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Received July 4, 2021
Accepted September 4, 2021
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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
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Effect of nonlinear drag on the onset and the growth of the miscibleviscous fingering in a porous medium
Department of Chemical Engineering, Jeju National University, Jeju 63243, Korea
mckim@cheju.ac.kr
Korean Journal of Chemical Engineering, March 2022, 39(3), 548-561(14), 10.1007/s11814-021-0954-6
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Abstract
The onset and growth of miscible viscous fingering in a porous medium was analyzed analytically. Taking the nonlinear drag into account, new stability equations were derived based on Forchheimer’s extension and solved with the quasi-steady state approximation in a similar domain (QSSAξ). Also, the validity of QSSAξ was tested by the numerical initial value calculation (IVC) study. Through the initial growth rate analysis without the steady state approximation, we showed that initially the system is unconditionally stable even in unfavorable viscosity distribution and there exists an initial condition with the largest growth rate. The present initial growth rate analysis without the QSSA is quite different from the previous analyses based on quasi-steady state approximation in the global domain (QSSAx), where the system is assumed to be unstable if the less viscosity fluid displaces the higher one. Employing the linear stability results as an initial condition, fully non-linear numerical simulations were conducted using the Fourier spectral method. The present linear and non-linear analyses predicted that the non-linear drag makes the system stable, i.e., it delays the onset of instability and suppresses the evolution of fingering motions.
Keywords
References
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Hota TK, Mishra M, J. Fluid Mech., 856, 552 (2018)
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Shoghi MR, Norouzi M, Rheol Acta, 54, 973 (2015)
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Yuan Q, Azaiez J, Fluid Dyn. Res., 47, 15506 (2015)
Beck JL, Phys. Fluids, 15, 1377 (1972)
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Nield DA, Bejan A, Convection in porous media, 4th Ed., Springer, N.Y. (2013).
Ward JC, J. Hydraul. Div., 90, 1 (1964)
Joseph DD, Nield DA, Papanicolaou G, Water Resour. Res., 18, 1049 (1982)
Kaviany M, Principle of heat transfer in porous media, 2nd Ed., Springer, N.Y. (1995).
Kim MC, Adv. Water Res., 35, 1 (2012)
Ryoo WS, Kim MC, Korean J. Chem. Eng., 35, 1423 (2018)
Kim MC, Choi CK, Korean J. Chem. Eng., 32, 2400 (2015)
Kim MC, Korean J. Chem. Eng., 38, 144 (2021)
Kim MC, Korean Chem. Eng. Res., 59, 138 (2021)
Meng X, Guo Z, Int. J. Heat Mass Transfer, 100, 767 (2016)
Kim MC, Chem. Eng. Sci., 126, 349 (2015)
Kim MC, Kim YH, Chem. Eng. Sci., 134, 632 (2015)
Adress JTH, Cardsso SSS, Chaos, 22, 37113 (2012)
Perkins TK, Johnston OC, Hoffman RN, Soc. Pet. Eng. J., 5, 301 (1965)
