Korean Chemical Engineering Research

The Korean Institute of Chemical Engineers (한국화학공학회)
권호 표지
DOI QR코드

DOI QR Code

Linear Stability of Compositional Convection in a Mushy Layer during Solidification of Ammonium Chloride Solution

염화암모늄 수용액 응고시에 Mush 층에서 성분적 대류의 선형안정성

  • Hwang, In Gook (Department of Chemical Engineering, The University of Suwon)
  • 황인국 (수원대학교 화학공학과)
  • Received : 2011.05.02
  • Accepted : 2012.05.30
  • Published : 2012.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

The onset of convection in a mushy layer is analyzed by using linear stability theory in time-dependent solidification of a binary melt. A simplified model of a near-eutectic mush, in which the mush is assumed to be a porous block, is used and the propagation theory is applied to determine the critical conditions for the onset of convection. The present critical Rayleigh number is higher than the existing experimental result and also theoretical results obtained by considering the mushy layer with an overlying liquid layer. The constant pressure (permeable) condition applied on the mush-liquid interface produces a lower critical Rayleigh number, which is closer to the experimental results of aqueous ammonium chloride solution, compared with the impermeable condition.

이성분 용융액의 시간의존형 응고계에서 mush 층의 대류발생을 선형 안정성 이론으로 해석하였다. 본 연구에서는 근공융물 mush 층을 다공성 블록으로 가정한 단순화된 모델에 전파이론을 적용하여 대류발생 임계조건을 구하였다. 본 연구 모델에서는 기존의 실험결과 및 mush층 위의 액체층을 포함하여 고려한 이론적 연구의 결과보다 더 높은 임계 Rayleigh 수가 얻어졌다. mush 층의 윗 경계면에 일정압력(투과)조건을 적용하는 경우가 비투과조건에 비해 임계 Rayleigh 수를 더 작게 하며 염화암모늄 수용액의 응고실험결과와 더 근접한 것으로 조사되었다.

Keywords

References

  1. Tait, S., Jahrling, K. and Jaupart, C., "The Planform of Compositional Convection and Chimney Formation in a Mushy Layer," Nature, 359, 7406-408(1992).
  2. 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
  3. Chen, C. F., "Experimental Study of Convection in a Mushy Layer during Directional Solidification," J. Fluid Mech., 293, 81-98 (1995). https://doi.org/10.1017/S0022112095001649
  4. Fowler, A. C., "The Formation of Freckles in Binary Alloys," IMA J. Appl. Maths, 35, 159-174(1985). https://doi.org/10.1093/imamat/35.2.159
  5. 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
  6. 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
  7. Hwang, I. G. and Choi, C. K., "The Onset of Mushy-Layer-Mode Instabilities During Solidification in Ammonium Chloride Solution," J. Crystal Growth, 220, 326-335(2000). https://doi.org/10.1016/S0022-0248(00)00863-0
  8. Hwang, I. G. and Choi, C. K., "Convective Instabilities of the Melt during Solidification Cooled from Below," Korean Chem. Eng. Res.(HWAHAK KONGHAK), 47, 174-178(2009).
  9. 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
  10. Chung, C. A. and Chen, F., "Onset of Plume Convection in Mushy Layers," J. Fluid Mech., 408, 53-82(2000). https://doi.org/10.1017/S0022112099007429
  11. S. Govender, "Linear Stability of Solutal Convection in Solidifying Mushy Layers: Permeable Mush-Melt Interface," Transport in Porous Media, 67, 431-439(2007). https://doi.org/10.1007/s11242-006-9034-y