Korean Chemical Engineering Research

The Korean Institute of Chemical Engineers (한국화학공학회)
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Natural Convection During Directional Solidification of a Binary Mixture

이성분 혼합액의 방향성 응고에서 자연 대류

  • Hwang, In Gook (Department of Chemical and Biochemical Engineering, The University of Suwon) ;
  • Choi, Chang Kyun (School of Chemical and Biological Engineering, Seoul National University)
  • 황인국 (수원대학교 공과대학 화공생명공학과) ;
  • 최창균 (서울대학교 공과대학 화학생물공학부)
  • Received : 2009.01.23
  • Accepted : 2009.02.11
  • Published : 2009.04.30
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Abstract

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 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.

이성분 혼합물의 응고중에 수지상 결정으로 이루어진 mush 층이 형성될 수 있다. 본 연구진이 개발한 전파이론으로 mush 층에서 성분적 대류의 발생을 해석하였다. Emms와 Fowler의 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.

Keywords

References

  1. Choi, C. K., Kang, K. H., Kim, M. C. and Hwang, I. G., "Convective Instabilities and Transport Properties in Horizontal Fluid Layers," Korean J. Chem. Eng., 15, 192-198(1998) https://doi.org/10.1007/BF02707072
  2. Choi, C. K., Park, J. H., Kim, M. C., Lee, J. D., Kim, J. J. and Davis, E. J., "The Onset of Convective Instability in a Horizontal Fluid Layer Subjected to a Constant Heat Flux from Below," Int. J. Heat Mass Transfer, 47, 4377-4384(2004) https://doi.org/10.1016/j.ijheatmasstransfer.2004.04.028
  3. Choi, C. K., Chung, T. J. and Kim, M. C., "Buoyancy Effects in Plane Couette Flow Heated Uniformly from Below with Constant Heat Flux," Int. J. Heat Mass Transfer, 47, 2629-2636(2004) https://doi.org/10.1016/j.ijheatmasstransfer.2003.12.010
  4. Yoo, J. S. and Choi, C. K., "Thermal Instability in a Fluid Layer Subjected to Transient Cooling from Above," Korean J. Chem. Eng., 4, 128-134(1987) https://doi.org/10.1007/BF02697428
  5. Yoon, D. Y., Choi, C. K. and Yoo, J. S., 'Analysis of Thermal Instability in a Horizontal Porous Layer Heated from Below,' Int. Chem. Eng., 32, 181-191(1992)
  6. Yoon, D. Y., Kim, M. C. and Choi, C. K., "Oscillatory Convection in a Horizontal Porous Layer Saturated with a Viscoelastic Fluid," Korean J. Chem. Eng., 20, 27-31(2003) https://doi.org/10.1007/BF02697180
  7. Kim, M. C., Chung, T. J. and Choi, C. K., 'Onset of Buoyancy- Driven Convection in the Horizontal Fluid Layer Heated from Below with Time-Dependent Manner,' Korean J. Chem. Eng., 20, 69-74(2004) https://doi.org/10.1007/BF02705382
  8. Kim, M. C., Chung, T. J. and Choi, C. K., "The Onset of Taylor-like Vortices in the Flow Induced by an Impulsively Started Rotating Cylinder," Theoret. Comput. Fluid Dynamics, 18, 105-114(2004) https://doi.org/10.1007/s00162-004-0126-4
  9. Hwang, I. G. and Choi, C. K., 'Convective Instabilities of the Melt during Solidification Cooled from below,' HWAHAK KONGHAK, 32, 718-725(1994)
  10. Hwang, I. G. and Choi, C. K., "Onset of Convection in a Porous Mush during Binary Solidification," Korean J. Chem. Eng., 25, 199-202 (2008) https://doi.org/10.1007/s11814-008-0036-z
  11. Choi, C. K., Park, J. H., Park, H. K., Cho, H. J., Chung, T. J. and Kim, M. C., "Temporal Evolution of Thermal Convection in an Initially Stably-Stratified Horizontal Fluid Layer," Int. J. Thermal Sci., 43, 817-823(2004) https://doi.org/10.1016/j.ijthermalsci.2004.02.022
  12. Flemings, M. C., Solidification Processing, McGraw-Hill, New York(1974)
  13. Huppert, H. E. and Worster, M. G., "Dynamic Solidification of a Binary Melt," Nature, 314, 703-707(1985) https://doi.org/10.1038/314703a0
  14. Coriell, S. R., Cordes, M. R., Boettinger, W. J. and Sekerka, R. F., "Convective and Interfacial Instabilities During Unidirectional Solidification of a Binary Alloy," J. Crystal Growth, 49, 13-28(1980) https://doi.org/10.1016/0022-0248(80)90056-1
  15. Tait, S. and Jaupart, C., "Compositional Convection in a Reactive Crystalline Mush and the Evolution of Porosity," J. Geophys. Res., 97, 6735-6756(1992) https://doi.org/10.1029/92JB00016
  16. Worster, M. G., "Instabilities of the Liquid and Mushy Regions during Solidification of Alloys," J. Fluid Mech., 237, 649-669(1992) https://doi.org/10.1017/S0022112092003562
  17. Amberg, G. and Homsy, G. M., "Nonlinear Analysis of Buoyant Convection in Binary Solidification with Application to Channel Formation," J. Fluid Mech., 252, 79-98(1993) https://doi.org/10.1017/S0022112093003672
  18. Emms, P. W. and Fowler, A. C., "Compositional Convection in the Solidification of Binary Alloys," J. Fluid Mech, 262, 111-139 (1994) https://doi.org/10.1017/S0022112094000443
  19. Loper, D. E., "On the Boundary Conditions at a Mush-Melt Interface," J. Crystal Growth, 222, 655-666(2001) https://doi.org/10.1016/S0022-0248(00)00953-2
  20. Riahi, D. N., "Nonlinear Oscillatory Convection in Rotating Mushy Layers," J. Fluid Mech., 553, 389-400(2006) https://doi.org/10.1017/S0022112006009037
  21. Hwang, I. G. and Choi, C. K., 'The Onset of Convection in a Mushy Layer during Time-Dependent Solidification,' Heat Transfer 1998 (Proceedings of 11th International Heat Transfer Conference), Kyongju, 7, 193-198(1998)
  22. Nield, D. A. and Bejan, A., Convection in Porous Media, Springer-Verlag, New York(1992)