이성분 혼합액의 방향성 응고에서 자연 대류

황인국; 최창균; In Gook Hwang; Chang Kyun Choi

Korean Chemical Engineering Research, Vol.47, No.2, 174-178, April, 2009

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이성분 혼합액의 방향성 응고에서 자연 대류

Natural Convection During Directional Solidification of a Binary Mixture

황인국^†, 최창균 ¹

수원대학교 공과대학 화공생명공학과, 445-743 경기도 화성시 봉담읍 와우리 산 2-2
¹서울대학교 공과대학 화학생물공학부, 151-744 서울특별시 관악구 관악로 599

In Gook Hwang^†, and Chang Kyun Choi¹

Department of Chemical and Biochemical Engineering, The University of Suwon, San 2-2, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-Do 445-743, Korea
¹School of Chemical and Biological Engineering, Seoul National University, San 56-1, Sillim-dong, Gwanak-gu, Seoul 151-744, Korea

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초록

이성분 혼합물의 응고중에 수지상 결정으로 이루어진 mush 층이 형성될 수 있다. 본 연구진이 개발한 전파이론으로 mush 층에서 성분적 대류의 발생을 해석하였다. Emms와 Fowler[18]의 모델로부터 유도한 자기유사 안정성 방정식을 사용하여 대류 발생에 대한 임계 Rayleigh 수를 수치방법으로 계산하였다. 과열량이 아주 크거나 mush 층의 성장률이 아주 작은 극한의 경우에 본 연구 결과는 준정적 안정성 해석 결과와 같아진다.

A mushy layer of dendritic crystals is often formed during solidification of a binary mixture. Natural convection in the mushy layer is analyzed by using the propagation theory we have developed. The critical Rayleigh numbers for the onset of convection are evaluated numerically using the self-similar stability equations based on Emms and Fowler’s[18] model. The present results approach those from quasi-static stability analysis in the limit of a large superheat or a small growth rate of the mushy layer.

Keywords:Propagation Theory;Natural Convection;Solidification;Mushy Layer

[References]

Choi CK, Kang KH, Kim MC, Hwang IG, Korean J. Chem. Eng., 15(2), 192 (1998)
Choi CK, Park JH, Kim MC, Lee JD, Kim JJ, David EJ, Int. J. Heat Mass Transf., 47(19-20), 4377 (2004)
Choi CK, Chung TJ, Kim MC, Int. J. Heat Mass Transf., 47(12-13), 2629 (2004)
YOO JS, CHOI CK, Korean J. Chem. Eng., 4(2), 128 (1987)
Yoon DY, Choi CK, Yoo JS, Int. Chem. Eng., 32, 181 (1992)
Yoon DY, Kim MC, Choi CK, Korean J. Chem. Eng., 20(1), 27 (2003)
Kim MC, Chung TJ, Choi CK, Korean J. Chem. Eng., 20, 69 (2004)
Kim MC, Chung TJ, Choi CK, Theoret. Comput. Fluid Dynamics, 18, 105 (2004)
Hwang IG, Choi GK, HWAHAK KONGHAK, 32(5), 718 (1994)
Hwang IG, Choi CK, Korean J. Chem. Eng., 25(2), 199 (2008)
Choi CK, Park JH, Park HK, Cho HJ, Chung TJ, Kim MC, Int. J. Thermal Sci., 43, 817 (2004)
Flemings MC, Solidification Processing, McGraw-Hill, New York (1974)
Huppert HE, Worster MG, Nature, 314, 703 (1985)
Coriell SR, Cordes MR, Boettinger WJ, Sekerka RF, J. Crystal Growth, 49, 13 (1980)
Tait S, Jaupart C, J. Geophys. Res., 97, 6735 (1992)
Worster MG, J. Fluid Mech., 237, 649 (1992)
Amberg G, Homsy GM, J. Fluid Mech., 252, 79 (1993)
Emms PW, Fowler AC, J. Fluid Mech, 262, 111 (1994)
Loper DE, J. Cryst. Growth, 222(3), 655 (2001)
Riahi DN, J. Fluid Mech., 553, 389 (2006)
Hwang IG, Choi CK, Kyongju, 7, 193 (1998)
Nield DA, Bejan A, Convection in Porous Media, Springer-Verlag, New York (1992)

[Referenced By]

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[1] Choi CK, Kang KH, Kim MC, Hwang IG, Korean J. Chem. Eng., 15(2), 192 (1998)

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

[3] Choi CK, Chung TJ, Kim MC, Int. J. Heat Mass Transf., 47(12-13), 2629 (2004)

[4] YOO JS, CHOI CK, Korean J. Chem. Eng., 4(2), 128 (1987)

[5] Yoon DY, Choi CK, Yoo JS, Int. Chem. Eng., 32, 181 (1992)

[6] Yoon DY, Kim MC, Choi CK, Korean J. Chem. Eng., 20(1), 27 (2003)

[7] Kim MC, Chung TJ, Choi CK, Korean J. Chem. Eng., 20, 69 (2004)

[8] Kim MC, Chung TJ, Choi CK, Theoret. Comput. Fluid Dynamics, 18, 105 (2004)

[9] Hwang IG, Choi GK, HWAHAK KONGHAK, 32(5), 718 (1994)

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

[11] Choi CK, Park JH, Park HK, Cho HJ, Chung TJ, Kim MC, Int. J. Thermal Sci., 43, 817 (2004)

[12] Flemings MC, Solidification Processing, McGraw-Hill, New York (1974)

[13] Huppert HE, Worster MG, Nature, 314, 703 (1985)

[14] Coriell SR, Cordes MR, Boettinger WJ, Sekerka RF, J. Crystal Growth, 49, 13 (1980)

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

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

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

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

[19] Loper DE, J. Cryst. Growth, 222(3), 655 (2001)

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

[21] Hwang IG, Choi CK, Kyongju, 7, 193 (1998)

[22] Nield DA, Bejan A, Convection in Porous Media, Springer-Verlag, New York (1992)