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From Rayleigh–Bénard convection to porous-media convection: how porosity affects heat transfer and flow structure

Published online by Cambridge University Press:  18 May 2020

Shuang Liu
Affiliation:
Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, International Joint Laboratory on Low Carbon Clean Energy Innovation, Department of Energy and Power Engineering, Tsinghua University, Beijing100084, China Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing100084, China
Linfeng Jiang
Affiliation:
Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, International Joint Laboratory on Low Carbon Clean Energy Innovation, Department of Energy and Power Engineering, Tsinghua University, Beijing100084, China
Kai Leong Chong
Affiliation:
Physics of Fluids Group and Max Planck Center Twente, University of Twente, PO Box 217, 7500AEEnschede, The Netherlands
Xiaojue Zhu
Affiliation:
Center of Mathematical Sciences and Applications, and School of Engineering and Applied Sciences, Harvard University, Cambridge, MA02138, USA
Zhen-Hua Wan
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui230027, China
Roberto Verzicco
Affiliation:
Physics of Fluids Group and Max Planck Center Twente, University of Twente, PO Box 217, 7500AEEnschede, The Netherlands Dipartimento di Ingegneria Industriale, University of Rome ‘Tor Vergata’, Via del Politecnico 1, 00133Roma, Italy Gran Sasso Science Institute, Viale F. Crispi 7, 67100L’Aquila, Italy
Richard J. A. M. Stevens
Affiliation:
Physics of Fluids Group and Max Planck Center Twente, University of Twente, PO Box 217, 7500AEEnschede, The Netherlands
Detlef Lohse
Affiliation:
Physics of Fluids Group and Max Planck Center Twente, University of Twente, PO Box 217, 7500AEEnschede, The Netherlands Max Planck Institute for Dynamics and Self-Organization, 37077Göttingen, Germany
Chao Sun*
Affiliation:
Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, International Joint Laboratory on Low Carbon Clean Energy Innovation, Department of Energy and Power Engineering, Tsinghua University, Beijing100084, China Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing100084, China
*
Email address for correspondence: chaosun@tsinghua.edu.cn

Abstract

We perform a numerical study of the heat transfer and flow structure of Rayleigh–Bénard (RB) convection in (in most cases regular) porous media, which are comprised of circular, solid obstacles located on a square lattice. This study is focused on the role of porosity $\unicode[STIX]{x1D719}$ in the flow properties during the transition process from the traditional RB convection with $\unicode[STIX]{x1D719}=1$ (so no obstacles included) to Darcy-type porous-media convection with $\unicode[STIX]{x1D719}$ approaching 0. Simulations are carried out in a cell with unity aspect ratio, for Rayleigh number $Ra$ from $10^{5}$ to $10^{10}$ and varying porosities $\unicode[STIX]{x1D719}$, at a fixed Prandtl number $Pr=4.3$, and we restrict ourselves to the two-dimensional case. For fixed $Ra$, the Nusselt number $Nu$ is found to vary non-monotonically as a function of $\unicode[STIX]{x1D719}$; namely, with decreasing $\unicode[STIX]{x1D719}$, it first increases, before it decreases for $\unicode[STIX]{x1D719}$ approaching 0. The non-monotonic behaviour of $Nu(\unicode[STIX]{x1D719})$ originates from two competing effects of the porous structure on the heat transfer. On the one hand, the flow coherence is enhanced in the porous media, which is beneficial for the heat transfer. On the other hand, the convection is slowed down by the enhanced resistance due to the porous structure, leading to heat transfer reduction. For fixed $\unicode[STIX]{x1D719}$, depending on $Ra$, two different heat transfer regimes are identified, with different effective power-law behaviours of $Nu$ versus $Ra$, namely a steep one for low $Ra$ when viscosity dominates, and the standard classical one for large $Ra$. The scaling crossover occurs when the thermal boundary layer thickness and the pore scale are comparable. The influences of the porous structure on the temperature and velocity fluctuations, convective heat flux and energy dissipation rates are analysed, further demonstrating the competing effects of the porous structure to enhance or reduce the heat transfer.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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