Stability analysis of compositional convection in a mushy layer in the time-dependent solidification system

In Gook Hwang

Korean Journal of Chemical Engineering, Vol.30, No.5, 1023-1028, May, 2013

DOI10.1007/s11814-013-0013-z Export Citation

Stability analysis of compositional convection in a mushy layer in the time-dependent solidification system

In Gook Hwang^†

Department of Chemical Engineering, University of Suwon, Gyeonggi-do 445-743, Korea

E-mail:

Instabilities of convection in a mushy layer with a permeable interface underlying a liquid layer are studied in the time-dependent solidification system in which a binary melt cooled from below. The self-similar stability equations in the liquid and mushy layers are derived by propagation theory. The onset of mushy-layer-mode convection is examined considering the variation of permeability with porosity in the mushy layer. The numerical results show that the critical Darcy-Rayleigh number defined in terms of the mean permeability increases with increasing the concentration ratio and decreases with increasing the superheat. When the concentration ratio is small, a small convective cell appears in the vicinity of the liquid-mush interface. The influences of various non-uniform permeability models on the stability of compositional convection are discussed.

Keywords:Convective Instability;Solidification;Mushy Layer;Permeability Variation

[References]

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Tait S, Jaupart C, J. Geophys. Res., 97, 6735 (1992)
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Srivastava AK, Bhadauria BS, Communications in Nonlinear Science and Numerical Simulation., 16, 3548 (2011)
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Govender S, Transp. Porous Media, 67(3), 431 (2007)
Peppin SSL, Huppert HE, Worster MG, J. Fluid Mech., 599, 465 (2008)
Hwang IG, Choi CK, J. Cryst. Growth, 267(3-4), 714 (2004)
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Kim MC, Yoon DY, Cho E, Korean J. Chem. Eng., 26(6), 1461 (2009)
Hwang IG, Choi CK, Korean J. Chem. Eng., 25(2), 199 (2008)
Hwang IG, Choi CK, Korean J. Chem. Eng., 26(4), 930 (2009)
Choi CK, Park JH, Kim MC, Lee JD, Kim JJ, David EJ, Int. J. Heat Mass Transf., 47(19-20), 4377 (2004)
Bhatta D, Muddamallappa MS, Riahi DN, Transp. Porous Media, 82(2), 385 (2010)
Nandapurkar P, Poirier DR, Heinrich JC, Felicelli S, Metall. Trans., 20B, 711 (1989)
Happel J, Brenner H, Low reynolds number hydrodynamics, Martinus Nijhoff Publishers, Dordrecht, Netherlands (1986)
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[Referenced By]

[1] Chung CA, Worster MG, J. Fluid Mech., 455, 387 (2002)

[2] O’Rourke JG, Riggs AJE, Guertler CA, Miller PW, Padhi CM, Popelka MM, Wells AJ, West AC, Zhong JQ, Wettlaufer JS, Phys. Fluids., 24, 103305 (2012)

[3] Whiteoak SH, Huppert HE, Worster MG, J. Cryst. Growth, 310(15), 3545 (2008)

[4] Guba P, Worster MG, J. Fluid Mech., 553, 419 (2006)

[5] Butler SL, Phys. Fluids., 23, 016602 (2011)

[6] Fowler AC, IMA J. Appl. Math., 35, 159 (1985)

[7] Worster MG, J. Fluid Mech., 237, 649 (1992)

[8] Chen F, Lu JW, Yang TL, J. Fluid Mech., 276, 163 (1994)

[9] Chung CA, Chen F, J. Fluid Mech., 412, 93 (2000)

[10] Chen F, Chung CA, Lai MH, Phys. Fluids., 14, 1295 (2002)

[11] Emms PW, Fowler AC, J. Fluid Mech., 262, 111 (1994)

[12] Tait S, Jaupart C, J. Geophys. Res., 97, 6735 (1992)

[13] Riahi DN, Mechanics Research Communications., 39, 18 (2012)

[14] Amberg G, Homsy GM, J. Fluid Mech., 252, 79 (1993)

[15] Chung CA, Chen F, J. Fluid Mech., 408, 53 (2000)

[16] Srivastava AK, Bhadauria BS, Communications in Nonlinear Science and Numerical Simulation., 16, 3548 (2011)

[17] Riahi DN, J. Fluid Mech., 553, 389 (2006)

[18] Govender S, Transp. Porous Media, 67(3), 431 (2007)

[19] Peppin SSL, Huppert HE, Worster MG, J. Fluid Mech., 599, 465 (2008)

[20] Hwang IG, Choi CK, J. Cryst. Growth, 267(3-4), 714 (2004)

[21] Kim MC, Choi CK, Korean J. Chem. Eng., 23(6), 874 (2006)

[22] Kim MC, Korean J. Chem. Eng., 27(3), 741 (2010)

[23] Kim MC, Yoon DY, Cho E, Korean J. Chem. Eng., 26(6), 1461 (2009)

[24] Hwang IG, Choi CK, Korean J. Chem. Eng., 25(2), 199 (2008)

[25] Hwang IG, Choi CK, Korean J. Chem. Eng., 26(4), 930 (2009)

[26] Choi CK, Park JH, Kim MC, Lee JD, Kim JJ, David EJ, Int. J. Heat Mass Transf., 47(19-20), 4377 (2004)

[27] Bhatta D, Muddamallappa MS, Riahi DN, Transp. Porous Media, 82(2), 385 (2010)

[28] Nandapurkar P, Poirier DR, Heinrich JC, Felicelli S, Metall. Trans., 20B, 711 (1989)

[29] Happel J, Brenner H, Low reynolds number hydrodynamics, Martinus Nijhoff Publishers, Dordrecht, Netherlands (1986)

[30] Katz RF, Worster MG, J. Comput. Phys., 22, 9823 (2008)