Characteristics and Stability of Compositional Convection in Binary Solidification with a Constant Solidification Velocity

- Journal title : Korean Chemical Engineering Research
- Volume 52, Issue 2, 2014, pp.199-204
- Publisher : The Korean Institute of Chemical Engineers
- DOI : 10.9713/kcer.2014.52.2.199

Title & Authors

Characteristics and Stability of Compositional Convection in Binary Solidification with a Constant Solidification Velocity

Hwang, In Gook;

Hwang, In Gook;

Abstract

In binary solidification compositional convection in a porous mushy layer influences the quality of the final products. We consider the mushy layer solidifying from below with a constant solidification velocity. The disturbance equations for the mushy layer are derived using linear stability theory. The basic-state temperature fields and the distribution of the porosity in the mushy layer are investigated numerically. When the superheat is large, the thickness of the mushy layer is relatively small compared to the thickness of the thermal boundary layer. With decreasing the superheat the critical Rayleigh number based on the thickness of the mushy layer increases and the mushy layer becomes stable to the compositional convection. The critical Rayleigh number obtained from the continuity conditions of temperature and heat flux at the mush-liquid interface is smaller than that from the isothermal condition at the upper boundary of the mushy layer.

Keywords

Binary Solidification;Compositional Convection;Mushy Layer;Rayleigh Number;Linear Stability;

Language

Korean

Cited by

References

1.

Glicksman, M. E., Coriell, S. R. and McFadden, G. B., "Interaction of Flows with the Crystal-Melt Interface," Ann. Rev. Fluid Mech., 18, 307-335(1986).

2.

Sample, A. K. and Hellawell, A., "The Mechanisms of Formation and Prevention of Channel Segregation during Alloy Solidification," Metall. Trans., A15, 2163-2173(1988).

4.

Davis, S. H., "Hydrodynamic Interactions in Directional Solidification," J. Fluid Mech., 212, 241-262(1990).

5.

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).

6.

Jackson A. J., "Constitutional Supercooling Surface Roughening," J. Crys. Growth, 264, 519-529(2004).

7.

Tait, S. and Jaupart, C., "Compositional Convection in a Reactive Crystalline Mush and the Evolution of Porosity," J. Geophys. Res., 97, 6735-6756(1992).

8.

Worster, M. G., "Instabilities of the Liquid and Mushy Regions during Solidification of Alloys," J. Fluid Mech., 237, 649-669(1992).

9.

Anderson, D. M. and Worster, M. G., "Weakly Nonlinear Analysis of Convection in Mushy Layers during the Solidification of Binary Alloys," J. Fluid Mech., 302, 307-331(1995).

10.

Okhuysen, B. S. and Riahi, D. N., "On the Buoyant Convection in Binary Solidification," Theoretical and Applied Mechanics (TAM) Technical Reports, 1059, Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign(2005). https://www.ideals.illinois.edu/handle/2142/317.

11.

Okhuysen, B. S. and Riahi, D. N., "On Weakly Nonlinear Convection in Mushy Layers During Solidification of Alloys," J. Fluid Mech., 596, 143-167(2008).

12.

Bhatta, D., Muddamallappa, M. S. and Riahi, D. N., "On Perturbation and Marginal Stability Analysis of Magneto-Convection in Active Mushy Layer," Trans. Porous Media, 82, 385-399(2010).

13.

Hwang, I. G. and Choi, C. K., "Natural Convection during Directional Solidification of a Binary Mixture," Korean Chem. Eng. Res.(HWAHAK KONGHAK), 47, 174-178(2009).