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The effect of cell tilting on turbulent thermal convection in a rectangular cell

Published online by Cambridge University Press:  02 December 2014

Shuang-Xi Guo ,
Sheng-Qi Zhou ,
Xian-Rong Cen ,
Ling Qu ,
Yuan-Zheng Lu ,
Liang Sun  and
Xiao-Dong Shang
Shuang-Xi Guo
Affiliation:
State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 510301, PR China
Sheng-Qi Zhou*
Affiliation:
State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 510301, PR China
Xian-Rong Cen
Affiliation:
State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 510301, PR China
Ling Qu
Affiliation:
State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 510301, PR China
Yuan-Zheng Lu
Affiliation:
State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 510301, PR China University of Chinese Academy of Sciences, Beijing 100049, PR China
Liang Sun
Affiliation:
School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230022, PR China
Xiao-Dong Shang
Affiliation:
State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 510301, PR China
*
†Email address for correspondence: [email protected]
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Abstract

In this study the influence of cell tilting on flow dynamics and heat transport is explored experimentally within a rectangular cell (aspect ratios ${\it\Gamma}_{x}=1$ and ${\it\Gamma}_{y}=0.25$). The measurements are carried out over a wide range of tilt angles ($0\leqslant {\it\beta}\leqslant {\rm\pi}/2\ \text{rad}$) at a constant Prandtl number ($\mathit{Pr}\simeq 6.3$) and Rayleigh number ($\mathit{Ra}\simeq 4.42\times 10^{9}$). The velocity measurements reveal that the large-scale circulation (LSC) is sensitive to the symmetry of the system. In the level case, the high-velocity band of the LSC concentrates at about a quarter of the cell width from the boundary. As the cell is slightly tilted (${\it\beta}\simeq 0.04\ \text{rad}$), the position of the high-velocity band quickly moves towards the boundary. With increasing ${\it\beta}$, the LSC changes gradually from oblique ellipse-like to square-like, and other more complicated patterns. Oscillations have been found in the temperature and velocity fields for almost all ${\it\beta}$, and are strongest at around ${\it\beta}\simeq 0.48\ \text{rad}$. As ${\it\beta}$ increases, the Reynolds number ($\mathit{Re}$) initially also increases, until it reaches its maximum at the transition angle ${\it\beta}=0.15\ \text{rad}$, after which it gradually decreases. The cell tilting causes a pronounced reduction of the Nusselt number ($\mathit{Nu}$). As ${\it\beta}$ increases from 0 to 0.15, 1.05 and ${\rm\pi}/2\ \text{rad}$, the reduction of $\mathit{Nu}$ is approximately 1.4 %, 5 % and 18 %, respectively. Over the ranges of $0\leqslant {\it\beta}\leqslant 0.15\ \text{rad}$, $0.15\leqslant {\it\beta}\leqslant 1.05\ \text{rad}$ and $1.05\leqslant {\it\beta}\leqslant {\rm\pi}/2\ \text{rad}$, the decay slopes are $8.57\times 10^{-2}$, $3.27\times 10^{-2}$ and $0.24\ \text{rad}^{-1}$, respectively.

JFM classification

Turbulent Flows: Turbulent convection
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Papers
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Journal of Fluid Mechanics , Volume 762 , 10 January 2015 , pp. 273 - 287
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© 2014 Cambridge University Press 

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