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Opposing-buoyancy mixed convection through and around arrays of heated cylinders

Published online by Cambridge University Press:  23 September 2022

Tingting Tang ,
Zhiyong Li ,
Shimin Yu ,
Jianhui Li Open the ORCID record for Jianhui Li [Opens in a new window]  and
Peng Yu Open the ORCID record for Peng Yu [Opens in a new window]
Tingting Tang
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Center for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen 518055, PR China
Zhiyong Li
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Dongguan University of Technology, Dongguan 523808, PR China
Shimin Yu
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Harbin Institute of Technology, Harbin 150001, PR China
Jianhui Li
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
Peng Yu*
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Center for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen 518055, PR China
*
†Email address for correspondence: yup6@sustech.edu.cn
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Abstract

We numerically investigated the opposing-buoyancy mixed convection through and around square arrays of $10\times 10$ heated circular cylinders with the solid fraction ($\phi$) ranging from 0.0079 to 0.66 and the Richardson number ($Ri$) varying from 0 to 1 at a fixed Reynolds number ($Re$) of 100. Our simulations revealed that the large mean recirculation in the far wake can be detached from or connected with the vortex pair in the near wake for different combinations of $Ri$ and $\phi$. Also, it was found that the array with relatively small $\phi$ can significantly promote flow instability even at moderate $Ri$. The instability, which is closely related to the fluctuating heat flux, develops from the lateral sides to the downstream side of the array and gives rise to the large mean recirculation in the far wake. The power spectra density of the array-scale force coefficients demonstrates that the flow undergoes different bifurcation behaviours under various parameter combinations, which reflects the interaction between the near-wake and far-wake vortexes. Interestingly, the Strouhal–Richardson number curves can be collapsed onto the same curve when $Ri$ is increased by a $\phi$-dependent factor. Also, for $\phi \leqslant 0.22$, both the mean drag coefficient and the mean Nusselt number of the array were found to decrease linearly with $Ri$ since the buoyancy within the array becomes prominent in this range of $\phi$.

JFM classification

Convection: Convection in porous media Convection: Buoyancy-driven instability

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 949 , 25 October 2022 , A8
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© The Author(s), 2022. Published by Cambridge University Press

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