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Artikel
Nonlinear analysis of bouyant convection in binary solidfication with application to channel formation.
| Författare: |
Amberg, G.A., Homsy, G.M. |
| Dokumenttyp: |
Artikel |
| Tillstånd: |
Publicerad |
| Tidskrift: |
J. Fluid Mech. |
| Volym: |
252
79-98 |
| År: |
1993 |
AbstractThe authors consider the problem of nonlinear thermal-solutal convection in the mushy zone accompanying unstable directional solidification of binary systems. Attention is focused on possible nonlinear mechanisms of chimney formation leading to the occurrence of freckles in solid castings, and in particular the coupling between the convection and the resulting porosity of the mush. They make analytical progress by considering the case of small growth Peclet number, delta , small departures from the eutectic point, and infinite Lewis number. Their linear stability results indicate a small O( delta ) shift in the critical Darcy-Rayleigh number, in accord with previous analyses. They find that nonlinear two-dimensional rolls may be either sub- or supercritical, depending upon a single parameter combining the magnitude of the dependence of mush permeability on solids fraction and the variations in solids fraction owing to melting or freezing. A critical value of this combined parameter is given for the transition from supercritical to subcritical rolls.
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