Nonlinear compositional convection in mushy layers
Riahi, Daniel N.
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https://hdl.handle.net/2142/336
Description
Title
Nonlinear compositional convection in mushy layers
Author(s)
Riahi, Daniel N.
Issue Date
2005-12
Abstract
This paper presents some extensions of two main problems of nonlinear compositional convection in horizontal mushy layers during the solidification of binary alloys that were recently investigated by the author (Riahi 2002, 2004). Under a near-eutectic approximation and the limit of large far-field temperature, we determine a number of two- and three-dimensional weakly nonlinear solutions, and the stability of these solutions with respect to arbitrary three-dimensional disturbances is then investigated. First, the problem of the oscillatory modes of convection, which was investigated recently in the absence of the main permeability parameter K1 (Riahi 2002), is extended to include the effects of K1, over a range of values of the other parameters, for both two- and three-dimensional motion. It was found, in particular, that the results reported in Riahi (2002) are recovered if K1 is zero or sufficiently small. In such case two-dimensional solutions in the form of simple-travelling rolls are mostly the only stable and preferred solutions. However, as in the more realistic cases, if K1 is not sufficiently small, then such solutions are replaced by preferred and stable three-dimensional solutions, which are mostly simple travelling waves in the form of rectangles, squares or hexagons. Next, we revisit the problem of mixed oscillatory and steady modes of convection (Riahi 2004), where some results appeared to be sensitive with respect to the approximated value 3.14 of ð used in the numerical calculation. Here we find some updated results, which are based on a more accurate value of 3.141592654 for ð, plus some additional new results. In particular, we find a preferred and stable mixed standing and steady modes of hexagonal solution over a relatively wide range of the parameter values whose properties are now appeared to be in much better agreement with the available experimental results (Tait et al. 1992).
Publisher
Department of Theoretical and Applied Mechanics (UIUC)
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