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

  • Shuang-Xi Guo (a1), Sheng-Qi Zhou (a1), Xian-Rong Cen (a1), Ling Qu (a1), Yuan-Zheng Lu (a1) (a2), Liang Sun (a3) and Xiao-Dong Shang (a1)...

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.

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Corresponding author

Email address for correspondence: sqzhou@scsio.ac.cn

References

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