skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Inclined porous medium convection at large Rayleigh number

Abstract

High-Rayleigh-number ($Ra$$) convection in an inclined two-dimensional porous layer is investigated using direct numerical simulations (DNS) and stability and variational upper-bound analyses. When the inclination angle$$\unicode[STIX]{x1D719}$$of the layer satisfies$$0^{\circ }<\unicode[STIX]{x1D719}\lesssim 25^{\circ }$$, DNS confirm that the flow exhibits a three-region wall-normal asymptotic structure in accord with the strictly horizontal ($$\unicode[STIX]{x1D719}=0^{\circ }$$) case, except that as$$\unicode[STIX]{x1D719}$$is increased the time-mean spacing between neighbouring interior plumes also increases substantially. Both DNS and upper-bound analysis indicate that the heat transport enhancement factor (i.e. the Nusselt number)$$Nu\sim CRa$$with a$$\unicode[STIX]{x1D719}$$-dependent prefactor$$C$$. When$$\unicode[STIX]{x1D719}>\unicode[STIX]{x1D719}_{t}$$, however, where$$30^{\circ }<\unicode[STIX]{x1D719}_{t}<32^{\circ }$$independently of$$Ra$$, the columnar flow structure is completely broken down: the flow transitions to a large-scale travelling-wave convective roll state, and the heat transport is significantly reduced. To better understand the physics of inclined porous medium convection at large$$Ra$$and modest inclination angles, a spatial Floquet analysis is performed, yielding predictions of the linear stability of numerically computed, fully nonlinear steady convective states. The results show that there exist two types of instability when$$\unicode[STIX]{x1D719}\neq 0^{\circ }$$: a bulk-mode instability and a wall-mode instability, consistent with previous findings for$$\unicode[STIX]{x1D719}=0^{\circ }$(Wenet al., J. Fluid Mech., vol. 772, 2015, pp. 197–224). The background flow induced by the inclination of the layer intensifies the bulk-mode instability during its subsequent nonlinear evolution, thereby favouring increased spacing between the interior plumes relative to that observed in convection in a horizontal porous layer.

Authors:
ORCiD logo; ORCiD logo
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Center for Frontiers of Subsurface Energy Security (CFSES); Univ. of Texas, Austin, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1538909
DOE Contract Number:  
SC0001114
Resource Type:
Journal Article
Journal Name:
Journal of Fluid Mechanics
Additional Journal Information:
Journal Volume: 837; Journal ID: ISSN 0022-1120
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
Mechanics; Physics

Citation Formats

Wen, Baole, and Chini, Gregory P. Inclined porous medium convection at large Rayleigh number. United States: N. p., 2018. Web. doi:10.1017/jfm.2017.863.
Wen, Baole, & Chini, Gregory P. Inclined porous medium convection at large Rayleigh number. United States. doi:10.1017/jfm.2017.863.
Wen, Baole, and Chini, Gregory P. Fri . "Inclined porous medium convection at large Rayleigh number". United States. doi:10.1017/jfm.2017.863.
@article{osti_1538909,
title = {Inclined porous medium convection at large Rayleigh number},
author = {Wen, Baole and Chini, Gregory P.},
abstractNote = {High-Rayleigh-number ($Ra$) convection in an inclined two-dimensional porous layer is investigated using direct numerical simulations (DNS) and stability and variational upper-bound analyses. When the inclination angle$\unicode[STIX]{x1D719}$of the layer satisfies$0^{\circ }<\unicode[STIX]{x1D719}\lesssim 25^{\circ }$, DNS confirm that the flow exhibits a three-region wall-normal asymptotic structure in accord with the strictly horizontal ($\unicode[STIX]{x1D719}=0^{\circ }$) case, except that as$\unicode[STIX]{x1D719}$is increased the time-mean spacing between neighbouring interior plumes also increases substantially. Both DNS and upper-bound analysis indicate that the heat transport enhancement factor (i.e. the Nusselt number)$Nu\sim CRa$with a$\unicode[STIX]{x1D719}$-dependent prefactor$C$. When$\unicode[STIX]{x1D719}>\unicode[STIX]{x1D719}_{t}$, however, where$30^{\circ }<\unicode[STIX]{x1D719}_{t}<32^{\circ }$independently of$Ra$, the columnar flow structure is completely broken down: the flow transitions to a large-scale travelling-wave convective roll state, and the heat transport is significantly reduced. To better understand the physics of inclined porous medium convection at large$Ra$and modest inclination angles, a spatial Floquet analysis is performed, yielding predictions of the linear stability of numerically computed, fully nonlinear steady convective states. The results show that there exist two types of instability when$\unicode[STIX]{x1D719}\neq 0^{\circ }$: a bulk-mode instability and a wall-mode instability, consistent with previous findings for$\unicode[STIX]{x1D719}=0^{\circ }$(Wenet al., J. Fluid Mech., vol. 772, 2015, pp. 197–224). The background flow induced by the inclination of the layer intensifies the bulk-mode instability during its subsequent nonlinear evolution, thereby favouring increased spacing between the interior plumes relative to that observed in convection in a horizontal porous layer.},
doi = {10.1017/jfm.2017.863},
journal = {Journal of Fluid Mechanics},
issn = {0022-1120},
number = ,
volume = 837,
place = {United States},
year = {2018},
month = {1}
}

Works referenced in this record:

Instabilities of Steady, Periodic, and Quasi-Periodic Modes of Convection in Porous Media
journal, May 1987

  • Kimura, S.; Schubert, G.; Straus, J. M.
  • Journal of Heat Transfer, Vol. 109, Issue 2
  • DOI: 10.1115/1.3248087

A proof that convection in a porous vertical slab is stable
journal, February 1969


Natural convection in a sloping porous layer
journal, January 1973


Route to chaos in porous-medium thermal convection
journal, May 1986


High-Rayleigh-number convection in a fluid-saturated porous layer
journal, January 1999


High Rayleigh number convection in a three-dimensional porous medium
journal, May 2014

  • Hewitt, Duncan R.; Neufeld, Jerome A.; Lister, John R.
  • Journal of Fluid Mechanics, Vol. 748
  • DOI: 10.1017/jfm.2014.216

Bounds for heat transport in a porous layer
journal, December 1998


Convection of a fluid in a porous medium
journal, October 1948

  • Lapwood, E. R.
  • Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 44, Issue 4
  • DOI: 10.1017/S030500410002452X

Structure and stability of steady porous medium convection at large Rayleigh number
journal, May 2015

  • Wen, Baole; Corson, Lindsey T.; Chini, Gregory P.
  • Journal of Fluid Mechanics, Vol. 772
  • DOI: 10.1017/jfm.2015.205

Solutions and stability criteria of natural convective flow in an inclined porous layer
journal, June 1985


Plume formation and resonant bifurcations in porous-media convection
journal, August 1994


Numerical study of natural convection in a tilted rectangular porous material
journal, April 1987

  • Moya, Sara L.; Ramos, Eduardo; Sen, Mihir
  • International Journal of Heat and Mass Transfer, Vol. 30, Issue 4
  • DOI: 10.1016/0017-9310(87)90204-3

High-resolution simulation and characterization of density-driven flow in CO2 storage in saline aquifers
journal, April 2010


The onset of Darcy-B�nard convection in an inclined layer heated from below
journal, March 2000

  • Rees, D. A. S.; Bassom, A. P.
  • Acta Mechanica, Vol. 144, Issue 1-2
  • DOI: 10.1007/BF01181831

Transitions in time-dependent thermal convection in fluid-saturated porous media
journal, August 1982


Ultimate Regime of High Rayleigh Number Convection in a Porous Medium
journal, May 2012


Computational approaches to aspect-ratio-dependent upper bounds and heat flux in porous medium convection
journal, December 2013


Third-order-accurate semi-implicit Runge–Kutta scheme for incompressible Navier–Stokes equations
journal, January 2006

  • Nikitin, Nikolay
  • International Journal for Numerical Methods in Fluids, Vol. 51, Issue 2
  • DOI: 10.1002/fld.1122

Multiple steady states for unicellular natural convection in an inclined porous layer
journal, October 1987

  • Sen, Mihir; Vasseur, P.; Robillard, L.
  • International Journal of Heat and Mass Transfer, Vol. 30, Issue 10
  • DOI: 10.1016/0017-9310(87)90089-5

Transition to oscillatory convective heat transfer in a fluid-saturated porous medium
journal, July 1987

  • Aidun, Cyrus K.; Steen, Paul H.
  • Journal of Thermophysics and Heat Transfer, Vol. 1, Issue 3
  • DOI: 10.2514/3.38

Stability of columnar convection in a porous medium
journal, November 2013

  • Hewitt, Duncan R.; Neufeld, Jerome A.; Lister, John R.
  • Journal of Fluid Mechanics, Vol. 737
  • DOI: 10.1017/jfm.2013.559

An experimental study of natural convection in inclined porous media
journal, April 1974


Stability of three-dimensional columnar convection in a porous medium
journal, September 2017

  • Hewitt, Duncan R.; Lister, John R.
  • Journal of Fluid Mechanics, Vol. 829
  • DOI: 10.1017/jfm.2017.561

Buoyant currents arrested by convective dissolution: BUOYANT CURRENTS ARRESTED BY DISSOLUTION
journal, May 2013

  • MacMinn, Christopher W.; Juanes, Ruben
  • Geophysical Research Letters, Vol. 40, Issue 10
  • DOI: 10.1002/grl.50473

Convection Currents in a Porous Medium
journal, June 1945

  • Horton, C. W.; Rogers, F. T.
  • Journal of Applied Physics, Vol. 16, Issue 6
  • DOI: 10.1063/1.1707601