Convection in directionally solidifying alloys under inclined rotation
Resource
Journal of Fluid Mechanics 412: 93-123
Journal
Journal of Fluid Mechanics
Pages
93-123
Date Issued
2000
Date
2000
Author(s)
Chung, C.A.
DOI
20060927121658742823
Abstract
In an experiment on binary alloys directionally solidifying from below, Sample &
Hellawell (1984) showed that the plume convection can be successfully prohibited by
rotating the cooling tank around an inclined axis. In the present paper we interpret
their experimental observation by an analytical approach. Results show that there is a
flow induced by the inclination. The induced flow in the fluid layer is a parallel shear
flow consisting of three parts: the thermal boundary-layer flow, the solute boundarylayer
flow, and the Ekman-layer flow. In the mush, the induced flow is also a parallel
flow but of much smaller velocity, consisting of two flows of opposite directions. The
induced velocity in the fluid layer increases with inclination angle and decreases with
the eective Taylor number Te. The induced velocity in the mush also increases with
inclination angle but remains virtually the same on varying the speed of rotation. The
linear stability analysis of the mushy layer shows that, due mostly to the reduction
of buoyancy, the mush becomes more stable as the inclination angle increases. In the
precession-only case, the most-unstable mode of instability is the longitudinal mode,
which propagates in a direction perpendicular to the induced flow. In the spin (with
or without precession) case, the instability modes propagating in dierent directions
are of equal stability. Because the induced flow changes direction with a frequency
equal to the spin angular velocity, the flow scans over all the directions of the system
and stabilizes equally the modes in dierent directions. We conclude on the basis of
the present results and from the practical point of view that spin-only rotation is
more eective than the precession-only rotation in stabilizing the convection during
solidication.
Publisher
臺北市:國立臺灣大學應用力學研究所
Type
other
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