Articles & Issues
- Language
- English
- Conflict of Interest
- In relation to this article, we declare that there is no conflict of interest.
- Publication history
-
Received January 6, 2018
Accepted March 12, 2018
-
This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits
unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright © KIChE. All rights reserved.
All issues
Effect of vertically varying permeability on the onset of convection in a porous medium
Department of Chemical Engineering, Hongik University, Seoul 04066, Korea 1Department of Chemical Engineering, Jeju National University, Jeju 63243, Korea
mckim@cheju.ac.kr
Korean Journal of Chemical Engineering, June 2018, 35(6), 1247-1256(10), 10.1007/s11814-018-0045-5
Download PDF
Abstract
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 buoyancydriven 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.
Keywords
References
Horton CW, Rogers FT, J. Appl. Phys., 6, 367 (1945)
Lapwood ER, Proc. Camb. Philos. Soc, 44, 508 (1948)
Nield DA, Bejan A, Convection in Porous Media, 4th Ed., Springer (2013).
Caltagirone JP, Q. J. Mech. Appl. Math., 33, 47 (1980)
Ennis-King J, Preston I, Paterson L, Phys. Fluids, 17, 084107 (2005)
Xu X, Chen S, Zhang D, Adv. Water Resour., 29, 397 (2006)
Hassanzadeh H, Pooladi-Darvish M, Keith DW, Transp. Porous Media, 65(2), 193 (2006)
Rapaka S, Chen S, Pawar RJ, Stauffer PH, Zhang D, J. Fluid Mech., 609, 285 (2008)
Riaz A, Hesse M, Tchelepi HA, Orr FM, J. Fluid Mech., 548, 87 (2006)
Selem A, Rees DAS, J. Porous Med., 10, 1 (2007)
Wessel-Berg D, SIAM J. Appl. Math., 70, 1219 (2009)
Kim MC, Choi CK, Phys. Fluids, 19, 088103 (2007)
Riaz A, Cinar Y, J. Petrol. Sci. Eng., 124, 367 (2014)
Rapaka S, Pawar RJ, Stauffer PH, Zhang D, Chen S, J. Fluid Mech., 641, 227 (2009)
Nield DA, Kuznetsov AV, Transp. Porous Media, 85(3), 691 (2010)
Ranganathan P, Farajzadeh R, Bruining H, Zitha PLJ, Transp. Porous Media, 95(1), 25 (2012)
Kong XZ, Saar MO, Int. J. Greenhouse Gas Control, 19, 160 (2013)
Hill AA, Morad MR, Proc. R. Soc. A, 470, 201403 (2014)
Kim MC, Choi CK, Korean J. Chem. Eng., 32(12), 2400 (2015)
Chandrasekhar S, Hydrodynamic and Hydromagnetic Stability, Oxford U. P. (1961).
Harfash AJ, Hill AA, Int. J. Heat Mass Transfer, 72, 609 (2014)
Harfash AJ, Transp. Porous Media, 102(1), 43 (2014)
Ben Y, Demekhin EA, Chang HC, Phys. Fluids, 14, 999 (2002)
Kim MC, Choi CK, Phys. Fluids, 24, 044102 (2012)
Slim AC, Ramakrishnan TS, Phys. Fluids, 22, 124103 (2010)
Kim MC, Korean J. Chem. Eng., 35(2), 364 (2017)
Lick W, J. Fluid Mech., 21, 565 (1965)
Tan CT, Homsy GM, Phys. Fluids, 29, 3549 (1986)
Ghesmat K, Hassanzadeh H, Abedi J, J. Fluid Mech., 673, 480 (2011)
Tan CT, Homsy GM, Phys. Fluids, 31, 1330 (1988)
Zimmerman WB, Homsy GM, Phys. Fluids A, 4, 2348 (1992)
Manickam O, Homsy GM, J. Fluid Mech., 288, 75 (1995)
Lapwood ER, Proc. Camb. Philos. Soc, 44, 508 (1948)
Nield DA, Bejan A, Convection in Porous Media, 4th Ed., Springer (2013).
Caltagirone JP, Q. J. Mech. Appl. Math., 33, 47 (1980)
Ennis-King J, Preston I, Paterson L, Phys. Fluids, 17, 084107 (2005)
Xu X, Chen S, Zhang D, Adv. Water Resour., 29, 397 (2006)
Hassanzadeh H, Pooladi-Darvish M, Keith DW, Transp. Porous Media, 65(2), 193 (2006)
Rapaka S, Chen S, Pawar RJ, Stauffer PH, Zhang D, J. Fluid Mech., 609, 285 (2008)
Riaz A, Hesse M, Tchelepi HA, Orr FM, J. Fluid Mech., 548, 87 (2006)
Selem A, Rees DAS, J. Porous Med., 10, 1 (2007)
Wessel-Berg D, SIAM J. Appl. Math., 70, 1219 (2009)
Kim MC, Choi CK, Phys. Fluids, 19, 088103 (2007)
Riaz A, Cinar Y, J. Petrol. Sci. Eng., 124, 367 (2014)
Rapaka S, Pawar RJ, Stauffer PH, Zhang D, Chen S, J. Fluid Mech., 641, 227 (2009)
Nield DA, Kuznetsov AV, Transp. Porous Media, 85(3), 691 (2010)
Ranganathan P, Farajzadeh R, Bruining H, Zitha PLJ, Transp. Porous Media, 95(1), 25 (2012)
Kong XZ, Saar MO, Int. J. Greenhouse Gas Control, 19, 160 (2013)
Hill AA, Morad MR, Proc. R. Soc. A, 470, 201403 (2014)
Kim MC, Choi CK, Korean J. Chem. Eng., 32(12), 2400 (2015)
Chandrasekhar S, Hydrodynamic and Hydromagnetic Stability, Oxford U. P. (1961).
Harfash AJ, Hill AA, Int. J. Heat Mass Transfer, 72, 609 (2014)
Harfash AJ, Transp. Porous Media, 102(1), 43 (2014)
Ben Y, Demekhin EA, Chang HC, Phys. Fluids, 14, 999 (2002)
Kim MC, Choi CK, Phys. Fluids, 24, 044102 (2012)
Slim AC, Ramakrishnan TS, Phys. Fluids, 22, 124103 (2010)
Kim MC, Korean J. Chem. Eng., 35(2), 364 (2017)
Lick W, J. Fluid Mech., 21, 565 (1965)
Tan CT, Homsy GM, Phys. Fluids, 29, 3549 (1986)
Ghesmat K, Hassanzadeh H, Abedi J, J. Fluid Mech., 673, 480 (2011)
Tan CT, Homsy GM, Phys. Fluids, 31, 1330 (1988)
Zimmerman WB, Homsy GM, Phys. Fluids A, 4, 2348 (1992)
Manickam O, Homsy GM, J. Fluid Mech., 288, 75 (1995)
