Inertial and coriolis effects on oscillatory flow in a horizontal dendrite layer

Abstract

Flow instability due to oscillatory modes of disturbances in a horizontal dendrite layer during alloy solidification is investigated under an external constraint of rotation. The flow in the dendrite layer, which is modeled as flow in a porous layer and with the inertial effects included, is assumed to rotate about the vertical axis at a constant angular velocity. The investigation is an extension of the work in Riahi (On stationary and oscillatory modes of flow instablity in a rotating porous layer during alloy solidification. J. Porous Media, 6, 177–187, 2003), which was for the case in the absence of the inertial effects. Results of the stability analyses indicate, in particular, that the Coriolis effect can enhance the physical domain for the oscillatory flow, while the inertial effect tends to reduce such domain. Sufficiently strong inertial effect can eliminate presence of the oscillatory mode only for the rotation rate beyond some value. The effect of interaction between the local volume fraction of solid and the flow associated with the Coriolis term was found to be stabilizing.