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 nonlinearmore » evolution, thereby favouring increased spacing between the interior plumes relative to that observed in convection in a horizontal porous layer.« less

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. 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


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


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


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


Numerical Linear Algebra
book, January 1997


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


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


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


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


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


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


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


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


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


Convection Currents in a Porous Medium
journal, June 1945