Oscillatory instabilities of the liquid and mushy layers during solidification of alloys under rotational constraint

Abstract

Summary. Linear flow instabilities due to oscillatory disturbances of the liquid and mushy regions during solidification of binary alloys are investigated under a rotational constraint where the rotation axis is inclined to gravity vector. Results of stability analyses and numerical computations for a preferred centrifugal mode of general oscillatory disturbances at zero and non-zero rotation rates are determined which provide information about the preference of oscillatory flow and its role on the solidification system as modified by the rotational effects. The main results are due to a preferred oscillatory mode of convection which is more significant for non-zero rotation case and is restricted mostly to the mushy region. The preferred oscillatory mode of convection is a traveling wave in the presence of rotation, but it is a standing wave in the absence of rotation. The results for different Prandtl numbers indicate that the freckles formation tendency for metallic alloys is less than that for aqueous solutions. Freckles are imperfections that reduce the quality of the solidified materials.

On nonlinear convection in mushy layers Part 1. Oscillatory modes of convection

“…The one-layer model treated in Anderson & Worster (1996) did not have double-diffusive effects, due to strong coupling between the solute and thermal fields, which was imposed by the condition of thermodynamic equilibrium. The oscillatory instability discovered by Anderson & Worster (1996) was due to a mechanism internal to the mushy layer, similar to the oscillatory instability detected earlier by Sayre & Riahi (1995, 1997 in a linear and two-layer model and in the absence of any doublediffusive effect, and it implied the existence of an important interaction between convection and solidification within the mushy layer.…”