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Effects of pore scale and conjugate heat transfer on thermal convection in porous media

Published online by Cambridge University Press:  29 June 2022

David Korba Open the ORCID record for David Korba [Opens in a new window]  and
Like Li Open the ORCID record for Like Li [Opens in a new window]
David Korba
Affiliation:
Department of Mechanical Engineering, Mississippi State University, Mississippi State, MS 39762, USA Center for Advanced Vehicular Systems, Mississippi State University, Mississippi State, MS 39762, USA
Like Li*
Affiliation:
Department of Mechanical Engineering, Mississippi State University, Mississippi State, MS 39762, USA Center for Advanced Vehicular Systems, Mississippi State University, Mississippi State, MS 39762, USA
*
†Email address for correspondence: [email protected]
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Abstract

The study of thermal convection in porous media is of both fundamental and practical interest. Typically, numerical studies have relied on the volume-averaged Darcy–Oberbeck–Boussinesq (DOB) equations, where convection dynamics are assumed to be controlled solely by the Rayleigh number (Ra). Nusselt numbers (Nu) from these models predict Nu–Ra scaling exponents of 0.9–0.95. However, experiments and direct numerical simulations (DNS) have suggested scaling exponents as low as 0.319. Recent findings for solutal convection between DNS and DOB models have demonstrated that the ‘pore-scale parameters’ not captured by the DOB equations greatly influence convection. Thermal convection also has the additional complication of different thermal transport properties (e.g. solid-to-fluid thermal conductivity ratio ks/kf and heat capacity ratio σ) in different phases. Thus, in this work we compare results for thermal convection from the DNS and DOB equations. On the effects of pore size, DNS results show that Nu increases as pore size decreases. Mega-plumes are also found to be more frequent and smaller for reduced pore sizes. On the effects of conjugate heat transfer, two groups of cases (Group 1 with varying ks/kf at σ = 1 and Group 2 with varying σ at ks/kf = 1) are examined to compare the Nu–Ra relations at different porosity (ϕ) and ks/kf and σ values. Furthermore, we report that the boundary layer thickness is determined by the pore size in DNS results, while by both the Rayleigh number and the effective heat capacity ratio, $\bar{\phi } = \phi + (1 - \phi )\sigma$, in the DOB model.

JFM classification

Convection: Convection in porous media Convection: Plumes/thermals Convection: Buoyant boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 944 , 10 August 2022 , A28
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Korba and Li supplementary movie 1

Temperature evolution for DOB simulation at $Ra = 5000$, $k_s/k_f = 1$ and $\sigma = 1$

Download Korba and Li supplementary movie 1(Video)
Video 7.9 MB

Korba and Li supplementary movie 2

Temperature evolution for DOB simulation at $Ra = 10 \: 000$, $k_s/k_f = 1$ and $\sigma = 1$

Download Korba and Li supplementary movie 2(Video)
Video 8.6 MB

Korba and Li supplementary movie 3

Temperature evolution for DOB simulation at $Ra = 20 \: 000$, $k_s/k_f = 1$ and $\sigma = 1$

Download Korba and Li supplementary movie 3(Video)
Video 9.4 MB

Korba and Li supplementary movie 4

Temperature evolution for DNS at $Ra = 5000$, $k_s/k_f = 1$, $\sigma = 1$, $H/m = 25$ and $\phi = 0.56$

Download Korba and Li supplementary movie 4(Video)
Video 8.9 MB

Korba and Li supplementary movie 5

Temperature evolution for DNS at $Ra = 10 \: 000$, $k_s/k_f = 1$, $\sigma = 1$, $H/m = 25$ and $\phi = 0.56$

Download Korba and Li supplementary movie 5(Video)
Video 10 MB

Korba and Li supplementary movie 6

Temperature evolution for DNS at $Ra = 20 \: 000$, $k_s/k_f = 1$, $\sigma = 1$, $H/m = 25$ and $\phi = 0.56$

Download Korba and Li supplementary movie 6(Video)
Video 9.2 MB