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 }$(Wenet al., J. Fluid Mech., vol. 772, 2015, pp. 197–224). The background flow induced by the inclination of the layer intensifies the bulk-mode instability during its subsequent nonlinearmore »
- Authors:
- Publication Date:
- Research Org.:
- Energy Frontier Research Centers (EFRC) (United States). Center for Frontiers of Subsurface Energy Security (CFSES); Univ. of Texas, Austin, TX (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1538909
- DOE Contract Number:
- SC0001114
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Fluid Mechanics
- Additional Journal Information:
- Journal Volume: 837; Journal ID: ISSN 0022-1120
- Publisher:
- Cambridge University Press
- Country of Publication:
- United States
- Language:
- English
- Subject:
- Mechanics; Physics
Citation Formats
Wen, Baole, and Chini, Gregory P. Inclined porous medium convection at large Rayleigh number. United States: N. p., 2018.
Web. doi:10.1017/jfm.2017.863.
Wen, Baole, & Chini, Gregory P. Inclined porous medium convection at large Rayleigh number. United States. https://doi.org/10.1017/jfm.2017.863
Wen, Baole, and Chini, Gregory P. Fri .
"Inclined porous medium convection at large Rayleigh number". United States. https://doi.org/10.1017/jfm.2017.863.
@article{osti_1538909,
title = {Inclined porous medium convection at large Rayleigh number},
author = {Wen, Baole and Chini, Gregory P.},
abstractNote = {High-Rayleigh-number ($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},
url = {https://www.osti.gov/biblio/1538909},
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
A proof that convection in a porous vertical slab is stable
journal, February 1969
- Gill, A. E.
- Journal of Fluid Mechanics, Vol. 35, Issue 3
Natural convection in a sloping porous layer
journal, January 1973
- Bories, S. A.; Combarnous, M. A.
- Journal of Fluid Mechanics, Vol. 57, Issue 1
Route to chaos in porous-medium thermal convection
journal, May 1986
- Kimura, S.; Schubert, G.; Straus, J. M.
- Journal of Fluid Mechanics, Vol. 166, Issue -1
High-Rayleigh-number convection in a fluid-saturated porous layer
journal, January 1999
- Otero, Jesse; Dontcheva, Lubomira A.; Johnston, Hans
- Journal of Fluid Mechanics, Vol. 500
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
Bounds for heat transport in a porous layer
journal, December 1998
- Doering, Charles R.; Constantin, Peter
- Journal of Fluid Mechanics, Vol. 376
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
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
Solutions and stability criteria of natural convective flow in an inclined porous layer
journal, June 1985
- Caltagirone, J. P.; Bories, S.
- Journal of Fluid Mechanics, Vol. 155
Plume formation and resonant bifurcations in porous-media convection
journal, August 1994
- Graham, Michael D.; Steen, Paul H.
- Journal of Fluid Mechanics, Vol. 272
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
High-resolution simulation and characterization of density-driven flow in CO2 storage in saline aquifers
journal, April 2010
- Pau, George S. H.; Bell, John B.; Pruess, Karsten
- Advances in Water Resources, Vol. 33, Issue 4
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
Transitions in time-dependent thermal convection in fluid-saturated porous media
journal, August 1982
- Schubert, G.; Straus, J. M.
- Journal of Fluid Mechanics, Vol. 121, Issue -1
Three-dimensional benchmark for variable-density flow and transport simulation: matching semi-analytic stability modes for steady unstable convection in an inclined porous box
journal, December 2009
- Voss, Clifford I.; Simmons, Craig T.; Robinson, Neville I.
- Hydrogeology Journal, Vol. 18, Issue 1
Ultimate Regime of High Rayleigh Number Convection in a Porous Medium
journal, May 2012
- Hewitt, Duncan R.; Neufeld, Jerome A.; Lister, John R.
- Physical Review Letters, Vol. 108, Issue 22
Computational approaches to aspect-ratio-dependent upper bounds and heat flux in porous medium convection
journal, December 2013
- Wen, Baole; Chini, Gregory P.; Dianati, Navid
- Physics Letters A, Vol. 377, Issue 41
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
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
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
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
An experimental study of natural convection in inclined porous media
journal, April 1974
- Kaneko, T.; Mohtadi, M. F.; Aziz, K.
- International Journal of Heat and Mass Transfer, Vol. 17, Issue 4
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
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
Convection Currents in a Porous Medium
journal, June 1945
- Horton, C. W.; Rogers, F. T.
- Journal of Applied Physics, Vol. 16, Issue 6