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:

Wen, Baole ;

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Chini, Gregory P.

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Publication Date:

2018-01-05

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