| Summary: | 博士 === 國立臺灣大學 === 應用力學研究所 === 86 === Directional solidification process is a casting technique with which many adva
nced metals, such as the gas turbine blade are manufactured. Sometimes in the
casting there exist the so called freckle type defects, which are supposed to
be the results of the chimney-like plume convection in the mushy layer during
the solidifying period. The freckle defects reduce the mechanical strength of
the casting and as a result cause the casting fail to meet the specification.
Although the plume convection is inferred to be induced by the subcritical mus
hy mode convection, which occurs under the nonlinear perturbation imposed by t
he salt-finger convection right above the interface between the mushy layer an
d the melt fluid. Neither the inducing mechanism nor the prevention of the plu
me has been theoretically verified. The main goals of the dissertation are fol
lowing. (a) Theoretically identifying the stable mechanism induced by the slow
rates of mold rotation, about axes inclined to the vertical. This process, ob
served experimentally by Sample & Hellawell in 1984,is very sufficient in prev
enting the plume convection. (b) Making sure if the mushy layer convection is
sub-critical under the finite perturbation.Firstly, A linear stability analysi
s is implemented for the system in which a unidirectional shear layer flow exi
sts in the melt fluid layer. Results show that a shear flow of small magnitude
will inhibit the salt-finger convection whose wave propagating direction is a
rbitrary except perpendicular to the shear. A large shear flow, in the other h
and, will destabilize the melt fluid. Secondly, we consider the system in whic
h the mold rotates slowly about axes inclined to the vertical. Results reveal
that both in the melt fluid and the mushy layer, there exists a shear flow, wh
ich synchronously change its flow direction with the spin rotation. A linear s
tability analysis is then applied to a single mushy layer model. Results show
that inclining rotation of the mold stabilizes the mushy layer according to tw
o mechanism. One is the induced shear flow in the mush; the other is the reduc
tion of buoyancy force along the solidifying direction due to the tilt of the
mold. Finally A weakly nonlinear analysis is implemented for the system of sin
gle mushy layer model. The results show that the mushy layer convection is ind
eed subcritical under finite perturbations, and for a large portion of system
parameters, the flow direction in the center of hexagon cells is down just as
the observation in the early experiment by Tait, etc in 1992.We propose the th
eoretical explanation and draw the inference regarding the inhibition of plume
by the slow rotation of mold about axes inclined to the vertical as follow. (
a) Rotation about inclined axes stabilizes the mushy layer and causes the conv
ection in the mush more difficult to occur. (b) Since rotation about inclined
axes also induces, in the melt fluid, a shear flow whose magnitude increases a
s tilt angle increases. We infer that the melt fluid is more stable if the til
t is within a certain angle, but when the tilt exceeds the certain angle, the
salt-finger convection in the melt occurs more quickly than the case of vertic
al mold. (c) There may exist a critical value of tilt angle within which the p
lume convection will not occur. Regarding the prevention of the plume convecti
on and the resultant freckles in the casting, the defects can be reduced throu
gh the following two methods. (a) Inhibiting the salt-finger convection in the
melt fluid, such that the finite perturbations to the mush can be decreased.
(b) Enhancing the stability mechanism of the mushy layer itself in order to re
sist the disturbances imposed by the salt-finger convection.
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