On stationary and oscillatory modes of flow instability in a rotating porous layer during alloy solidification

Linear flow instability due to either stationary (nonoscillatory) or oscillatory modes of disturbances in a horizontal porous layer during alloy solidification is investigated under an external constraint of rotation. The porous layer, which is referred to as a mushy layer in the solidification literature, is assumed to rotate about the vertical axis at a constant angular velocity. The investigation is based on the model of Amberg and Homsy (1993) and under the limit of large Stefan number as treated by Anderson and Worster (1996) in the absence of the rotational constraint. An oscillatory mode was found for the first time to dominate over the stationary mode and over several other detected oscillatory modes at the onset of motion. In contrast to the stationary mode, the most critical oscillatory mode was uncovered to reduce the tendency for chimney formation in the rotating porous layer. In engineering applications, presence of these chimneys is undesirable since their presence can produce imperfections that reduce the quality of the solidified material. Results of the stability analyses indicate both stabilizing and destabilizing effects of the Coriolis force on the flow in the porous layer. For example, the effects of the Coriolis force can be stabilizing in the sense that the critical value of the Rayleigh number at the onset of motion increases with the rotation rate, while the effects of the Coriolis force can be destabilizing in the sense that the oscillatory instability is enhanced in the presence of rotation.