Effect of vertically varying permeability on the onset of convection in a porous medium

Considering the vertically varying permeability of a porous medium, we conducted theoretical and numerical analyses on the onset of buoyancy-driven instability in an initially quiescent, fluid-saturated, horizontal porous layer. Darcy’s law was employed to explain the fluid flow through a porous med...

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Bibliographic Details
Published in:The Korean journal of chemical engineering 2018, 35(6), 219, pp.1247-1256
Main Authors: Ryoo, Won Sun, Kim, Min Chan
Format: Article
Language:English
Subjects:
Biotechnology
Buoyancy
Catalysis
Chemistry
Chemistry and Materials Science
Computational fluid dynamics
Computer simulation
Convection
Fluid flow
Heterogeneity
Industrial Chemistry/Chemical Engineering
Linear analysis
Mass transfer
Materials Science
Motion stability
Nonlinear analysis
Parameters
Permeability
Porous media
Simulation
Stability analysis
Transport Phenomena
화학공학
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Summary:Considering the vertically varying permeability of a porous medium, we conducted theoretical and numerical analyses on the onset of buoyancy-driven instability in an initially quiescent, fluid-saturated, horizontal porous layer. Darcy’s law was employed to explain the fluid flow through a porous medium and linear and nonlinear analyses are conducted. In the semi-infinite domain, the growth of disturbance and the onset of convection were analyzed with and without the quasi-steady state approximation. The present analysis of initial growth rate shows that the system is initially unconditionally stable regardless of a vertical heterogeneity parameter. The onset conditions of buoyancy-driven instabilities were investigated as a function of the Darcy-Rayleigh number and the heterogeneity parameter. To find the effect of a vertical heterogeneity on the flow after the onset of convection, nonlinear numerical simulations also were conducted using the result of the linear analysis as a starting point. Nonlinear numerical simulations show that the finger-like instability motion is not readily observable at a critical time and it becomes visible approximately when a mass transfer rate substantially increases.
ISSN:0256-1115
1975-7220
DOI:10.1007/s11814-018-0045-5