On steady convection in a porous medium

Palm, Enok; Weber, Jan Erik H.; Kvernvold, Oddmund

doi:10.1017/s002211207200059x

Cited by 129 publications

(72 citation statements)

References 7 publications

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“…The structure and stability of steady 2D porous medium convection at small to moderate Rayleigh number has been discussed in detail in many previous studies (Elder 1967;Palm et al 1972;Horne & OSullivan 1974;Schubert & Straus 1982;Aidun & Steen 1987;Kimura et al 1987;Graham & Steen 1992, 1994. The study of high-Rayleighnumber steady solutions, however, has been rather limited, in part because these solutions are unstable and exhibit fine-scale spatial structure.…”

Section: Introductionmentioning

confidence: 99%

Structure and stability of steady porous medium convection at large Rayleigh number

2015

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This version is available at https://strathprints.strath.ac.uk/52305/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. A systematic investigation of unstable steady-state solutions of the Darcy-OberbeckBoussinesq equations at large values of the Rayleigh number Ra is performed to gain insight into two-dimensional porous medium convection in domains of varying aspectratio L. The steady convective states are shown to transport less heat than the statistically steady 'turbulent' flow realised at the same parameter values: the Nusselt number N u ∼ Ra for turbulent porous medium convection, while N u ∼ Ra 0.6 for the maximum heat-transporting steady solutions. A key finding is that the lateral scale of the heat-fluxmaximising solutions shrinks roughly as L ∼ Ra −0.5 , reminiscent of the decrease of the mean inter-plume spacing observed in turbulent porous medium convection as the thermal forcing is increased. A spatial Floquet analysis is performed to investigate the linear stability of the fully nonlinear steady convective states, extending a recent study by Hewitt et al. (J. Fluid Mech. 737, 2013) by treating a base convective state -and secondary stability modes -that satisfy appropriate boundary conditions along plane parallel walls. As in that study, a bulk instability mode is found for sufficiently small aspect-ratio base states. However, the growth rate of this bulk mode is shown to be significantly reduced by the presence of the walls. Beyond a certain critical Ra-dependent aspect-ratio, the base state is most strongly unstable to a secondary mode that is localised near the heated and cooled walls. Direct numerical simulations, strategically initialised to investigate the fully nonlinear evolution of the most dangerous secondary instability modes, suggest that the (long time) mean inter-plume spacing in statistically-steady porous medium convection results from a balance between the competing effects of these two types of inst...

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Section: Introductionmentioning

confidence: 99%

Structure and stability of steady porous medium convection at large Rayleigh number

2015

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“…Provision is made near the end of the article (p 50, col. 2) to transform the sphere into a cylinder, maintaining th.e same biospherical coordinate system. A continuation of the work done by Elder (1967), Palm (1972) and Busse (1972). The termal gradient ~cts as the driving force for the convective action.…”

Section: R L Rollinsmentioning

confidence: 89%

“…Holman {1976) presents the general heat conduction equation as: Soil is not an isotropic homogeneous material having properties that are constant in time and space. Heat flow in soil is greatly influenced by the material inhabiting the pore spaces between soil grains, and the conditions at the grain to grain contact junctions (Palm, 1972). These .…”

Section: Soil Thermal Propertiesmentioning

confidence: 99%

Thermal properties of soils and soils testing

1981

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“…These values correspond to rolls with a square cross-section. [4] subsequently analysed the moderately supercritical flow using a series representation in terms of powers of (Ra − Ra c )/Ra. A very detailed numerical stability analysis was undertaken by Straus (1974) [5] who delineated the region in (Ra, k)-space within which steady rolls form the stable planform of convection.…”

Section: Introductionmentioning

confidence: 99%

Horizontal Cellular Oscillations Caused by Time-Periodic Resonant Thermal Forcing in Weakly Nonlinear Darcy-Bénard Convection

Jais

Rees

2017

Fluids

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Abstract:The onset of Rayleigh-Bénard convection in a horizontally unbounded saturated porous medium is considered. Particular attention is given to the stability of weakly nonlinear convection between two plane horizontal surfaces heated from below. The primary aim is to study the effects on postcritical convection of having small amplitude time-periodic resonant thermal forcing. Amplitude equations are derived using a weakly nonlinear theory and they are solved in order to understand how the flow evolves with changes in the Darcy-Rayleigh number and the forcing frequency. When convection is stationary in space, it is found to consist of one of two different types depending on its location in parameter space: either a convection pattern where each cell rotates in the same way for all time with a periodic variation in amplitude (Type I) or a pattern where each cell changes direction twice within each forcing period (Type II). Asymptotic analyses are also performed (i) to understand the transition between convection of types I and II; (ii) for large oscillation frequencies and (iii) for small oscillation frequencies. In a large part of parameter space the preferred pattern of convection when the layer is unbounded horizontally is then shown to be one where the cells oscillate horizontally-this is a novel form of pattern selection for Darcy-Bénard convection.

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On steady convection in a porous medium

Cited by 129 publications

References 7 publications

Structure and stability of steady porous medium convection at large Rayleigh number

Structure and stability of steady porous medium convection at large Rayleigh number

Thermal properties of soils and soils testing

Horizontal Cellular Oscillations Caused by Time-Periodic Resonant Thermal Forcing in Weakly Nonlinear Darcy-Bénard Convection

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