수직 방향 응고시에 열-용질 대류의 발생

황인국; 최창균

HWAHAK KONGHAK, Vol.29, No.6, 727-735, December, 1991

Export Citation

수직 방향 응고시에 열-용질 대류의 발생

The Onset of Thermosolutal Convection during Upwards Solidification

황인국, 최창균

초록

이성분 용융액의 수직 방향 응고시에 열-용질 대류의 발생에 대해 선형 안정성 이론을 근거로 조사하였다. 본 연구의 주요한 관심은 열-용질 대류 발생에 있어 온도의 안정화 효과이다. 열 Rayleigh수가 증가하면 임계 용질 Rayleigh수가 증가하는 결과로부터 열 Rayleigh수가 증가가 대류발생에 안정화 효과를 주는 것을 알았다. 또한 Lewis수나 Schmidt수가 커지면 계는 불안정해지고, 대류 발생시에는 계면 가까운 곳에 한정되는 다중셀 대류가 나타남을 알 수 있었다. 열 Rayleigh수가 증가함에 따라 이러한 열-용질 대류는 점점 응고 계면에 가까운 곳에서 발생하게 되며 다중셀의 경향이 더 나타났다.

The onset of thermosolutal convection during upwards solidification of a binary melt is investiga-ted by using linear stability theory. The present study concerns the stabilizing effect of temperature on the onset of thermosolutal convection. The results show that the critical solutal Rayleigh number increases with increasing the thermal Rayleigh number. This reflects the fact that an increase in thermal Rayleigh number makes the system more stable, while the system becomes more unstable with an increase in Lewis number or schmidt number. Multicell convection is exhibited at onset condition and this thermosolutal convec-tion is confined mainly to the vicinity of the interface. With increasing the thermal Rayleigh number, this trend becomes more pronounced with multicell patterns more distinguished.

[References]

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[1] Glicksman ME, Coriell SR, McFadden GB, Ann. Rev. Fluid Mech., 18, 307 (1986)

[2] Davis SH, J. Fluid Mech., 212, 241 (1990)

[3] Huppert HE, J. Fluid Mech., 212, 209 (1990)

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

[5] Hurle DTJ, Jakeman E, Wheeler AA, J. Cryst. Growth, 58, 163 (1982)

[6] Huppert HE, Turner JS, J. Fluid Mech., 106, 299 (1981)

[7] Coriell SR, McFadden GB, Sekerka RF, Annu. Rev. Mater. Sci., 15, 119 (1985)

[8] Mullins WW, Sekerka RF, J. Appl. Phys., 35, 444 (1964)

[9] Hurle DTJ, Jakeman E, Wheeler AA, Phys. Fluids, 26, 624 (1983)

[10] McFadden GB, Rehm RG, Coriell SR, Chuck W, Morrish KA, Metall. Trans. A, 15, 2125 (1984)

[11] Thi HN, Billia B, Jamgotchian H, J. Fluid Mech., 204, 581 (1989)

[12] Young GW, Davis SH, Phys. Rev., B, Condens. Matter, 34, 3388 (1986)

[13] Hurle DTJ, J. Cryst. Growth, 72, 738 (1988)

[14] Smith MK, J. Fluid Mech., 188, 547 (1988)

[15] Turner JS, Annu. Rev. Fluid Mech., 17, 11 (1988)

[16] Chen F, Chen CF, J. Heat Transfer, 110, 403 (1988)

[17] McFadden GB, Coriell SR, Boisvert RF, Phys. Fluids, 28, 2716 (1985)

[18] McCay TD, McCay MH, Proc. 22nd Int. Symp. on Manufacturing and Materials Processing, Dubrovnik (1990)

[19] Hopkins JA, McCay MH, Smith LM, McCay TD, Proc. 22nd Int. Symp. on Manufacturing and Materials Processing, Bubrovnik (1990)