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Stability analysis of compositional convection in a mushy layer in the time-dependent solidification system

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Abstract

Instabilities of convection in a mushy layer with a permeable interface underlying a liquid layer are studied in the time-dependent solidification system in which a binary melt cooled from below. The self-similar stability equations in the liquid and mushy layers are derived by propagation theory. The onset of mushy-layer-mode convection is examined considering the variation of permeability with porosity in the mushy layer. The numerical results show that the critical Darcy-Rayleigh number defined in terms of the mean permeability increases with increasing the concentration ratio and decreases with increasing the superheat. When the concentration ratio is small, a small convective cell appears in the vicinity of the liquid-mush interface. The influences of various non-uniform permeability models on the stability of compositional convection are discussed.

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References

  1. C. A. Chung and M.G. Worster, J. Fluid Mech., 455, 387 (2002).

    Article  Google Scholar 

  2. J.G. O’Rourke, A. J. E. Riggs, C. A. Guertler, P.W. Miller, C. M. Padhi, M. M. Popelka, A. J. Wells, A.C. West, J.-Q. Zhong and J. S. Wettlaufer, Phys. Fluids, 24, 103305 (2012).

    Article  Google Scholar 

  3. S.H. Whiteoak, H. E. Huppert and M.G. Worster, J. Cryst. Growth, 310, 3545 (2008).

    Article  CAS  Google Scholar 

  4. P. Guba and M. G. Worster, J. Fluid Mech., 553, 419 (2006).

    Article  Google Scholar 

  5. S. L. Butler, Phys. Fluids, 23, 016602 (2011).

    Article  Google Scholar 

  6. A. C. Fowler, IMA J. Appl. Math., 35, 159 (1985).

    Article  Google Scholar 

  7. M. G. Worster, J. Fluid Mech., 237, 649 (1992).

    Article  CAS  Google Scholar 

  8. F. Chen, J.W. Lu and T. L. Yang, J. Fluid Mech., 276, 163 (1994).

    Article  CAS  Google Scholar 

  9. C. A. Chung and F. Chen, J. Fluid Mech., 412, 93 (2000).

    Article  CAS  Google Scholar 

  10. F. Chen, C. A. Chung and M. H. Lai, Phys. Fluids, 14, 1295 (2002).

    Article  CAS  Google Scholar 

  11. P.W. Emms and A.C. Fowler, J. Fluid Mech., 262, 111 (1994).

    Article  CAS  Google Scholar 

  12. S. Tait and C. Jaupart, J. Geophys. Res., 97, 6735 (1992).

    Article  CAS  Google Scholar 

  13. D. N. Riahi, Mechanics Research Communications, 39, 18 (2012).

    Article  Google Scholar 

  14. G. Amberg and G.M. Homsy, J. Fluid Mech., 252, 79 (1993).

    Article  CAS  Google Scholar 

  15. C. A. Chung and F. Chen, J. Fluid Mech., 408, 53 (2000).

    Article  CAS  Google Scholar 

  16. A. K. Srivastava and B. S. Bhadauria, Communications in Nonlinear Science and Numerical Simulation, 16, 3548 (2011).

    Article  Google Scholar 

  17. D. N. Riahi, J. Fluid Mech., 553, 389 (2006).

    Article  Google Scholar 

  18. S. Govender, Trans. Porous Media, 67, 431 (2007).

    Article  Google Scholar 

  19. S. S. L. Peppin, H. E. Huppert and M.G. Worster, J. Fluid Mech., 599, 465 (2008).

    Article  CAS  Google Scholar 

  20. I. G. Hwang and C. K. Choi, J. Cryst. Growth, 267, 714 (2004).

    Article  CAS  Google Scholar 

  21. M.C. Kim and C. K. Choi, Korean J. Chem. Eng., 23, 874 (2006).

    Article  CAS  Google Scholar 

  22. M. C. Kim, Korean J. Chem. Eng., 27, 741 (2010).

    Article  CAS  Google Scholar 

  23. M.C. Kim, D.Y. Yoon and E. Cho, Korean J. Chem. Eng., 26, 1461 (2009).

    Article  CAS  Google Scholar 

  24. I.G. Hwang and C. K. Choi, Korean J. Chem. Eng., 25, 199 (2008).

    Article  CAS  Google Scholar 

  25. I.G. Hwang and C.K. Choi, Korean J. Chem. Eng., 26, 930 (2009).

    Article  CAS  Google Scholar 

  26. C. K. Choi, J. H. Park, M. C. Kim, J. D. Lee, J. J. Kim and E. J. Davis, Int. J. Heat Mass Transfer, 47, 4377 (2004).

    Article  CAS  Google Scholar 

  27. D. Bhatta, M. S. Muddamallappa and D. N. Riahi, Trans. Porous Media, 82, 385 (2010).

    Article  Google Scholar 

  28. P. Nandapurkar, D. R. Poirier, J. C. Heinrich and S. Felicelli, Metall. Trans., 20 B, 711 (1989).

    CAS  Google Scholar 

  29. J. Happel and H. Brenner, Low reynolds number hydrodynamics, Martinus Nijhoff Publishers, Dordrecht, Netherlands (1986).

    Google Scholar 

  30. R. F. Katz and M.G. Worster, J. Comput. Phys., 227, 9823 (2008).

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Chemical Engineering, University of Suwon, Gyeonggi-do, 445-743, Korea

    In Gook Hwang

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  1. In Gook Hwang
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Correspondence to In Gook Hwang.

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Hwang, I.G. Stability analysis of compositional convection in a mushy layer in the time-dependent solidification system. Korean J. Chem. Eng. 30, 1023–1028 (2013). https://doi.org/10.1007/s11814-013-0013-z

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  • DOI: https://doi.org/10.1007/s11814-013-0013-z

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