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Asymptotic behaviour of heat transfer in two-dimensional turbulent convection with high-porosity fluid-saturated media

Published online by Cambridge University Press:  30 July 2021

Wei Qiang Open the ORCID record for Wei Qiang [Opens in a new window] ,
Mingli Xie ,
Zhikang Liu ,
Yong Wang ,
Hui Cao  and
Hanwen Zhou
Wei Qiang*
Affiliation:
School of Computer Science, China University of Geosciences, Wuhan 430078, PR China
Mingli Xie
Affiliation:
School of Computer Science, China University of Geosciences, Wuhan 430078, PR China
Zhikang Liu
Affiliation:
School of Computer Science, China University of Geosciences, Wuhan 430078, PR China
Yong Wang
Affiliation:
School of Computer Science, China University of Geosciences, Wuhan 430078, PR China
Hui Cao
Affiliation:
School of Automation, China University of Geosciences, Wuhan 430074, PR China
Hanwen Zhou
Affiliation:
School of Earth Science, China University of Geosciences, Wuhan 430074, PR China
*
†Email address for correspondence: qw@cug.edu.cn
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Abstract

We study the asymptotic behaviour of convective heat transfer for turbulent flows in high-porosity fluid-saturated media by two-dimensional high-resolution numerical simulation. The generalized Navier–Stokes equations for incompressible fluid flow and the heat transport equation in porous media at the representative element volume scale are solved by the lattice Boltzmann method, wherein the non-Darcian effects are taken into consideration. The asymptotic behaviour of the Nusselt number $N$ has been revealed for Rayleigh numbers $10^4\leq R\leq 10^{11}$ and Darcy numbers $10^{-6}\leq \xi \leq 10^6$: all the data for various Darcy numbers gradually collapse onto a unique line with increasing Rayleigh number. The asymptote can be well represented by $N=0.146\times R^{0.286}$ for $R>2\times 10^7$, which approaches the relationship for the Rayleigh–Bénard turbulent convection of free fluid flows. The transition can be characterized by a scaling analysis with $R^{}\xi ^{3/2}\sim 1$, below which, however, the data collapse onto the Darcy limit for porous media. The Reynolds number and the Nusselt number both increase with Darcy number above the onset of convection, whereas a premature saturation of the Nusselt number is observed in comparison with that of the Reynolds number. The counter-gradient heat transport by the large-scale flows is quantified, which compensates for the increase of the gradient heat transport with Darcy number. The heat transfer in high-porosity fluid-saturated media with a very small Darcy number $\xi \geq 10^{-6}$ can be comparable to that of free fluid flows for a sufficiently high Rayleigh number $R\geq 10^{11}$.

JFM classification

Convection: Convection in porous media Turbulent Flows: Turbulent convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , A30
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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