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Turbulent thermal convection in mixed porous–pure fluid domains

Published online by Cambridge University Press:  24 April 2023

Victoria Hamtiaux  and
Miltiadis V. Papalexandris Open the ORCID record for Miltiadis V. Papalexandris [Opens in a new window]
Victoria Hamtiaux
Affiliation:
Université catholique de Louvain, Institute of Mechanics, Materials and Civil Engineering, Louvain-la-Neuve, Belgium
Miltiadis V. Papalexandris*
Affiliation:
Université catholique de Louvain, Institute of Mechanics, Materials and Civil Engineering, Louvain-la-Neuve, Belgium
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we report on a direct numerical simulation (DNS) study of turbulent thermal convection in mixed porous–pure fluid domains. The computational domain consists of a cavity that contains a porous medium placed right above the bottom wall. The solid matrix is internally heated which, in turn, induces the convective motions of the fluid. The Rayleigh number of the flow in the pure fluid region above the porous medium is of the order of $10^7$. In our study, we consider cases of different sizes of the porous medium, as well as cases with both uniform and non-uniform heat loading of the solid matrix. For each case, we analyse the convective structures in both the porous and the pure fluid domains and investigate the effect of the porous medium on the emerging flow patterns above it. Results for the flow statistics, as well as for the Nusselt number and each of its components, are also presented herein. Further, we make comparisons of the flow properties in this pure fluid region with those in Rayleigh–Bénard convection. Our simulations predict that, depending on the area coverage, the large-scale circulation above the porous medium can be in a single-roll, dual-roll or intermediate state. Also, when the area coverage increases, the temperatures inside it increase due to reduced fluid circulation. Accordingly, when the area coverage increases, then the Nusselt number becomes smaller whereas the Rayleigh number is increased.

JFM classification

Convection: Convection in cavities Turbulent Flows: Turbulent convection Convection: Convection in porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 961 , 25 April 2023 , A27
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large-scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503–537.CrossRefGoogle Scholar
Antoniadis, P.D. & Papalexandris, M.V. 2015 Dynamics of shear layers at the interface of a highly porous medium and a pure fluid. Phys. Fluids 27, 014104.CrossRefGoogle Scholar
Antoniadis, P.D. & Papalexandris, M.V. 2016 Numerical study of unsteady, thermally-stratified shear flows in superposed porous and pure-fluid domains. Intl J. Heat Mass Transfer 96, 643–659.CrossRefGoogle Scholar
Bagchi, A. & Kulacki, F.A. 2011 Natural convection in fluid–superposed porous layers heated locally from below. Intl J. Heat Mass Transfer 54, 3672–3682.CrossRefGoogle Scholar
Balay, S., et al. 2019 PETSc users manual. Tech. Rep. ANL-95/11 – Revision 3.11. Argonne National Laboratory.Google Scholar
Balay, S., Gropp, W.D., Curfman McInnes, L. & Smith, B.F. 1997 Efficient management of parallelism in object oriented numerical software libraries. In Modern Software Tools in Scientific Computing (ed. E. Arge, A.M. Bruaset & H.P. Langtangen), pp. 163–202. Argonne National Laboratory.CrossRefGoogle Scholar
Beckermann, C.H., Viskanta, R. & Ramadhyani, S. 1988 Natural convection in vertical enclosures containing simultaneously fluid and porous layers. J. Fluid Mech. 186, 257–284.CrossRefGoogle Scholar
Chen, F. & Chen, C.F. 1989 Experimental investigation of convective stability in a superposed fluid and porous layer when heated from below. J. Fluid Mech. 207, 311–321.CrossRefGoogle Scholar
Chen, F. & Chen, C.F. 1992 Convection in superposed fluid and porous layers. J. Fluid Mech. 234, 97–119.CrossRefGoogle Scholar
Cowin, S.C. 2013 Continuum Mechanics of Anisotropic Materials. Springer.CrossRefGoogle Scholar
Foroozani, N., Niemela, J.J., Armenio, V. & Sreenivasan, K.R 2014 Influence of container shape on scaling of turbulent fluctuations in convection. Phys. Rev. E 90, 063003.CrossRefGoogle ScholarPubMed
Foroozani, N., Niemala, J.J., Armenio, V. & Sreenivasan, K. 2017 Reorientations of the large-scale flow in turbulent convection in a cube. Phys. Rev. E 95, 015104.CrossRefGoogle Scholar
Goodman, M.A. & Cowin, S.C. 1972 A continuum theory for granular materials. Arch. Rat. Mech. Anal. 44, 249–266.CrossRefGoogle Scholar
Grötzbach, G. 1983 Spatial resolution requirements for direct numerical simulation of the Rayleigh–Bénard convection. J. Comput. Phys. 49, 241–264.CrossRefGoogle Scholar
Hay, W.A., Martin, J., Migot, B. & Papalexandris, M.V. 2021 Turbulent thermal convection driven by free-surface evaporation in cuboidal domains of different aspect ratios. Phys. Fluids 33, 015104.Google Scholar
Hay, W.A. & Papalexandris, M.V. 2019 Numerical simulations of turbulent thermal convection with a free-slip upper boundary. Proc. R. Soc. Lond. A 475, 20190601.Google Scholar
Hay, W.A. & Papalexandris, M.V. 2020 Evaporation-driven turbulent convection in water pools. J. Fluid Mech. 904, A14.CrossRefGoogle Scholar
Hirata, S.C., Goyeau, B., Gobin, D., Carr, M. & Cotta, R.M. 2007 Linear stability of natural convection in superposed fluid and porous layers: influence of the interfacial modelling. Intl J. Heat Mass Transfer 50, 1356–1367.CrossRefGoogle Scholar
Horn, S., Shishkina, O. & Wagner, C. 2013 On non-Oberbeck–Boussinesq effects in three-dimensional Rayleigh–Bénard convection in glycerol. J. Fluid. Mech. 724, 175–202.CrossRefGoogle Scholar
d'Hueppe, A., Chandesris, M., Jamet, D. & Goyeau, B. 2011 Boundary conditions at a fluid–porous interface for a convective heat transfer problem: analysis of the jump relations. Intl J. Heat Mass Transfer 54, 3683–3693.CrossRefGoogle Scholar
d'Hueppe, A, Chandesris, M., Jamet, D. & Goyeau, B. 2012 Coupling a two-temperature model and a one-temperature model at a fluid-porous interface. Intl J. Heat Mass Transfer 55, 2510–2523.CrossRefGoogle Scholar
Huguet, L., Alboussiere, T., Bergman, M.I., Deguen, R., Labrosse, S. & Lesœur, G. 2016 Structure of a mushy layer under hypergravity with implications for Earth's inner core. Geophys. J. Intl 204, 1729–1755.CrossRefGoogle Scholar
Incropera, F.P., DeWitt, D.P., Bergman, T.L. & Lavine, A.S. 2007 Fundamentals of Heat and Mass Transfer, 6th edn. Wiley.Google Scholar
Kathare, V., Kulacki, F.A. & Davidson, J.H. 2010 Buoyant convection in superposed metal foam and water layers. Trans. ASME J. Heat Transfer 132, 014503.CrossRefGoogle Scholar
Kawano, K., Motoki, S., Shimizu, M. & Kawahara, G. 2021 Ultimate heat transfer in ‘wall-bounded’ convective turbulence. J. Fluid Mech. 914, A13.CrossRefGoogle Scholar
Kim, S.J. & Choi, C.Y. 1996 Convective heat transfer in porous and overlying fluid layers heated from below. Intl J. Heat Mass Transfer 39, 319–329.CrossRefGoogle Scholar
Kim, S. & Kim, M.C. 2002 A scale analysis of turbulent heat transfer driven by buoyancy in a porous layer with homogeneous heat sources. Intl Commun. Heat Mass Transfer 29, 127–134.CrossRefGoogle Scholar
Koch, D.L. & Ladd, A.J.C. 1997 Moderate Reynolds number flows through periodic and random arrays of aligned cylinders. J. Fluid Mech. 349, 31–66.CrossRefGoogle Scholar
Le Reun, T. & Hewitt, D.R 2020 Internally heated porous convection: an idealized model for enceladus’ hydrothermal activity. J. Geophys. Res. 125, e2020JE006451.CrossRefGoogle Scholar
Le Reun, T. & Hewitt, D.R 2021 High-Rayleigh-number convection in porous–fluid layers. J. Fluid Mech. 920, A35.CrossRefGoogle Scholar
Lessani, B. & Papalexandris, M.V. 2006 Time-accurate calculation of variable density flows with strong temperature gradients and combustion. J. Comput. Phys. 212, 218–246.CrossRefGoogle Scholar
Lessani, B. & Papalexandris, M.V. 2008 Numerical study of turbulent channel flow with strong temperature gradients. Intl J. Numer. Meth. Heat Fluid Flow 18, 545–556.CrossRefGoogle Scholar
Lesseux, D. & Valdés-Parada, F. 2017 Symmetry properties of macroscopic transport coefficients in porous media. Phys. Fluids 29, 043303.CrossRefGoogle Scholar
Limare, A., Jaupart, C., Kaminski, E., Fourel, L. & Farnetani, C.G. 2019 Convection in an internally heated stratified heterogeneous reservoir. J. Fluid Mech. 870, 67–105.CrossRefGoogle Scholar
Lohse, D. & Xia, K. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364.CrossRefGoogle Scholar
Marichal, J. & Papalexandris, M.V. 2022 On the dynamics of the large scale circulation in turbulent convection with a free-slip upper boundary. Intl J. Heat Mass Transfer 183, 122220.CrossRefGoogle Scholar
Nield, D.A. & Bejan, A. 2017 Convection in Porous Media, 5th edn. Springer.CrossRefGoogle Scholar
Niemela, J.J., Skrbek, L., Sreenivasan, K.R. & Donnelly, R.J. 2000 Turbulent convection at very high Rayleigh numbers. Nature 404, 837–840.CrossRefGoogle ScholarPubMed
Ochoa-Tapia, J.A. & Whitaker, S. 1995 Momentum transfer at the boundary between a porous medium and a homogeneous fluid—I. Theoretical development. Intl J. Heat Mass Transfer 38, 2635–2646.CrossRefGoogle Scholar
Paolucci, S. 1982 Filtering of sound from the Navier–Stokes equations. Tech. Rep. SAND-82-8257. Sandia National Laboratories.Google Scholar
Papalexandris, M.V. & Antoniadis, P.D. 2015 A thermo-mechanical model for flows in superposed porous and fluid layers with interphasial heat and mass exchange. Intl J. Heat Mass Transfer 88, 42–54.CrossRefGoogle Scholar
Poulikakos, D. 1987 Thermal instability in a horizontal fluid layer superposed on a heat-generating porous bed. Numer. Heat Transfer 12, 83–99.CrossRefGoogle Scholar
Poulikakos, D., Bejan, A., Selimos, B. & Blake, K.R. 1986 High Rayleigh number convection in a fluid overlaying a porous bed. Intl J. Heat Fluid Flow 7, 109–116.Google Scholar
Prasad, V. 1993 Flow instabilities and heat transfer in fluid overlying horizontal porous layers. Exp. Therm. Fluid Sci. 6, 135–146.Google Scholar
Rhee, S.J., Dhir, V.K. & Catton, I. 1978 Natural convection heat transfer in beds of inductively heated particles. Trans. ASME J. Heat Transfer 100, 78–85.CrossRefGoogle Scholar
Roberts, P.H. 1967 Convection in horizontal layers with internal heat generation. Theory. J. Fluid Mech. 30, 33–49.CrossRefGoogle Scholar
Schulenberg, T. & Müller, U. 1984 Natural convection in saturated porous layers with internal heat sources. Intl J. Heat Mass Transfer 27, 677–685.Google Scholar
Shishkina, O., Stevens, R., Grossmann, S. & Lohse, D. 2010 Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution. New J. Phys. 12, 075022.Google Scholar
Siggia, E.D. 1994 High Rayleigh number convection. Annu. Rev. Fluid Mech. 26, 137–168.CrossRefGoogle Scholar
Somerton, C.W. & Catton, I. 1982 On the thermal instability of superposed porous and fluid layers. Trans. ASME J. Heat Transfer 104, 160–165.Google Scholar
Song, M. & Viskanta, R. 1994 Natural convection flow and heat transfer within a rectangular enclosure containing a vertical porous layer. Intl J. Heat Mass Transfer 37, 2425–2438.CrossRefGoogle Scholar
Straughan, B. 2013 Stability and Wave Motion in Porous Media. Springer.Google Scholar
Thirlby, R. 1970 Convection in an internally heated layer. J. Fluid Mech. 44, 673–693.Google Scholar
Vafai, K. 2015 Handbook of Porous Media. CRC.Google Scholar
Varsakelis, C. & Papalexandris, M.V. 2010 The equilibrium limit of a constitutive model for two-phase granular mixtures and its numerical approximation. J. Comput. Phys. 229, 4183–4207.CrossRefGoogle Scholar
Verzicco, R. 2003 Turbulent thermal convection in a closed domain: viscous boundary layer and mean flow effects. Eur. Phys. J. B 35, 133–141.CrossRefGoogle Scholar
Vilella, K., Limare, A., Jaupart, C., Farnetani, C.G., Fourel, L. & Kaminski, E. 2018 Fundamentals of laminar free convection in internally heated fluids at values of the Rayleigh–Roberts number up to $10^9$. J. Fluid Mech. 846, 966–998.CrossRefGoogle Scholar
Wagner, S. & Shishkina, O. 2013 Aspect-ratio dependency of Rayleigh–Bénard convection in box-shaped containers. Phys. Fluids 25, 085110.CrossRefGoogle Scholar
Wagner, W. & Kretzschmar, H.J. 2007 International Steam Tables – Properties of Water and Steam based on the Industrial Formulation IAPWS-IF97. Springer.Google Scholar
Whitaker, S. 1999 The Method of Volume Averaging. Kluwer Academic Publishers.CrossRefGoogle Scholar
Zhao, P. & Chen, C.F. 2001 Stability analysis of double-diffusive convection in superposed fluid and porous layers using a one-equation model. Intl J. Heat Mass Transfer 44 (24), 4625–4633.Google Scholar
Zikanov, O., Slinn, D.N. & Dhanak, M.R. 2002 Turbulent convection driven by surface cooling in shallow water. J. Fluid Mech. 464, 81–111.CrossRefGoogle Scholar