The flow induced by yawing motion in unidirectionally solidifying alloys

As the cooling tank is yawing, there occurs an induced flow in the binary solution cooled from below. The induced flow may stabilize the potentially unstable solution during directional solidification and suppress the formation of freckles in the cast alloys. We investigate this induced flow by an analytical approach. Results show that the induced flow in the melt region consists of three paralleling shear flows of different length scales. The one in the vicinity above the melt/mush interface has the largest velocity gradient. The amplitude of the induced velocity in the melt is much larger than that in the dendritic mushy region, and the former is virtually inversely proportional to the yawing frequency while the latter is completely independent of the yawing frequency. The amplitudes of the induced velocities in both the melt and the mush are proportional to the yawing amplitude. The phase of induced flow in the melt lags by about 90° behind the yawing motion while the induced flow in the mush is of the same phase with yawing. The sharp velocity gradient of the induced flow in the shallow layer above the melt/mush interface may play a crucial role in stabilizing the potentially very unstable fluid in the solute boundary layer above the interface. This suggests that the yawing motion may be an efficient scheme for the prohibition of the occurrence of the plume convection and for the suppression of the formation of freckles as well.