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Flow reversals in two-dimensional thermal convection in tilted cells

Published online by Cambridge University Press:  18 June 2018

Qi Wang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230027, China
Shu-Ning Xia
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
Bo-Fu Wang
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
De-Jun Sun
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230027, China
Quan Zhou
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
Zhen-Hua Wan*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230027, China
*
Email address for correspondence: wanzh@ustc.edu.cn

Abstract

The influence of tilt on flow reversals in two-dimensional thermal convection in rectangular cells with two typical aspect ratios, $\unicode[STIX]{x1D6E4}=\text{width/height}=1$ and 2, are investigated by means of direct numerical simulations. For $\unicode[STIX]{x1D6E4}=1$, tilt tends to suppress flow reversals. However, it is found that flow reversals characterized by two main rolls are promoted by tilt for $\unicode[STIX]{x1D6E4}=2$, which are even observed for some cases of small Prandtl numbers ($Pr$) and large tilt angles ($\unicode[STIX]{x1D6FD}$). Different from level cases where the four corner rolls all have opportunities to grow and trigger a flow reversal, the reversals in an anticlockwise tilted cell with $\unicode[STIX]{x1D6E4}=2$ are always led by the growth of the bottom-right or the top-left corner roll. Tilt is favourable for the growth of the bottom-right or the top-left corner roll and thus for breaking the balance between the two main rolls and triggering a flow reversal. The mode decomposition analysis shows that the appearance of the intermediate single-roll mode is crucial for reversals, and flow reversals in a tilted cell with $\unicode[STIX]{x1D6E4}=2$ can be viewed as a mode competition process between single-roll mode and horizontally adjacent double-roll mode. They can only occur in a limited range of $\unicode[STIX]{x1D6FD}$ where the two modes have comparable strength. Furthermore, the Nusselt numbers at the hot plate $Nu_{h}$ and at the cold plate $Nu_{c}$ behave differently during a flow reversal for $\unicode[STIX]{x1D6E4}=2$ due to the preference of single corner roll growth.

Type
JFM Papers
Copyright
© 2018 Cambridge University Press 

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