigh number range $10^{7}\leqslant Ra\leqslant 10^{11}$ and three-dimensional (3D) simulations at $Ra=10^{8}$. The Prandtl number is fixed to $Pr=0.7$ for both the 2D and the 3D cases. At a fixed Rayleigh number $Ra$, reduction of the Nusselt number $Nu$ is observed for small roughness height $h$, whereas heat-transport enhancement occurs for large $h$. The crossover between the two regimes yields a critical roughness height $h_{c}$, which is found to decrease with increasing $Ra$ as $h_{c}\sim Ra^{-0.6}$. Through dimensional analysis, we provide a physical explanation for this dependence. The physical reason for the $Nu$ reduction is that the hot/cold fluid is trapped and accumulated inside the cavity regions between the rough elements, leading to a much thicker thermal boundary layer and thus impeding the overall heat flux through the system.

JFM classification

Convection: Convection Turbulent Flows: Turbulent convection Turbulent Flows: Turbulent Flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 836 , 10 February 2018 , R2
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Copyright
© 2017 Cambridge University Press 

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Zhang et al. supplementary movie

The movie about the instantaneous temperature (color) and velocity (arrows) fields near the center of the bottom plate. The data are obtained in the smooth cell (upper left) and in the rough cells with triangular roughness elements (black lines) of height h/h_c = 0.28 (upper right), 0.71 (lower left), and 1.42 (lower right).

Download Zhang et al. supplementary movie(Video)
Video 13.5 MB