Flow Instabilities in a Horizontal Dendrite Layer Rotating about an Inclined Axis

摘要

This paper studies the instabilities in the flow of melt within a horizontal dendrite layer with deformed upper boundary and rotating about an inclined axis during the solidification of a binary alloy. Linear stability analysis provides results about various flow features, such as the critical mode of convection, neutral stability curve, preferred flow pattern, and the solid fraction distribution within the dendrite layer. The results uncover an oscillatory instability, which is due to the horizontal component of the rotation axis. The preferred shape of the deformed upper boundary of the layer is found to be that of longitudinal traveling rolls. The results about the solid fraction distribution within the dendrite layer indicate the beneficial effects of the rotation of the layer about an inclined axis in the sense that the tendency for the chimney formation in the layer is reduced as compared to the corresponding results for the cases where the layer either is not rotated or is rotated about a vertical axis only. In materials processing the formation of such chimneys is undesirable because chimney convection can lead to defects and imperfections in the produced solid material.