Effect of coriolis force on instabilities of liquid and mushy regions during alloy solidification

Abstract

Linear flow instabilities of the liquid and mushy regions during directional solidification of a binary alloy are studied for a horizontal solidified system rotating about an axis inclined with respect to the gravity vector. Stability analysis and numerical computation are carried out to determine the results for the stationary disturbances at several values of the rotation rates and for given values of the other parameters of the problem. The results provide information about the effects of Corioiis force on various flow features in the liquid and mushy layers including critical modes of convection, neutral stability curves, preferred flow pattern, streamlines and density plots for the solid fraction perturbation in the mushy layer. The preferred structure of the mush-liquid interface is found to be that of longitudinal rolls. The main mode of convection is found to be the so-called mushy layer mode of convection, which can generate double-cell structure in the vertical direction in the presence of the Coriolis force. The Coriolis force appears to strengthen the mushy layer mode of convection, while it can virtually eliminate the so-called boundary layer mode of convection which can be present in the absence of rotation. The rotational effects were found to significantly weaken the convection modes in the liquid layer, while they strengthen the convection modes in the mushy layer. The Coriolis force appears to be generally stabilizing in the sense that the motion in the liquid zone is significantly weakened, tendency for the chimney formation in the mushy zone is reduced and the critical values of the controlling parameters (liquid and mush Rayleigh numbers) and the wave numbers of the critical modes of convective flow mostly increase with increasing the rotation rate