위로부터 응고되는 점도변화 용융액의 열적 불안정성

황인국; 최창균

HWAHAK KONGHAK, Vol.34, No.5, 644-650, October, 1996

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위로부터 응고되는 점도변화 용융액의 열적 불안정성

Thermal Instability of a Variable-Viscosity Melt Solidified from Above

황인국, 최창균

초록

전파이론에 근거하여 위로부터 순수한 단일성분 용융액이 냉각되어 응고될 때 열적 불안정성에 대해 선형안정성이 이론으로 조사하였다. 열경계층의 두께를 길이척도로 설정하여 선형 교란방정식을 유사변환하였다. 용융액에서 온도에 따른 점도변화를 고려하여 부력에 의한 대류발생조건을 수치해법으로 구하였다. 본 연구결과, 임계 열 Rayleigh 수의 값은 고체_액체 무차원 상변화율이 증가함에 따라 증가하지만, Prandtl 수와 Stefan 수가 증가하면 임계값은 감소하는 것을 알 수 있었다. 또한 점도변화의 효과는 계를 인정하게 하고, 대류발생시에 응고계면 바로 아래에 정체층이 생기게 됨을 알 수 있었다.

Thermal instability during solidification of a pure melt cooled from above was investigated under a linear stability theory by using the propagation theory. The linearized disturbance equations were transformed similarly by using the thermal boundary-layer thickness as the length scaling factor. The onset conditions of buoyancy-driven convection of the melt with temperature- dependent viscosity were obtained numerically. The results showed that the critical thermal Rayleigh number increases with increasing the dimensionless phase-change rate of a solid-liquid interface, while it decreases with increasing the Prandtl number and Stefan number. Also, it was found that the effect of variable viscosity makes the system more stable and a stagnant layer forms beneath the interface at the onset of convection.

Keywords:Propagation Theory;Rayleigh Number;Solidification;Thermal Instability;Variable Viscosity

[References]

Glicksman ME, Coriell SR, McFadden GB, Annu. Rev. Fluid Mech., 118, 307 (1986)
Davis SH, J. Fluid Mech., 212, 241 (1990)
Dietshe C, Muller U, J. Fluid Mech., 161, 249 (1985)
Guerin RZ, Billia B, Haldenwang P, Roux B, Phys. Fluids, 31, 2086 (1988)
Neilson DG, Incropera FP, Int. J. Heat Mass Transf., 34, 1717 (1991)
Carslaw HS, Jaeger JC, "Conduction of heat in Solids," 2nd ed., Oxford University Press, London (1959)
Gresho PM, Sani RL, Int. J. Heat Mass Transf., 14, 207 (1971)
Foster TD, Phys. Fluids, 8, 1249 (1965)
Jhaveri BS, Homsy GM, J. Fluid Mech., 114, 251 (1982)
Wankat PC, Homsy GM, Phys. Fluids, 20, 1200 (1977)
Lee JD, Choi CK, Shin CB, Int. Chem. Eng., 30, 761 (1990)
Yoon DY, Choi CK, Yoo JS, Int. Chem. Eng., 32, 181 (1992)
Hwang IG, Choi GK, HWAHAK KONGHAK, 32(5), 718 (1994)
Davaille A, Jaupart C, J. Fluid Mech., 253, 141 (1993)
Chen YM, Pearlstein AJ, Phys. Fluids, 31, 1380 (1988)
Stengel KC, Oliver DS, Booker JR, J. Fluid Mech., 120, 411 (1993)
White DB, J. Fluid Mech., 191, 247 (1988)
Richter FM, Nataf HC, Daly SF, J. Fluid Mech., 129, 173 (1983)
Smith MK, J. Fluid Mech., 188, 547 (1988)
Blair LM, Quinn JA, J. Fluid Mech., 36, 385 (1969)
Patrick MA, Wragg AA, Int. J. Heat Mass Transf., 18, 1397 (1975)

[1] Glicksman ME, Coriell SR, McFadden GB, Annu. Rev. Fluid Mech., 118, 307 (1986)

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

[3] Dietshe C, Muller U, J. Fluid Mech., 161, 249 (1985)

[4] Guerin RZ, Billia B, Haldenwang P, Roux B, Phys. Fluids, 31, 2086 (1988)

[5] Neilson DG, Incropera FP, Int. J. Heat Mass Transf., 34, 1717 (1991)

[6] Carslaw HS, Jaeger JC, "Conduction of heat in Solids," 2nd ed., Oxford University Press, London (1959)

[7] Gresho PM, Sani RL, Int. J. Heat Mass Transf., 14, 207 (1971)

[8] Foster TD, Phys. Fluids, 8, 1249 (1965)

[9] Jhaveri BS, Homsy GM, J. Fluid Mech., 114, 251 (1982)

[10] Wankat PC, Homsy GM, Phys. Fluids, 20, 1200 (1977)

[11] Lee JD, Choi CK, Shin CB, Int. Chem. Eng., 30, 761 (1990)

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

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

[14] Davaille A, Jaupart C, J. Fluid Mech., 253, 141 (1993)

[15] Chen YM, Pearlstein AJ, Phys. Fluids, 31, 1380 (1988)

[16] Stengel KC, Oliver DS, Booker JR, J. Fluid Mech., 120, 411 (1993)

[17] White DB, J. Fluid Mech., 191, 247 (1988)

[18] Richter FM, Nataf HC, Daly SF, J. Fluid Mech., 129, 173 (1983)

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

[20] Blair LM, Quinn JA, J. Fluid Mech., 36, 385 (1969)

[21] Patrick MA, Wragg AA, Int. J. Heat Mass Transf., 18, 1397 (1975)